Freda Bedi Cont'd (#3)

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Re: Freda Bedi Cont'd (#3)

Postby admin » Sun May 15, 2022 5:52 am

Giovanni Domenico Cassini
by Wikipedia
Accessed: 5/14/22

Why the focus on religion? Because the role of colonialism (and generally of economic and political interests) in the birth of Orientalism dwindles to insignificance compared to the role of religion....

It is a central thesis of this book that Europe's discovery of Asian religions was deeply linked to the development of Orientalism and its gradual emancipation from biblical studies. The birth of modern Orientalism was not a Caesarean section performed by colonialist doctors at the beginning of the nineteenth century when Europe's imperialist powers began to dominate large swaths of Asia. Rather, it was the result of a long process that around the turn of the eighteenth century produced a paradigm change....

Voltaire's "Indian" campaign ended up playing a crucial role in raising the kind of questions about origins and ancient religions that played at least as important a role in the establishment of state-supported, university-based Orientalism as did the much-touted colonialism and imperialism. Rather than thirst for political and economic power, what was primarily at work here was ideological power: the power of Europe's long-established worldview and religious ideology that Voltaire provocatively labeled "l'infame" and that he tried to destabilize through an avalanche of articles, pamphlets, and books....

The idea of a pan-Asian religion or doctrine -- conceived either positively as an ancient theology or negatively as an ancient idolatry -- was not only common throughout Diderot's century but dominant. It is a subject well worth exploring; after all, almost every chapter of this book shows that this was a far more influential factor in the birth of Orientalism than the much-evoked and blamed colonialism....

This rich religious and ideological background is also bound to remain invisible when looking through the coarse lens of preconceived ideas such as Edward Said's Orientalist "colonialism" or Western "exploitation."...

We have already seen that the emergence in the European mind of a pan-Asiatic religion (that we now readily identify as Buddhism) did not happen overnight in some nineteenth-century study. Such scenarios of a nineteenth-century "creation" of Buddhism grew on a soil fertilized by several biases. The "Indian" bias links the European discovery of Buddhism to India as Buddhism's country of origin, the "textual" bias to the study of Buddhist texts in Indian languages, and the "colonialist" bias posits that such discovery and study were primarily linked to colonial interests. This accounts for the exaggerated role of British "pioneers" in recent studies. Charles Allen's "men who discovered India's lost religion," for example, are without exception British colonialist "Sahibs" (Allen 2002)....

The discovery of long-vanished Indian Buddhism, by contrast, indeed happened to a large extent in the nineteenth-century "European philological workshop" (Masuzawa 2005:126). The present chapter will show, however, that prior to that there were "workshops" not manned by Sanskritists but rather by French missionaries and by academics who studied and translated Arabic and Chinese sources long before the first British colonialists began to dabble in Sanskrit....

"Orientalism" has been portrayed by Edward Said in his eponymous book, first published in 1979, as a very influential, state-sponsored, essentially imperialist and colonialist enterprise. For Said, the Orientalist ideology was rooted in ....


-- The Birth of Orientalism, by Urs App

[A] false dichotomy) is a logical fallacy, which occurs when a limited number of options are incorrectly presented as being mutually exclusive to one another.

-- False Dilemmas and False Dichotomies: What They Are and How to Respond to Them, by Effectiviology

[T]he director of the Paris observatory in the 1670s Gian-Domenico Cassini (1624-1712) submitted a proposal to the minister Colbert to send Jesuits to China to make some astronomical observations, and to advance their knowledge of latitudes, longitudes and magnetic declinations....One of the missions that was sent to Thailand finally landed up in Pondicherry.

A leading French astronomer stationed in China was Pere Antoine Gaubil (1689-1759), whose astronomical researches had exercised influence on the French astronomer, theorist and mathematical physicist, Pierre Simon Laplace (1749-1827)....

Pere Gaubil was in constant touch with the French Jesuit astronomer and cartographer Pere Claude Stanisla Boudier (1687-1757) stationed at Chandernagor in India. Boudier's reputation as an astronomer earned him an invitation to Jai Singh' s court in 1734. During his journey to and sojourn at Jaipur, he, like his counterparts in China determined the longitude of 63 Indian cities, in addition to measuring the meridional altitudes of a few stars. [Ansari 1985: 372]. In addition, he observed the first satellite of Jupiter on April 2, 1734 at Fatehpur, and again at Jaipur on August 15 of the same year. He also observed the solar eclipse of May 3, 1734 at Delhi and had earlier reported the lunar eclipse of December 1, 1732....

Pere Pons arrived in India in 1726 and after spending a few years in Thanjavur was appointed superior of the French Mission in Bengal. Other than compiling a Sanskrit grammar, and a treatise on Sanskrit poetics that was sent to Europe, he visited Delhi and Jaipur with Pere Boudier, mentioned earlier, to make some astronomical observations ...

Perusing these records, we recognise firstly the importance and authority of Gaubil among the Jesuit astronomers in India, for he appeared to be providing them the numbers that they considered standard, and thus aided their calibration. It was Gaubil who forwarded their results to Cassini, and thus the latter was the final authority certifying the results of the expedition. Secondly, the study of the motion of the stars and the planets, enabled the savants, through the Jesuits, to map the co-ordinates of the globe, symbolically weaving Paris, Rome, Delhi, Jaipur and Beijing into the new fabric of modern science of which the Jesuits were the prominent cultural vectors, and subsequently the agents of cultural imperialism.

-- French Jesuit Scientists in India: Historical Astronomy in the Discourse on India, 1670-1770, by Dhruv Raina


Image
Giovanni Domenico Cassini
Born: 8 June 1625, Perinaldo, Republic of Genova
Died: 14 September 1712 (aged 87), Paris, France
Nationality: Italian, French
Alma mater: The Jesuit College at Genoa
Known for: Cassini Division; Cassini identity; Cassini's laws; Cassini oval; First to observe the division in the rings of Saturn
Scientific career
Fields: Mathematics, astrology, astronomy, engineering
Institutions: University of Bologna

Giovanni[a] Domenico Cassini, also known as Jean-Dominique Cassini (8 June 1625 – 14 September 1712) was an Italian (naturalised French)[1] mathematician, astronomer and engineer. Cassini was born in Perinaldo,[2][3] near Imperia, at that time in the County of Nice, part of the Savoyard state.[4][5] Cassini is known for his work on astronomy and engineering. He discovered four satellites of the planet Saturn and noted the division of the rings of Saturn; the Cassini Division was named after him. Giovanni Domenico Cassini was also the first of his family to begin work on the project of creating a topographic map of France.

The Cassini space probe, launched in 1997, was named after him and became the fourth to visit the planet Saturn and the first to orbit the planet.

Life

Time in Italy


Cassini was the son of Jacopo Cassini, a Tuscan, and Giulia Crovesi. In 1648 Cassini accepted a position at the observatory at Panzano, near Bologna, to work with Marquis Cornelio Malvasia, a rich amateur astronomer, initiating the first part of his career.[6] During his time at the Panzano Observatory, Cassini was able to complete his education under the scientists Giovanni Battista Riccioli and Francesco Maria Grimaldi. In 1650 the senate of Bologna appointed him as the principal chair of astronomy at the University of Bologna.[6]

While in his position in Bologna, he observed and wrote a treatise on the comet of 1652. He was also employed by the senate of Bologna as hydraulic engineer, and appointed by Pope Alexander VII inspector of fortifications in 1657. He was subsequently director of waterways in the papal states.[7]

In San Petronio, Bologna, Cassini convinced church officials to create an improved sundial meridian line at the San Petronio Basilica, moving the pinhole gnomon that projected the Sun's image up into the church's vaults 66.8 meters (219 ft) away from the meridian inscribed in the floor. The much larger image of the Sun's disk projected by the camera obscura effect allowed him to measure the change in diameter of the Sun's disk over the year as the Earth moved toward and then away from the Sun. He concluded the changes in size he measured were consistent with Johannes Kepler's 1609 heliocentric theory, where the Earth was moving around the Sun in an elliptical orbit instead of the Ptolemaic system where the Sun orbited the Earth in an eccentric orbit.[8]

Cassini remained in Bologna working until Colbert recruited him to come to Paris to help set up the Paris Observatory. Cassini departed from Bologna on 25 February 1669.[6]

Moving to France

Image
An engraving of the Paris Observatory during Cassini's time. The tower on the right is the "Marly Tower", a dismantled part of the Machine de Marly, moved there by Cassini for mounting long focus and aerial telescopes.

Cassini's determinations of the rotational periods of Jupiter and Mars in 1665–1667 enhanced his fame, and in 1669, with the reluctant assent of the Pope, he moved to France and through a grant from Louis XIV of France helped to set up the Paris Observatory, which opened in 1671;[7] he would remain the director of the observatory for the rest of his career until his death in 1712. For the remaining forty-one years of his life Cassini served as astronomer/astrologer to Louis XIV ("The Sun King"); serving the expected dual role yet focusing the overwhelming majority of his time on astronomy rather than the astrology he had studied so much in his youth. Cassini thoroughly adopted his new country, to the extent that he became interchangeably known as Jean-Dominique Cassini, although that is also the name of his great-grandson, Dominique, comte de Cassini.

During this time, Cassini's method of determining longitude was used to measure the size of France accurately for the first time. The country turned out to be considerably smaller than expected, and the king quipped that Cassini had taken more of his kingdom from him than he had won in all his wars.

On 14 July 1673 Cassini obtained the benefits of French citizenship. In 1674 he married Geneviève de Laistre, the daughter of the lieutenant general of the comté of Clermont. "From this marriage Cassini had two sons; the younger, Jacques Cassini, succeeded him as astronomer and geodesist under the name of Cassini II."[6]

In 1711 Cassini went blind and he died on 14 September 1712 in Paris at the age of 87.[2]

Astronomer

Cassini observed and published surface markings on Mars (earlier seen by Christiaan Huygens but not published), determined the rotation periods of Mars and Jupiter, and discovered four satellites of Saturn: Iapetus and Rhea in 1671 and 1672, and Tethys and Dione (1684).[9] Cassini was the first to observe these four moons, which he called Sidera Lodoicea (the stars of Louis), including Iapetus, whose anomalous variations in brightness he correctly ascribed as being due to the presence of dark material on one hemisphere (now called Cassini Regio in his honour). In addition he discovered the Cassini Division in the rings of Saturn (1675).[6] He shares with Robert Hooke credit for the discovery of the Great Red Spot on Jupiter (ca. 1665). Around 1690, Cassini was the first to observe differential rotation within Jupiter's atmosphere.

In 1672 he sent his colleague Jean Richer to Cayenne, French Guiana, while he himself stayed in Paris. The two made simultaneous observations of Mars and, by computing the parallax, determined its distance from Earth. This allowed for the first time an estimation of the dimensions of the Solar System: since the relative ratios of various sun-planet distances were already known from geometry, only a single absolute interplanetary distance was needed to calculate all of the distances.

In 1677, the English philosopher John Locke visited Cassini in Paris. He writes, "At the Observatory, we saw the Moon in a twenty-two foot glass, and Jupiter, with his satellites, in the same. The most remote was on the east, and the other three on the west. We also saw Saturn and his rings, in a twelve-foot glass, and one of his satellites."[10]

Cassini initially held the Earth to be the centre of the Solar System, though later observations compelled him to accept the model of the Solar System proposed by Nicolaus Copernicus, and eventually that of Tycho Brahe. "In 1659 he presented a model of the planetary system that was in accord with the hypothesis of Nicolaus Copernicus. In 1661 he developed a method, inspired by Kepler's work, of mapping successive phases of solar eclipses; and in 1662 he published new tables of the sun, based on his observations at San Petronio."[6] Cassini also rejected Newton's theory of gravity, after measurements he conducted which wrongly suggested that the Earth was elongated at its poles. More than forty years of controversy about the subject were closed in favour of Newton's theory after the measurements of the French Geodesic Mission (1736 to 1744) and the Lapponian expedition in 1737 led by Pierre Louis Moreau de Maupertuis.

Cassini was also the first to make successful measurements of longitude by the method suggested by Galileo, using eclipses of the Galilean satellites as a clock.

In 1683, Cassini presented the correct explanation of the phenomenon of zodiacal light.[7] Zodiacal light is a faint glow that extends away from the Sun in the ecliptic plane of the sky, caused by dusty objects in interplanetary space.

Cassini is also credited with introducing Indian Astronomy to Europe. In 1688, the French envoy to Siam (Thailand), Simon de la Loubère, returned to Paris with an obscure manuscript relating to the astronomical traditions of that country, along with a French translation. The Siamese Manuscript [Rules of the Siamese Astronomy, for calculating the Motions of the Sun and Moon, translated from the Siamese, and since examined and explained by M. Cassini, a Member of the Royal Academy of Sciences, Excerpt from "A New Historical Relation of the Kingdom of Siam, by Monsieur De La Loubere, Envoy Extraordinary from the French King, to the King of Siam, in the years 1687 and 1688. Wherein a full and curious Account is given of the Chinese Way of Arithmetick, and Mathematick Learning. In Two Tomes, Illustrated with Sculptures. Done out of French, by A.P. Gen. R.S.S. 1693", Tome II, Pg. 186], as it is now called, somehow fell into Cassini's hands.
[T]he director of the Paris observatory in the 1670s Gian-Domenico Cassini (1624-1712) submitted a proposal to the minister Colbert to send Jesuits to China to make some astronomical observations, and to advance their knowledge of latitudes, longitudes and magnetic declinations....One of the missions that was sent to Thailand finally landed up in Pondicherry.

-- French Jesuit Scientists in India: Historical Astronomy in the Discourse on India, 1670-1770, by Dhruv Raina

A Greek scholar, who, like Pythagoras, once traveled in India, having learned the sciences of the Bracmanas, taught them in his turn his method of astronomy; and in order that his disciples might make it a mystery to others, he left them in his work the Greek names of the planets, the signs of the zodiac, and several terms like hora (twenty-fourth part of a day), Kendra (center), etc. I had this acquaintance at Dely, and it served me to make the astronomers of Raja Jaesing, who are in large numbers in the famous observatory which he had built in this capital, feel that formerly masters had come to them [from] Europe.

When we arrived at Jaëpur, the prince, to convince himself of the truth of what I had advanced, wanted to know the etymology of these Greek words, which I gave him.... Raja Jaësing will be regarded in the centuries to come as the restorer of Indian astronomy. The tables of M. de la Hire, under the name of this Prince, will be current everywhere in a few years.

-- Letter From Father Pons, Missionary of the Company of Jesus, to Father Du Halde, of the same Company. At Careical, on the coast of Tanjaour; in the East Indies, November 23, 1740. From "Lettres Edifiantes Et Curieuses, Ecrites Des Missions Etrangeres", by Charles Le Gobien

He was intrigued enough by it to spend considerable time and effort deciphering its cryptic contents, also determining on the way that the document originated in India.[11]

Curiously enough the first definite information respecting the Hindu system of astronomy, came to Europe from Siam, where, in the early centuries of our era, there was a flourishing Hindu state. In 1687 Louis XIV sent M. de la Loubere on an embassy to Siam, and he brought back with him a portion of a manuscript containing rules for computing the places of the sun and moon. This was submitted to the celebrated John Dominic Cassini, the Italian astronomer, whom Louis had brought to Paris to take charge of his observatory. In his hands the calculations described, without indication of the meaning of the constants employed, were lucidly explained. [!!!] His memoir was published in 1691, in De la Loubere's Relation de Siam (tome ii.), and afterwards reprinted with other papers by Cassini in the eighth volume of the Memoires de l'Academie Royale des Sciences, for 1666 to 1699 (pp. 279-362).

Cassini's principal deductions from the Siamese manuscript were -- (1) That the sidereal year employed was of 365d. 6h. 12m. 36s., being the 800th part of 292,207 days; (2) That the epoch of the constants was Saturday, 21st March, 638 A.D. at new moon (the mean conjunction occurring at Siam about 3h. 15m. A.M.) and when there was a considerable eclipse of the sun at 5h. 19m. P.M., 1 [I have revised the times from modern tables, assuming the longitude of Siam at 6h. 42m. E. from Greenwich; Cassini (Mem, de l'Acad, tome viii. p. 311) adopted 6h. 34m. E. from Paris, which is only 1-1/2m. in excess of this.] which eclipse, however, could not have been visible to the east of Orissa; (3) That since a correction to that effect is applied to the results, the rules and data were originally arranged for a place about 18-1/4°to the west of Siam: this he conjectures to have been "Narsinga,"2 [Mem. de l'Acad. 1666-1699, tome viii. p. 309.] which Bailly places "in Orissa" in lat. 17° 22' N., that is, about Pittapuram in the Godavari district; but Bailly suggests Benares as a more probable place, and "having about the same longitude";3 [Astron. Indienne et Orientale, p. 12.] (4) That at the epoch the sun's apogee was at 20° of Cancer, and the moon's at 21° of Capricorn; (5) That to the revolution of the moon's apsis a period of 3232 days was allowed; (6) That the greatest equation of the centre for the sun was 2° 12', though he gives a short table from the manuscript on the same page, which states it at 2° 14', while Bailly, professing to quote Cassini's figures, says4 [Astron. Indienne, p. viii. 7, 44.] he found it to be 2° 10' 32" -- which is the value assigned in the Surya Siddhanta, and which Bailly himself had obtained from another Indian work.5 [Mem. de l'Acad. tome viii. p. 304.] The moon's greatest equation of the centre Cassini found to be 4° 56'; (7) That the civil year began with the month of Karttika; (8) And that the constants employed made the artificial day or tithi bear to the civil or natural day the ratio of 692:703; hence 703 lunar months are equal to 20,760 days, and the synodical month was 29d. 12h. 44m. 2-39s.; and as 228 solar months were made equal to 235 lunar ones, he concluded that in 13,357 years there are 165,205 lunar months and 487,860 days, whence he deduced a tropical year of 365d. 5h. 55m. 13-77s., or almost exactly the same as Ptolemy's value.

7. With respect to these results, it may be noted -- (1) That the sidereal year of 365d. 6h. 12m. 36s. is exactly that of the now missing Paulisa-Siddhanta, and, from Al-Beruni's account of it, we learn that it used the same numbers as the Siamese to determine the year, viz. 292,207 days as the measure of 800 years.1 [Al-Beruni's India, Sachau's transl. vol. ii. p. 58; see below § 38.] (2) The ratio of the tithi to the natural day is a usual approximation in Hindu astronomy, giving 1 kshaya tithi in 64-1/11 or 63-10/11 days.2 [Wilkinson's Siddhanta S'iromani, Goladhyaya, iv. 12, where it is misprinted 64-1/11 for 64-1/11; conf. also Al-Beruni's India, Sachau's tr. vol. ii. pp. 37, 47, 52, and 54.] (3) But the ratio of 228 solar months (6939-6871 days), is introduced in the computations only where so close an approximation could produce no sensible error in the results; and Cassini has, perhaps, been misled here by the natural supposition that a tropical year must be as material an element in Hindu as it is in European astronomy. (4) From Al-Beruni, again, we learn that Pulisa assigned 488,219 revolutions of the moon's apsis to a Chaturyuga,3 [Al-Beruni's India, vol. ii. p. 18: the exact value with this element is 3231-98752 days, the difference between this and 3232 days amounts only to one day in 80-2 revolutions, or 686 years.] or almost exactly 3232 days to a revolution. We might infer, then, that the other elements used were also taken from the Paulisa-Siddhanta -- that the lunar month, for example, was of 29d. 12h. 44m. 2-75s. -- but that they had been engrossed in a Karana for the calculation of horoscopes and almanacs. This points, however, to Siam and the Eastern Peninsula as a promising field of search for the Paulisa1 [This portion of the paper was written before Thibaut's Panchasiddhantika, of Varaha Mihira, reached this country. It contains an outline of the Paulisa Siddhanta.] and possibly others of the Siddhantas that have been lost in India.

8. The next contribution to our knowledge of this subject is to be found in an appendix to the Historia Regni Graecorum Bactriani of T.S. Bayer (1694-1738), and is titled "Christophori Theodosii Waltheri Doctrina Temporum Indica ex libris Indicis et Brahmanum institutione, A.C. clclccxxxiii Trangambarae digesta, simul cum Paralipomenis recentioribus."2 [Petropoli, 1738.] The author remarks that Ptolemy alone divided the day into sixty parts, as the Hindus do, and these again sexagesimally. He cites the Hindu divisions of time from Amarasimha; gives the names of the nine graha in Sanskrit and Tamil; of the days of the week; of the months; the signs of the zodiac; the nakshatras, yogas, karanas; of the tithis in Sanskrit, Persian, and Dekhani; and an account of the yugas, and of the Panchanga or kalendar. To this curious tract is added a long note by Leonard Euler on the Hindu year of 365d. 6h. 12m. 30s.

9. Beschi had also given some account of the Indian almanac in his Tamil Grammar, published in 1738;3 [Beschi († 1742) also published Tiruchabei Kanidam, a Tamil work on astronomy.] but no contribution of real importance to Hindu astronomy was made for about eighty years after Cassini's paper.

-- Burgess, James (1893). "Notes on Hindu Astronomy and the History of Our Knowledge of It". Journal of the Royal Asiatic Society of Great Britain & Ireland: 722–723.

The Pauliṣa Siddhānta (literally, "The scientific-treatise of Pauliṣa Muni") refers to multiple Indian astronomical treatises, at least one of which is based on a Western source. "Siddhānta" literally means "doctrine" or "tradition".

It is often mistakenly thought to be a single work and attributed to Paul of Alexandria (c. 378 CE). However, this notion has been rejected by other scholars in the field, notably by David Pingree who stated that "...the identification of Paulus Alexandrinus with the author of the Pauliṣa Siddhānta is totally false". Similarly, K. V. Sarma writes that it is from a Greek source, known only as Pauliṣa.

The Alberuni wrote that the Siddhanta is based to the teaching of a Greek named Paulus.

The earlier Pauliṣa-siddhānta dates from the third or fourth century, and the later Pauliṣa-siddhānta from the eighth century.

Similar to the Yavanajātaka ("The Sayings of the Greeks"), the Pauliṣa Siddhānta is an example of Hellenistic astronomy (especially the Alexandrian school) in India during the first centuries CE.


The Pauliṣa Siddhānta was particularly influential on the work of the Indian astronomer Varāhamihira. It was considered one of "The Five Astronomical Canons" in India in the 5th century.

-- Paulisa Siddhanta, by Wikipedia

His explication of the manuscript appeared in La Loubère's book on the Kingdom of Siam in 1691,[12].

Ziegenbalg attributes the decline of the Catholic missions in part to the rivalry between their orders, and mentions the visit of the Papal legate Charles de Tournon to Pondicherry in 1703-1704, and his desire to rid the church of 'heathen' elements introduced by the missionaries, such as "the smearing of ash on the forehead, the shameful difference in the church and in the distribution of holy communion between high and low castes, the play-acting in Brahman habits, etc." He reports also what he has heard of Jesuit missions in China and Thailand, claiming that everywhere Jesuit cunning and unscrupulousness has eventually led to their ruin. [Many of the Jesuits in the Carnatic mission had been forced to leave Thailand in 1688.]

-- Bartholomäus Ziegenbalg, the Tranquebar Mission, and `the Roman Horror'
in Andreas Gross, Y. Vincent Kumaradoss, and Heike Liebau, eds., Halle and the Beginning of Protestant Christianity in India, vol. 2 (Halle: Verlag der Franckeschen Stiftungen zu Halle, 2006), 797–811, by Will Sweetman


Elizabeth (Lisa) Lyons is another great collector of Thai manuscripts who was living in Bangkok around the same time as Sarah Bekker. ...

One of the many items Lyons acquired for the Penn collection was as beautiful as Bekker’s Abhidhamma chet gamphi (Penn Libraries Ms. Coll. 990, Item 5). However, the authors found it, with some help from Forrest McGill at the Asian Art Museum (San Francisco), a bit “too beautiful.” They examined this manuscript held in the Penn Museum of Archaeology and Anthropology (Ms. 89-13-251). Initially this manuscript was loosely dated to the 1870s, but unlike manuscripts in other collections (including Penn’s), there was very little damage. The condition of the manuscript, including the cover, was remarkable. The authors were very pleased, and when they opened the manuscript they were further impressed with the quality of the paper and the dark color of the text (thin mul style khom script). There was no water damage and no marginalia or corrections (again—remarkable). The quality of the paintings is what was really striking. The colors were vibrant, the details fine, and the scenes iconic. The gold used in the paintings (a common feature of Thai manuscripts is to have actual gold leaf in paint) had not faded and was much thicker than any other example from the eighteenth or nineteenth centuries. It was a perfect manuscript for a museum display, the authors thought, as it would be appreciated for its beauty and show the value of good conservation efforts. However, they were a little suspicious of the dating to 1870s by Lyons and furthermore had not encountered a manuscript of this quality. McDaniel asked Forrest McGill for his opinion, and he immediately assumed it was made post-1950s and suggested, a suggestion the authors now think is correct, that it could be a forgery. McGill had seen forgeries like this done by a local artist from Thailand who had attempted to pass on fake manuscripts to foreign institutions in the 1970s. That suggestion led Kerekes and McDaniel to look closely at the paintings and compare them to others they had seen in other manuscripts. Indeed, one painting is directly copied, it seems, from a Phra Malai manuscript now held at the Chester Beatty Library (and mentioned in another article in this issue). In one painting, four monks with grotesque faces are seen reading a large manuscript, drinking tea, and chewing betel nut (a nice piece of social historical evidence for sure) while a half-naked woman and her children ignore the monks and play a board game in front of them (F.A6.L). The right side of the same folio depicts two men drinking tea and smiling coyly at each other on the grounds of a monastery, while a third man is seen in the window of the monastery in a way that suggests he is either napping or being pleasured orally by an unseen person. These scenes appear in other extant Thai manuscripts, but here the paintings in the Penn manuscript and the Chester Beatty Library (whose date we can confirm as from the nineteenth century) are nearly identical and the scenes are unique enough that there is no other explanation besides direct copying. It is known that the forger in question knew several manuscripts in Western collections. In another scene, the artist seems to have been trying to have a little salacious, or perhaps perverted, fun. In a common scene from Phra Malai manuscripts, we find men fighting with knives. This scene represents the fate of human beings near the end of the world. However, in this particular painting, the artist inserts a woman into the middle of the fight and graphically depicts her having intercourse with one of the fighting men. One could interpret this as a rape scene, but the woman is smiling and the other men seem to ignore her (F.B26.R). This is certainly unusual, even though Thai artists in the nineteenth century sometimes inserted scenes suggesting sexual encounters. There is little evidence from older manuscripts that graphically depict intercourse or fully naked women and men.

Kerekes noted two particular features of this “too beautiful” manuscript that also led the authors to suspect a late forgery. First, there are clearly newer painted folios that have been inserted into an older text as scenes from cleverly hidden and glued page breaks (F.B42.TB.LR). This could be a sign that an older text was added to make this new text larger or that paintings were removed and sold from an older manuscript and new paintings inserted. Second, on one page is a short sentence in modern Thai script in a manuscript that is otherwise in the Thai language in khom script (F.A12.B.M). The line tells the reader to take a break and drink tea! This is not found in other manuscripts and seems to have been a clever little joke. In conclusion, sometimes certain manuscripts are too good to be true, and forgeries do exist. Collectors often pay significant amounts of money for manuscripts, and when markets are created, sometimes, as in all situations, people rise to supply goods for that new market. When that market is premodern art, artists are sometimes tempted to create a “supply.”

Conclusion

Collections and collectors of Siamese/Thai manuscripts in the United States are vast in number and largely unexplored. This short overview was designed to be a roadmap for future scholars who seek to investigate individual manuscripts held at the University of Pennsylvania, The Walters Art Museum, and other collections, or begin to fully investigate the unstudied collections of Cornell, the University of Michigan, or the Library of Congress.

-- Siamese Manuscript Collections in the United States, by Susanne Ryuyin Kerekes, University of Pennsylvania and Justin McDaniel, University of Pennsylvania


Astrologer

Attracted to the heavens in his youth, his first interest was in astrology. While young he read widely on the subject of astrology, and soon was very knowledgeable about it; this extensive knowledge of astrology led to his first appointment as an astronomer. Later in life he focused almost exclusively on astronomy and all but denounced astrology as he became increasingly involved in the Scientific Revolution.

In 1645 the Marquis Cornelio Malvasia, a senator of Bologna with a great interest in astrology, invited Cassini to Bologna and offered him a position in the Panzano Observatory, which he was constructing at that time. Most of their time was spent calculating newer, better, and more accurate ephemerides for astrological purposes using the rapidly advancing astronomical methods and tools of the day.

Engineering

In 1653, Cassini, wishing to employ the use of a meridian line, sketched a plan for a new and larger meridian line but one that would be difficult to build. His calculations were precise; the construction succeeded perfectly; and its success gave Cassini a brilliant reputation for working with engineering and structural works.[6]

Cassini was employed by Pope Clement IX in regard to fortifications, river management, and flooding of the Po River. "Cassini composed several memoirs on the flooding of the Po River and on the means of avoiding it; moreover, he also carried out experiments in applied hydraulics."[6] In 1663 he was named superintendent of fortifications and in 1665 inspector for Perugia.[6] The Pope asked Cassini to take Holy Orders to work with him permanently but Cassini turned him down because he wanted to work on astronomy full-time.

In the 1670s, Cassini began work on a project to create a topographic map of France, using Gemma Frisius's technique of triangulation. The project was continued by his son Jacques Cassini and eventually finished by his grandson César-François Cassini de Thury and published as the Carte de Cassini in 1789[13] or 1793.[14] It was the first topographic map of an entire country.

Works

• Specimen observationum Bononiensium (in Latin). Bologna: eredi Evangelista Dozza (1.). 1656.
• Martis circa axem proprium revolubilis observationes Bononiae habitae (in Latin). Bologna: eredi Evangelista Dozza (1.). 1666.
• Spina celeste meteora osservata in Bologna il mese di marzo 1668 (in Italian). Bologna: Emilio Maria Manolessi & fratelli. 1668.
• Observations astronomiques faites en divers endroits du royaume, pendant l'année 1672 (in French).
• Abregé des observations et des reflections sur la comete qui a paru au mois de Decembre 1680, et aux mois de Ianvier, Fevrier et Mars de cette annee 1681 (in French). Paris: Estienne Michallet. 1681.
• Cassini, Giovanni Domenico (1682). Raccolta di varie scritture, e notitie concernenti l'interesse della remotione del Reno dalle Valli fatta in Bologna l'anno 1682. (In Bologna): [s.n.]
• Elemens de l'astronomie (in French). Paris: Imprimerie Royale. 1684.
• Découverte de la lumiere celeste qui paroist dans le zodiaque (in French). Paris: Imprimerie Royale. 1685.
• Régles de l'astronomie indienne pour calculer les mouvemens du soleil et de la lune (in French). Paris: Sébastien Mabre-Cramoisy, veuve. 1689.
• De l'origine et du progres de l'astronomie et de son usage dans la geographie et dans la navigation (in French). Vol. 1. Paris: Imprimerie Royale. 1693.
• Hypotheses et les tables des satellites de Jupiter, reformeés sur de nouvelles observations (in French). Paris: Jean Anisson. 1693.
• Meridiana del tempio di S. Petronio tirata e preparata per le osservazioni astronomiche l'anno 1655 (in Italian). Bologna: eredi Vittorio Benacci. 1695.
• Description et usage du planisphere céleste (in French).
• Cassini's works digitalized and available on the digital library of Paris Observatory

See also

• 24101 Cassini, an asteroid
• Aerial telescope – large telescopes used by Cassini
• Cassini (lunar crater)
• Cassini (Martian crater)
• Cassini Division in Saturn's rings
• Cassini oval
• Cassini Regio, dark area on Iapetus
• Cassini–Huygens Mission to Saturn
• Cassini's identity for Fibonacci numbers
• Cassini's laws
• History of the metre
• Neith (hypothetical moon)
• Seconds pendulum

References

1. His name may also be spelled Giovan Domenico Cassini or Gian Domenico Cassini.
1. Joseph A. Angelo, Encyclopedia of Space and Astronomy, Infobase Publishing – 2014, page 114
2. "Giovanni Domenico Cassini (June 8, 1625 – September 14, 1712)". Messier Seds.org. Retrieved 31 October 2012.
3. "Giovanni Domenico Cassini: The rings and moons of Saturn". Surveyor in Berlin.de. Archived from the original on 24 June 2013. Retrieved 31 October 2012.
4. Augusto De Ferrari (1978), "Cassini, Giovan Domenico" Dizionario Biografico degli Italiani 21 (Rome: Istituto dell'Enciclopedia Italiana).
5. Gandolfo, Andrea. La provincia di Imperia: storia, arti, tradizioni. Blue Edizioni, 2005.
6. Cassini, Gian Domenico (Jean-Dominique) (Cassini I). Complete Dictionary of Scientific Biography. Detroit: Charles Scribner's Sons, 2008. pp. 100–104. retrieved 30 May 2013.
7. One or more of the preceding sentences incorporates text from a publication now in the public domain: Clerke, Agnes Mary (1911). "Cassini s.v. Giovanni Domenico Cassini". In Chisholm, Hugh (ed.). Encyclopædia Britannica. Vol. 5 (11th ed.). Cambridge University Press. p. 459.
8. Broad, William J. (19 October 1999). "How the Church Aided 'Heretical' Astronomy". New York Times.
9. Van Helden, Albert (2009). "The beginnings, from Lipperhey to Huygens and Cassini". Experimental Astronomy. 25 (1–3): 3. Bibcode:2009ExA....25....3V. doi:10.1007/s10686-009-9160-y.
10. Locke, John (1864). The life and letters of John Locke : with extracts from his journals and common-place books. London: Bell & Daldy. p. 73.
11. Burgess, James (1893). "Notes on Hindu Astronomy and the History of Our Knowledge of It". Journal of the Royal Asiatic Society of Great Britain & Ireland: 722–723.
12. de La Loubère, Simon (1693). A New Historical Relation of the Kingdom of Siam. Translated by A.P. pp. 64–65. Retrieved 16 October 2017.
13. "Cesar-Francois Cassini de Thury (French surveyor)". Encyclopædia Britannica. Retrieved 5 November 2013.
14. "How topographic map is made – making, history, used, History, Map Scales, Symbols, and Colors, The Manufacturing Process of topographic map, Quality Control, The Future". Madehow.com. 2 September 2013. Retrieved 5 November 2013.

Further reading

• Dominique, comte de Cassini, Giovanni Dominico Cassini biography
• Barkin, Iu. V. (1978). "On Cassini's laws". Astronomicheskii Zhurnal. 55: 113–122. Bibcode:1978SvA....22...64B.
• Connor, Elizabeth (1947). "The Cassini Family and the Paris Observatory". Astronomical Society of the Pacific Leaflets. 5 (218): 146–153. Bibcode:1947ASPL....5..146C.
• Cassini, Anna, Gio. Domenico Cassini. Uno scienziato del Seicento, Comune di Perinaldo, 1994. (Italian)
• Giordano Berti (a cura di), G.D. Cassini e le origini dell'astronomia moderna, catalogo della mostra svoltasi a Perinaldo -Im-, Palazzo Comunale, 31 agosto – 2 novembre 1997. (Italian)
• Giordano Berti e Giovanni Paltrinieri (a cura di), Gian Domenico Cassini. La Meridiana del Tempio di S. Petronio in Bologna, Arnaldo Forni Editore, S. Giovanni in Persiceto, 2000. (Italian)
• De Ferrari, Augusto (1978). "Cassini, Giovan Domenico". Dizionario Biografico degli Italiani (in Italian). Enciclopedia Italiana. Retrieved 2 December 2016.
• Narayanan, Anil, History of Indian Astronomy: The Siamese Manuscript, Lulu Publishing, 2019.

External links

• This article incorporates text from a publication now in the public domain: Herbermann, Charles, ed. (1913). "Giovanni Domenico Cassini". Catholic Encyclopedia. New York: Robert Appleton Company.
• O'Connor, John J.; Robertson, Edmund F., "Giovanni Domenico Cassini", MacTutor History of Mathematics archive, University of St Andrews
• Giovanni Domenico Cassini – complete digitization of 14 volumes belonging to the Old Fund's Department of Astronomy, University of Bologna, held to mark the celebrations of the Cassini in 2005 (website in Italian)
• Giovanni Cassini Biography -Space.com
• esa.int — Jean-Dominique Cassini: Astrology to astronomy -ESA
• Geoastro.de Earth shape
• Virtual exhibition on Paris Observatory digital library
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Part 1 of 2

Surya Siddhanta
by Wikipedia
Accessed: 5/15/22

The Surya Siddhanta (IAST: Sūrya Siddhānta; lit. 'Sun Treatise') is a Sanskrit treatise in Indian astronomy from the late 4th-century or early 5th-century CE,[1][2] in fourteen chapters.[3][4][5] The Surya Siddhanta describes rules to calculate the motions of various planets and the moon relative to various constellations, diameters of various planets, and calculates the orbits of various astronomical bodies.[6][7] The text is known from a 15th-century CE palm-leaf manuscript, and several newer manuscripts.[8]

pp. 15–18.

1.5 Surya-Siddhanta

According to the early eleventh-century author Alberuni, the Surya-siddhanta (or some work of the same name) was composed by Lata (Sachau, 1910, p. 153). According to the text itself, it was spoken by an emissary of the sun-god to the Asura (demon) named Maya at the end of Krta-yuga, over two million years ago.

In his translation of the Surya-siddhanta, Ebenezer Burgess notes that some manuscripts seem to connect Maya with the Roman Empire. In the manuscripts without commentary, the sun-god is presented as saying to Maya, "Go therefore to Romaka-city, thine own residence; there, undergoing incarnation as a barbarian, owing to the curse of Brahma, I will impart to thee this science" (Burgess, 1860, p. 3). If Romaka is actually Rome (or a Roman city), this could be interpreted as evidence that the Surya-siddhanta was derived from Greco-Roman astronomy. Of course, it might also be seen as evidence of tampering with the text. [!!!]

The Surya-siddhanta in its present form can be dated firmly as far back as the fifteenth century A.D. There exists a fifteenth-century palm leaf manuscript (No. XXI. N. 8 of the Adyar Library, Madras) of the text of the Surya-siddhanta along with a commentary by Paramesvara (Shukla, 1957, p. 1). We will have occasion to refer to this manuscript in Appendix 8, where we argue that remnants of advanced astronomical knowledge may survive in the Surya-siddhanta.

The astronomy of the Surya-siddhanta presents an epicyclic theory of planetary motion similar to that of Claudius Ptolemy, but it also has many features that may be of Indian origin. It begins with a detailed discussion of the Indian system of world chronology known as the yuga system. This system is based on a catur-yuga of 4,320,000 solar years and a kalpa of one thousand catur-yugas.

In the Surya-siddhanta, these immense periods of time are used as a convenient device for presenting the orbits of the planets. The orbits are described by a series of cycles and epicycles that are combined trigonometrically to reproduce observed planetary motions. Each cyclic period is defined by giving its number of revolutions in a kalpa. Since this is given as a whole number, it follows that all planetary motions will return exactly to their starting point in one kalpa. A similar idea is found in the "great year" of Hellenistic astronomy, and the idea of cyclic time is also prominent in the Indian Puranas and in the Mahabharata.

The Surya-siddhanta describes the periodic motions of the sun, moon, and planets with good accuracy. It also gives the earth-moon distance to within about 11% of the modern value. However, its figures for the distances of the sun and planets are unrealistically small. They are calculated on the assumption that the sun, moon, and planets all move with the same (mean) speed in their orbits, and therefore orbital radii are proportional to orbital periods.

In contrast, Kepler's third law makes the radius proportional to the 2/3 power of the period. For the planets, the proportionality constant in Kepler's law is also much larger than the one used in Surya-siddhanta, which is based on the orbit of the moon.

It is noteworthy that Ptolemy also made the planetary orbits much too small, but he used a different approach. Each geocentric orbit ranges from its perigee (point closest to the earth) to its apogee (furthest point). His idea was that the apogee of each orbit must equal the perigee of the next one out, so that there would be no unused space (see Appendix 4). The result is that the orbit of Saturn is smaller than the earth's orbit as we know it today.

In the Surya-siddhanta, the motion of the planets is said to be controlled by cords of air. The text explains that

Forms of Time, of invisible shape, stationed in the zodiac (bhagana), called the conjunction (sighrocca), apsis (mandocca), and node (pata), are the causes of the motion of the planets. The planets, attached to these beings[???] by cords of air, are drawn away by them, with the right and left hand, forward or backward, according to nearness, toward their own place. A wind, moreover, called provector (pravaha) impels them toward their own apices (ucca): being drawn away forward and backward, they proceed by a varying motion (Burgess, 1860, p. 53).


It is interesting to compare this with the cosmology of the Puranas, where we find similar ideas. In the Bhagavata Purana, the rotation of the stars and planets around the polar axis is said to be caused by the daksinavarta wind. This is called the pravaha wind in the Visnu Purana, where a more detailed account is given of the control of planetary motions by cords of air:
I have thus described to you, Maitreya, the chariots of the nine planets, all which are fastened to Dhruva by aerial cords. The orbs of all the planets, asterisms, and stars are attached to Dhruva, and travel accordingly in their proper orbits, being kept in their places by their respective bands of air (Wilson, 1980, p. 346).

Chapters 4-6 of the Surya-siddhanta present rules for calculating the times of solar and lunar eclipses. These are based on the same theory of eclipses used in modern astronomy. However, the ascending node of the moon is identified as Rahu, the eclipse demon of the Puranas (see Section 3.4.1). Rahu's counterpart, Ketu, is not mentioned (Burgess, 1860, p. 56).

The Surya-siddhanta contains a chapter on cosmology and geography, in which the earth is portrayed as a self-supporting globe floating in space and surrounded by the planetary orbits. The Puranic Mount Meru is defined as a literal polar axis, passing through the poles, with dwellings of the gods at the northern end and dwellings of the demons at the southern end. In the four quarters, extending south from the north pole to the equator, are four continents with four equatorial cities, as follows (Burgess, 1860, p. 286).
TABLE 1.4

Jambudvipa in Surya-siddhanta

Direction / Continent / City


east / Bhadrasva / Yamakoti
south / Bharata / Lanka
west / Ketumala / Romaka
north / Kuru / Siddhapura

These can be compared with the continents (varsas) of the Puranic Jambudvipa (see also Section 2.4.1). The general view of scholars is that the flat Jambudvipa was adapted to the earth globe when Greek astronomy was introduced into India. However, we argue in this work that Jambudvipa of the Puranas was understood as a planisphere model of the earth when the Puranic texts were written. Thus the idea of an earth globe was originally there in the Puranic Jambudvipa. Whether or not this idea was imported from the Greeks is hard to say. The accepted dates for the surviving recensions of the Puranas would allow this, and Ptolemy is known to have authored a work on the planisphere projection, mapping a globe onto a plane.

Pg. 19-46

2. The Islands and Oceans of Bhu-mandala

2.1 Overview of Bhu-Mandala


The main focus of Bhagavata cosmology is on Bhu-mandala -- the "circle of the earth" -- and we will therefore begin by giving an overview of its qualitative and quantitative features. The structure of Bhu-mandala turns out to be primarily astronomical in nature, and we will discuss this in detail in later chapters.
astronomy: the study of objects and matter outside the earth's atmosphere and of their physical and chemical properties.

-- Astronomy, by Merriam-Webster

At the same time, its qualitative features refer both to earthly geography and to the world of demigods. Some of the qualitative details appear to be derived from a historical background that begins with the descriptive geography of India and adjoining parts of Asia. In this chapter we will look briefly at this history, but since it is difficult to reconstruct, our main emphasis throughout this book will be on the cosmology of the Bhagavatam as it stands in its present form.

Bhu-mandala is a disk that bisects the sphere of the Brahmanda, the Puranic universe, and it has the same diameter as this sphere. The most noteworthy feature of Bhu-mandala is that it is described in the Bhagavatam and other Puranas in geographical terms. The central region of Bhu-mandala is divided into seven annular or ring-shaped "islands" and "oceans" which alternate, forming a bull's eye pattern. Here the Sanskrit word for island is dvipa, which literally means two waters. This term is appropriate, since most of the dvipas are rings with an ocean on the inside and on the outside.

The seven dvipas and oceans are collectively called Sapta-dvipa, and they are surrounded by three larger ring-shaped regions which extend out to the edge of Bhu-mandala. Since they are presented as parts of the earth, many scholars have attempted to identify the seven dvipas with earthly regions or countries. Thus Colonel Wilford, an early Indologist, interpreted the dvipas as seven "climates", or zones of latitude, and he assigned specific countries to them, more or less by imagination (Wilson, 1980, p. 292).

Image
Figure 2.1 Sapta-dvipa (with dvipas labeled and shown as equal bands).

Image
Figure 2.2 Francis Wilford's interpretation of Sapta-dvipa as a series of "climates" in the northern hemisphere (Asiatic Researches, vol. 8, p. 367). Note the subdiagram of Jambudvipa's mountain ranges, just to the north of India.

M. P. Tripathi and D. C. Sircar identify Sakadvipa as the land of the Sakas -- the Greek Scythia -- corresponding to Sakasthana (Seistan in East Iran) and areas to the north of this region. Sircar identifies Kusadvipa with the ancient land of Kush, which he thinks is Ethiopia (Sircar, 1960, pp. 163-64). But Tripathi disagrees and identifies Kusadvipa with the land of the Kushans, powerful people from Central Asia who invaded northern India in the early centuries of our era (Tripathi, 1969, p. 181).

It is possible that the dvipas originally did refer to regions of this earth, but in the existing Puranas they are defined as gigantic circles that do not at all correspond to irregular earthly land masses.[!!!] We will argue that these structures play an essentially astronomical role in Puranic cosmology, although Wilford's climate theory is not completely off the mark.

The features of Bhu-mandala are all defined quantitatively using a unit, called the yojana, which is about eight miles in length. The innermost island of Bhu-mandala is Jambudvipa, which has the form of a disk 100,000 yojanas in diameter. Jambudvipa is surrounded by the salt water ocean (Lavanoda), which is a ring 100,000 yojanas across from its inner to its outer edge. This ocean, in turn, is surrounded by the ring-shaped island of Plaksadvipa, which is 200,000 yojanas across. The successive islands and oceans enlarge in as indicated in Table 2.1 (with distances expressed in thousands of yojanas).

In this table, thickness is the distance from the inner radius of a ring-shaped feature to its outer radius. The seven islands and oceans follow the rule that the thickness of an ocean equals the thickness of the island it surrounds and the thickness of that island is twice the thickness of the ocean it surrounds. The circular Jambudvipa is an exception. It surrounds no ocean, and its thickness is its diameter.

The doubling of thicknesses is belied by Figure 2.1, where we show the seven oceans and islands as equal bands. We do this because the oceans and islands do not fit easily in one picture if the doubling rule is followed. For this reason, most traditional diagrams of Bhu-mandala show equal bands.

Image
Table 2.1. Sizes of the Circular Features of Bhu-mandala

Feature 13. called Manasottara Mountain, is a circular mountain range, reminiscent of some of the large craters on the moon. Since it cuts Puskaradvipa in half (see 5.20.30), we listed it in the table as "1/2 Island & mtn." Manasottara Mountain links Bhu-mandala with the orbit of the sun. The axle of the sun's chariot is said to rest at one end on Mount Meru in the center of Bhu-mandala. On the other end, it is supported by a wheel that rolls continuously on the circular track of Manasottara Mountain.[???] As we will see, this solar chariot plays a key role in the astronomical interpretation of Bhu-mandala.

Image
Figure 2.3 The region called Loka (inhabited), with the Golden Land (Kancanibhumi), Lokaloka Mountain, and Aloka-varsa.

The Inhabited Region (Loka) is an exception to the rule of doubling that applies to Sapta-dvipa. Its width is defined in the Bhagavatam verse 5.20.35 to be equal to the radius of Manasottara Mountain, and this is somewhat more than twice the thickness of Svadudaka, the ring that it immediately surrounds. The next ring, called the Golden Land (Kancanibhumi), is assigned a thickness that brings its outer radius to exactly half the radius of Bhu-mandala. This is a bit over twice the radius of Loka. Thus the table of distances is generated (roughly) by doubling, but this doubling is carried out in different ways in different parts of the table.

We note that "Loka" means an inhabited area. In contrast, the Bhagavatam states that the Golden Land is uninhabited. The fifteenth-century commentator, Sridhara Swami, clarifies the dimensions of these two regions as follows. He says that the distance from Manasottara to Meru equals the width of the inhabited earth beyond Svadudaka, and it is 1-1/2 koti and 7-1/2 lakhs (15,750,000) of yojanas. Beyond this is another, golden land measuring eight koti; and thirty-nine lakhs (83,900,000) of yojanas. This reading gives the figures listed in our table. (Here koti and lakh are commonly used terms in Sanskrit designating ten million and one hundred thousand, respectively.)

There is one other circular mountain in addition to Manasottara. This is Lokaloka Mountain, with a radius of 125,000 thousand yojanas (see 5.20.38). This circle divides the illuminated region of Bhu-mandala from the dark, uninhabited region, called Alok-varsa, which extends from Lokaloka to the shell of the Brahmanda.

2.2 THE NOMENCLATURE OF SEVEN DVIPAS

In addition to their bare dimensions, the dvipas are vividly described as populated geographical regions. With one exception, each dvipa is named after a prominent plant said to grow there. The "oceans" are named after various liquids, such as salt water, sugarcane juice, and liquor. The inhabitants of the dvipas are described, and they are said to worship the Supreme God in the form of various demigods. This information is summed up in the following table. In the third column, the terms fire, water, and air refer to the demigods presiding over these elements.

Image
Table 2.2. The Oceans and Dvipas of Bhu-mandala

The five dvipas from Plaksadvipa to Sakadvipa follow a simple pattern, and each is described in a few lines in the Bhagavatam. Each of these dvipas is divided into seven regions called varsas, with seven mountains and seven rivers. Each varsa is ruled by a grandson of Maharaja Priyavrata, a famous personality who is said to have created a second sun by following 180° behind the sun on a brilliantly glowing chariot. The oceans are said to have been ruts, created by his chariot wheels.

According to the table, Kusadvipa is named after a kind of grass. It is noteworthy that a person performing a Vedic fire sacrifice will traditionally sit on a mat made of kusa grass and offer ghee into the fire. Therefore it may be no coincidence that fire is worshiped in Kusadvipa, which is surrounded by the Ghee Ocean.

In addition to its geography, founding kings, and peoples, each of the dvipas surrounding Jambudvipa is described as having a particular, unusual feature. These are listed as follows:

Image
Table 2.3. Unique Features of Dvipas

Image
Figure 2.4. The Plaksa tree (Ficus infectoria), with a fire of seven flames at its root.

These picturesque accounts of the islands and oceans of Bhu-mandala have sometimes invoked ridicule, as when Lord Macaulay disparaged seas of treacle in his "Minute on Indian Education" (Macaulay, 1952, p. 723). Certainly, this is not geography in the familiar European sense of the term. However, as we will see later on, the geography of Bhu-mandala encodes a combination of astronomical and geographical maps which is both rational and scientific.[???] It appears that the elements of Bhu-mandala geography have either been introduced or adapted to convey a number of meaningful messages, some of which may still remain obscure. This process may be linked to the historical development of Puranic cosmology, and we now turn to this topic.

2.3 HISTORICAL DEVELOPMENT OF BHU-MANDALA FEATURES

If we survey traditional Sanskrit cosmological texts, we find a number of variations in the nomenclature and layout of the geography of Bhu-mandala. Followers of the Puranas traditionally say that such variations pertain to different kalpas, or periods of creation, but modern scholars tend to see them in historical terms. In this section, we will carry out a comparative study of texts to see what we can learn about the historical development of cosmological ideas.1 [The references used in this study are: Bhagavata P. Bhaktivedanta, 1982; Visnu P. Wilson, 1980; Kurma P. Tagare, 1981; Vayu P. Tagare, 1987; Siva P., 1990; Narosimha P., Jena, 1987: Narada P., Tagare, 1980; Markandeya P., Pargiter, 1981; Vamana P., Mukhopadhyaya, 1968; Siddhanta-siromani, Wilkinson, 1861: Varaha P., Bhattacharya, 1981; Matsya P., Taluqdar, 1916; Mahabharata, Ganguli, 1970; Padma P., Deshpande, 1988: Ramayana, Shastri, 1976.]

Our main conclusion from the study is that the cosmology of the Bhagavatam is unified and well organized, in contrast to many other Puranas (and related texts) that present cosmology in an incomplete or inconsistent way. We seem to see a historical process of imperfect preservation, rather than one of creative development. Unfortunately, the creative phase of Puranic cosmology largely remains hidden, at least as far this study is concerned.

The Puranas largely agree on the names applied to the features of Bhu-mandala, but they may permute them, and some Puranas omit features present in others. Table 2.4 summarizes the situation found in eleven readily available Puranas, in the Mahabharata, and in the Jyotisa text, Siddhanta-siromani. In this table, the feature numbers from Table 2.1 (p. 22) are used to indicate the sequence of Bhu-mandala features listed in each text. The features run from Jambudvipa (1) in the center, out to the outermost feature mentioned. (Number 17a stands for the Golden Land, Kancanibhumi, which in Table 2.1 was combined with feature 17b, the Lokaloka Mountain.)

Image
Table 2.4 Different Versions of Bhu-mandala.

Several observations can be made here. First of all, the Siddhanta-siromani, the Matsya and Varaha Puranas, and the Mahabharata differ as a group from the other Puranas in the table. In the first three of these texts, Plaksadvipa (3) is replaced by Gomedadvipa (3') and switched with Sakadvipa (11).

In the Mahabharata, Plaksadvipa is missing, even though Sanjaya, the narrator, says he will describe seven islands (Ganguli, vol. V, p. 24). Only six islands are mentioned (respectively 1, 11, 7, 5, 9, 14), as well as five oceans (respectively 2, 8, 12, 6, 15). The relationship between the islands and oceans is not indicated, and we have therefore arranged them in the table (preserving order) so as to line up as much as possible with the Matsya Purana
. The good matches indicate a strong relationship between the arrangement given in the Mahabharata and the one given in this Purana.

In the Puranas, the seven dvipas and oceans of Bhu-mandala are alternating concentric rings, and their sizes are generally given by the doubling rule of Table 2.1 (p. 22). But in the Mahabharata, it is not clear that dvipas are intended to be concentric rings. Dvipas are said to be surrounded by oceans, but oceans are not said to be surrounded by dvipas. The dvipas in the Mahabharata are said to double as one goes north, but no mention is made of their extent in other directions. Doubling is applied even more extensively in the Mahabharata than in the Puranas, since various mountains are also said to double in size as one goes north (Ganguli, vol. V, pp. 26-27).

Since the Mahabharata is generally dated before the Puranas, one might suppose that its cosmography is ancestral to Puranic cosmography. This is possible. But the cosmography of the Mahabharata is incomplete and unsystematic, and if it does represent an ancestral system, it presents only a fragment of that system -- whatever it may have been.

This naturally leads to the thought that the text of the Mahabharata has become corrupt, and this idea is not new. For example, in his Mahabharatatatparyanirnaya, verses 2.3-4, the thirteenth-century philosopher and religious teacher, Madhavacarya, stated that

In some places (of the Mahabharata) verses have been interpolated [inserting something of a different nature into something else] and in others verses have been omitted. In some places, the verses have been transposed and in others, different readings have been given out of ignorance or otherwise.

Though the works are really indestructible, they must be deemed to be mostly altered. Mostly all of them have disappeared and not even one crore [ten million] (out of several crores of slokos) now exists
(Resnick, 1999).


Many Puranas also present cosmography in an inconsistent fashion. For example, the Varaha Purana mentions duplicate names for three of the oceans. (These are indicated by stacking one alternative above the other in the table.) The Padma Purana contains a nearly verbatim copy of cosmological material from the Mahabharata -- with the interlocutors Sanjaya and Dhrtarastra being replaced by the Puranic narrator, Suta, and a group of sages. But in another place, it gives a different list following the pattern of the Bhagavatam. Thus the Padma Purana contains a mixture of material from different works.[!!!]

Image
Figure 2.5 Approximate cosmographical map, based on the account in the Ramayana of the travels of the Vanaras (monkeys) in search of Sita (after Ali, 1966, p. 23).

The Ramayana does not mention doubling, and its earth, bounded by dark, inaccessible regions, does not seem to have a succession of alternating oceans and islands. The center is India, and Mount Meru is placed to the west rather than to the north. On the east there is an island of Yava, which might be Java. There is also a Milk Ocean (Ksiroda) and a fresh water sea (Jalada). The Salmali tree of Garuda is located in the east, and the Kraunca mountain is placed in the Himalayas to the north. Apart from this, there is little to remind us of the Puranic Bhu-mandala.

Although the Ramayana may seem to represent an earlier stage in the development of the cosmology, there are earlier references to oceans and land areas that surround one another and double in size from one to the next. For example, the Brhad-aranyaka Upanisad states that "This world is thirty-two times the space crossed by the sun's chariot in a day. The earth twice as that, surrounds it. Surrounding that earth is the ocean twice as large. Then, in between, there is the space as fine as a razor's edge, or as subtle as the wing of a fly" (Sivananda, 1985, p. 294). The Upanisads are generally thought to be much earlier than the Ramayana, but this description is reminiscent of the Puranas, which are held to be later. The reference to the sun's motion suggests that the "earth" and the "ocean" must be extremely large, and this is also seen in the Puranas. The "space as fine as a razor's edge" has been described as a minute opening between the two hemispherical shells of the Brahmanda through which souls may pass.[!!!]

Image
Figure 2.6 Cosmographical diagram described by Yajnavalkya in the Brhad-aranyaka Upanisad 3.3.2. Note: the sun's orbit corresponds to the dot in the middle of the globe.

The first nine Puranas agree on feature names and their order, but some of them list fewer features than others. These Puranas all seem to reflect a single system different from the one in the Matsya Purana. The Bhagavatam, followed by the Visnu Purana, gives the most detailed list of ring-structures in Bhu-mandala. At the same time, some Puranas, such as the Vayu, give much more detailed accounts of the geography of Jambudvipa than the Bhagavatam.

We may ask whether the Puranas with longer lists added some features, or whether the ones with shorter lists dropped some. Our impression on reading the texts is that in many cases, the Puranas refer to the geography of Bhu-mandala in a very cursory way, as though the reader was expected to be already familiar with it.[???] Thus some Puranas neglect to mention all of the feature names.

Since the Bhagavatam differs from all of the other Puranas in its assignment of the Milk (10) and Curd (12) Oceans (Table 2.1, p. 22), it appears that these have been switched for some reason in the Bhagavatam. Likewise, feature 16 (Loka) is listed only in the Bhagavatam, and we can ask whether it is unique to this text. The answer is that indirect evidence suggests that the Bhagavatam's calculations for Loka and the Golden Land were used in other texts as well.

Thus the Bhagavatam makes the radius of Lokaloka one fourth the diameter of the Brahmanda, and the distance from the Sweet Water Ocean to Lokaloka Mountain comes to about ten crores of Yojanas, where a crore is ten million. (The exact figure is 99,650,000 yojanas.) H. H. Wilson finds similar figures in the Siva Tantra. He says, "According to the Siva Tantra, the golden land is ten crores of Yojanas, making, with the seven continents, one fourth of the whole measurement" (Wilson, 1980, p. 294). Thus the Bhagavatam's calculations -- which make use of feature 16 -- appear to be reflected in the Siva Tantra, and they may have a further, unknown background.

In contrast, the Visnu and Kurma Puranas (which are closest to the Bhagavatam in Table 2.4) both say that the Golden Land has twice the thickness of the Sweet Water Ocean (Svadudaka). This results in a radius of 38,150,000 yojanas for LokaIoka Mountain. All of the Puranas agree that the Brahmanda is 250,000,000 yojanas in radius, and so the radius of Lokaloka Mountain comes to about 15% of the universal radius.

Il is not clear whether this version came before that of the Bhagavatam or after it. But if we assume the former, it is hard to say why the boundary of the Brahmanda was placed so far away from Lokaloka Mountain. The Visnu Purana cannot produce a figure as large as the universal radius by further doubling. For example, doubling thickness again by adding twice the Golden Land would bring one out to only 63,750,000 yojanas. In contrast, the Bhagavatam does generate the universal radius by doubling, and this involves feature 16.

In summary, it does not seem possible at present to trace the geography of Bhu-mandala back to its origins. The existing texts do not explain their calculations, and many of them appear to be corrupt and incomplete. At some point, descriptive geography (perhaps represented by the Ramayana) must have given way to a quasi-geographical system based on circles of immense size. As we will argue later on, the motivation for this was apparently astronomical and involved an analogy between the earth and the sun's path through the heavens. It could have happened at any time in the development of the tradition leading up to the Bhagavatam.

Image
Figure 2.7 The Visnu Purana places the Golden Land directly outside of Sapta-dvipa, with a thickness twice that of the Sweet Water Ocean. This gives the surrounding Lokaloka Mountain a radius only 15% of the radius of the Brahmanda, as shown here. (Compare with the Bhagavatam's version in Figure 1 of the Introduction.

2.4 THE ISLAND OF JAMBUDVIPA

In the Puranas, Jambudvipa is a disk 100,000 yojanas in diameter situated in the center of Bhu-mandala. In the center of Jambudvipa is Mount Meru (or Sumeru) which, in one interpretation, corresponds astronomically to the polar axis of the earth. But even though the center point of Meru may represent the north pole, the cardinal directions east, west, north, and south are defined from it. We will argue later on that Jambudvipa also represents a local map centered on the Pamir mountains, and these cardinal directions are appropriate for this map (see Section 5.1).

On the top of Mount Meru, the cardinal directions and intermediate directions (northeast, southeast, southwest, and northwest) are marked by the eight cities of the Loka-paIas, surrounding the central city of Brahma. It turns out that this arrangement of directional demigods is related to a system of Indian architecture in which a building site on the earth is identified with the ecliptic -- the path of the sun through the heavens. This is discussed below, in Section 2.5. It is significant, because a key interpretation of the earth-mandala is that it represents the ecliptic and the planetary orbits.

The disk of Jambudvipa is divided in the Puranas into nine varsas, or continents, by a series of mountain ranges, as shown in Figure 2.9. The disk is first of all divided into seven horizontal strips by six ranges that run east-west. In the Bhagavatam, each range is said to be 10,000 yojanas high and 2,000 yojanas wide. The three strips to the north and the three to the south are single varsas, and they are said to extend for 9,000 yojanas in a north-south direction. This leaves 34,000 yojanas for the seventh strip, which consists of three varsas. These features and their north-south dimensions are listed in Table 2.5, going from north to south.

Image
Figure 2.8 Close-up of Jambudvipa, showing Brahmapuri on top of Mount Sumeru.

Image
Figure 2.9 Map of Jambudvipa, with mountain ranges shown in black and the base of Mount Meru shown in the center.

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Table 2.5 Geographical Features of Jambudvipa, from North to South

According to 5.16.8, the east-west length of these mountains is supposed to be reduced by a little more than 10% as one goes from mountain to mountain from the center outward. This is roughly true if we extend each mountain range until it meets the circular boundary of Jambudvipa. These lengths appear in Table 2.6.

The central strip is divided into three varsas (making nine in total) by two mountain chains that run north-south and extend for 2,000 yojanas. Their north-south length must be 34,000 yojanas. Taking their width in the east-west direction to be 2,000 yojanas, and taking Ilavrta-varsa in the center to be square, the east-west dimensions of these features are in Table 2.7.

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Table 2.6 Lengths of Mountains in Jambudvipa, from North to South

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Table 2.7 Features Ranging from West to East in Jambudvipa

The inhabitants and topography of Jambudvipa are described in considerable detail. In 5.17.11, Bharata-varsa is singled out as the field of fruitive activities, and the other eight varsas are said to be meant for elevated persons who are enjoying the remainder of their pious credits after returning from the heavenly planets. This suggests that, in one sense, Bharata-varsa is the entire earth and the other eight varsas represent otherworldly, heavenly regions. This is one of the major interpretations of Jambudvipa and Bhu-mandala, and it is discussed in Chapter 6.

Within lIavrta-varsa there are a number of mountains and rivers surrounding Mount Meru. Meru is described in 5.16.7 as being 100,000 yojanas high, with 16,000 yojanas extending beneath the earth and 84,000 yojanas above the earth. It is said to be 32,000 yojanas in diameter at the top and 16,000 yojanas in diameter at the base.

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Table 2.10 This diagram of Jambudvipa shows the Deities worshiped in different varsas, nearly accordingly to the Bhagavatam. It is copied from a painting on the wall of the compound of the Kutalmanika temple in Kerala.

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Table 2.8 Worship in Jambudvipa

Mount Meru is therefore in the form of an inverted cone, and it is compared to the pericarp or seed pod of the lotus flower of Bhu-mandala. In the Vayu Purana, Meru is said to be four-sided, with the colors white (east), yellow (south), black (west), and red (north) (Tagare, 1987, pp. 237-38).

In each varsa it is said that an avatara of Visnu is worshiped by a particular famous devotee. In this way, Jambudvipa also plays the role of a divine mandala representing the faith of the Vaisnavas, for whom the Bhagavatam is an important sacred text. The avataras and their worshipers are listed in Table 2.8.

In Bharata-varsa, Nara-narayana is said to be worshiped by Narada Muni in Badarikasrama, a famous site of pilgrimage for thousands of Hindus. This provides a link with a known location in the Himalayas, but we do not have earthly counterparts for the other centers of worship.

2.4.1 Jambudvipa in the Mahabharata

The Bhisma Parva of the Mahabharata describes a circular island called Sudarsana which is very similar to the Puranic Jambudvipa. The geographical layout of this island is the same as that in Tables 2.5 and 2.7, with the exception that the vertical spacing between the east-west ranges is set at 1,000 yojanas (Ganguli, vol. V, pp. 13-14). However, the height of Mount Meru, situated between the MaIyavan and Gandhamadana mountains, is defined to be 84,000 yojanas, as in the Puranas.

Image
Figure 2.11 Circular continent of Sudarsana, as described in the Mahabharata (after Ali, 1966, pp. 32-33). This corresponds to Jambudvipa in the Puranas

While Sudarsana corresponds to the Puranic Jambudvipa, the term Jambudvipa is used in a different sense in the Mahabharata. Thus, in the Bhisma Parva it is said that "Jamvu Mountain" extends over 18,600 yojanas and the Salt Ocean is twice as big. Sikadvipa is twice as big as Jambudvipa, and another ocean surrounding Sakadvipa is twice the size of that island (Ganguli, vol. V, p. 24). Except for the small size of Jambudvipa, this sounds like Puranic geography as given in the Matsya Purana.

But in the Santi Parva, it is said that
King Yudhisthira once ruled Jambudvipa, Krauncadvipa on the west of Meru and equal to Jambudvipa, Sakadvipa on the east of Meru and equal to Krauncadvipa, and Bhadrasva, on the north of Meru and equal to Sakadvipa (Ganguli, vol. VIll, p. 24). This gives us three dvipas and one varsa arranged as equal units around Meru in the cardinal directions. This geographical arrangement is clearly quite different from the one given in the Bhisma Parva.

Then again, if we look back to the Bhisma Parva, we find the statement that "Beside Meru are situated, O lord, these four islands, viz., Bhadraswa, and Kelumala, and Jamvudwipa otherwise called Bharata, and Uttar-Kuru which is the abode of persons who have achieved the merit of righteousness" (Ganguli, vol. V, p. 14). It appears that the Mahabharata is reporting different geographical systems without attempting to systematically reconcile them.

Image
Figure 2.12 This diagram is based on a text from the Santi Parva of the Mahabharata. It differs from the Puranas and other parts of the Mahabharata by defining Jambudvipa as one of four regions surrounding Mount Meru.[/i]

According to Joseph Schwartzberg, [i]an earlier Hindu and Buddhist map of the earth placed four continents in the cardinal directions around Mount Meru, with the continent called Bharata or Jambudvipa to the south (Schwartzberg, 1987, p. 336). The Surya-siddhanta follows this pattern by putting Bhadrasva to the east, Bharata to the south, Ketumala to the west, and Kuru to the north
(Burgess, 1860, p. 286).

In Figure 2.13, published by the early Indologist Francis Wilford, Jambudvipa is presented as a lotus, with four continents arranged around Meru as listed in the Surya-siddhanta (Wilford, 1805). Note that Kuru-varsa (Curu) is identified as Siberia, so that Meru falls somewhere in the mountainous region north of India. Additional lands near India have been added as extra petals.

Schwartzberg maintains that the original system of four continents was modified over time until it took the form given in Figure 2.9. This may be true, but we may also be dealing with independent traditions making use of the same set of names for islands and continents.

Image
Figure 2.13 Jambudvipa, depicted as a lotus flower by the early Indologist Francis Wilford.

We can distinguish between the two maps of Jambudvipa on purely functional grounds. In relation to actual earthly geography, the four-continent map simply assigns names to lands in the four cardinal directions around Mount Meru (which lies somewhere to the north of India). In contrast, the map in Figure 2.9 gives a more detailed picture of the mountain ranges and valleys in this part of south-central Asia (see Chapter 5). This may explain how these two systems could coexist in the same text.[???]

A basic theme of this study is that models in the Bhagavatam are sometimes used to convey more than one meaning (see the Introduction to Bhagavata Cosmology). Here it appears that the Mahabharata is using geographical terms (such as Sakadvipa) with more than one meaning. One might argue that as alternative meanings accumulated over a long period of time, commentators became tolerant of apparently conflicting meanings, and they tended to resolve conflicts by looking at statements from the standpoint of local context.

2.5 LORDS OF THE DIRECTIONS

Concluding this chapter, we show how an apparently minor detail of Jambudvipa is connected with the astronomy of the ecliptic and with rich astronomical traditions of Indochina. This connection provides data which corroborates the close correlations between Bhu-mandala and modern astronomy [???!!!] that we will discuss in Chapter 4.

The Bhagavatam verse 5.21.7 describes four cities of the demigods situated on Manasottara mountain in the cardinal directions:

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Table 2.9 Directional Cities on Manasottara Mountain.

It turns out that these cities are connected with a larger system of directional demigods, and these in turn are connected with the traditional Indian system of architecture known as Vastu Sastra.

Image

Angkor Wat, a Hindu-Buddhist temple and World Heritage Site, is the largest religious monument in the world. This Cambodian temple deploys the same circles and squares grid architecture as described in Indian Vāstu Śastras.

Vastu shastra (vāstu śāstra - literally "science of architecture") are texts on the traditional Indian system of architecture. These texts describe principles of design, layout, measurements, ground preparation, space arrangement, and spatial geometry. The designs aim to integrate architecture with nature, the relative functions of various parts of the structure, and ancient beliefs utilising geometric patterns (yantra), symmetry, and directional alignments.

Vastu Shastra are the textual part of Vastu Vidya - the broader knowledge about architecture and design theories from ancient India. Vastu Vidya is a collection of ideas and concepts, with or without the support of layout diagrams, that are not rigid. Rather, these ideas and concepts are models for the organisation of space and form within a building or collection of buildings, based on their functions in relation to each other, their usage and the overall fabric of the Vastu. Ancient Vastu Shastra principles include those for the design of Mandir (Hindu temples), and the principles for the design and layout of houses, towns, cities, gardens, roads, water works, shops and other public areas.

In contemporary India, states Chakrabarti, consultants that include "quacks, priests and astrologers" fueled by greed are marketing pseudoscience and superstition in the name of Vastu-sastras. They have little knowledge of what the historic Vastu-sastra texts actually teach, and they frame it in terms of a "religious tradition", rather than ground it in any "architectural theory" therein....

According to Chakrabarti, Vastu Vidya is as old the Vedic period and linked to the ritual architecture. According to Michael W. Meister, the Atharvaveda contains verses with mystic cosmogony which provide a paradigm for cosmic planning, but they did not represent architecture nor a developed practice.

Vastu sastras are stated by some to have roots in pre-1st-century CE literature, but these views suffer from being a matter of interpretation. For example, the mathematical rules and steps for constructing Vedic yajna square for the sacrificial fire are in the Sulba-sutras dated to 4th-century BCE. However, these are ritual artifacts and they are not buildings or temples or broader objects of a lasting architecture. Varahamihira's Brihat Samhita dated to about the sixth century CE is among the earliest known Indian texts with dedicated chapters with principles of architecture. For example, Chapter 53 of the Brihat Samhita is titled "On architecture", and there and elsewhere it discusses elements of vastu sastra such as "planning cities and buildings" and "house structures, orientation, storeys, building balconies" along with other topics....

By 6th century AD, Sanskrit texts for constructing palatial temples were in circulation in India. Vāstu-Śastras include chapters on home construction, town planning, and how efficient villages, towns and kingdoms integrated temples, water bodies and gardens within them to achieve harmony with nature....

The Silpa Prakasa of Odisha, authored by Ramachandra Bhattaraka Kaulachara sometime in ninth or tenth century CE, is another Vāstu Śastra. Silpa Prakasa describes the geometric principles in every aspect of the temple and symbolism such as 16 emotions of human beings carved as 16 types of female figures.... in Saurastra tradition of temple building found in western states of India, the feminine form, expressions and emotions are depicted in 32 types of Nataka-stri[???] compared to 16 types described in Silpa Prakasa. Silpa Prakasa provides brief introduction to 12 types of Hindu temples....

Vāstu Śastra Vidya was ignored, during colonial era construction, for several reasons. These texts were viewed by 19th and early 20th century architects as archaic, the literature was inaccessible being in an ancient language not spoken or read by the architects, and the ancient texts assumed space to be readily available....

Vastu Shastra is a pseudoscience, states Narendra Nayak – the head of Federation of Indian Rationalist Associations. In contemporary India, Vastu consultants "promote superstition in the name of science". Astronomer Jayant Narlikar states Vastu Shastra has rules about integrating architecture with its ambience, but the dictates of Vastu and alleged harm or benefits being marketed has "no logical connection to environment". He gives examples of Vastu consultants claiming the need to align the house to magnetic axis for "overall growth, peace and happiness, or that "parallelogram-shaped sites can lead to quarrels in the family", states Narlikar. This is pseudoscience....

Many Agamas, Puranas and Hindu scriptures include chapters on architecture of temples, homes, villages, towns, fortifications, streets, shop layout, public wells, public bathing, public halls, gardens, river fronts among other things. In some cases, the manuscripts are partially lost, some are available only in Tibetan, Nepalese or South Indian languages, while in others original Sanskrit manuscripts are available in different parts of India.

-- Vastu shastra, by Wikipedia


Image
Figure 2.14 The asta-dikpalaka, the rulers of the eight directions (after Dubreuil-Jouveau, 1937, p. 107.

Verse 5.16.29 mentions cities of eight Loka-palas, or lords of the worlds, beginning with lndra. These cities are said to be situated on top of Mount Sumeru, surrounding the city of Lord Brahma (Brahmapuri). The Loka-palas are also known as the Asta-dik-palaka, or eight lords of the directions. They are situated as follows (Dubreuil-Jouveau, 1937, p. 107):

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Table 2.10 The Cities of Brahma and the Eight Loka-palas

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Figure 2.15 The figure of the Vastupurusa in the 8x8 Vastupurusa-mandala

Note that with the exception of Kuvera in the north, the lords of the cardinal directions are the same as the demigods ruling the cardinal points of Minasottara mountain.

In Vastu Sastra, the layout of a temple or residential house is based on an 8x8 or 9x9 grid of squares, known as the Vastupurusamandala. This grid is associated with the figure of a person called the Vastupurusa, as indicated for the 8x8 grid in the illustration. These grids are always aligned with the cardinal directions.

There are 28 squares in the outer border of the 8x8 grid, and 32 squares in the outer border of the 9x9 grid. These are associated with demigods called Padadevatas. The central 3x3 squares of the 9x9 grid are dedicated to Brahma, and thus the entire grid resembles the top of Mount Sumeru, with Brahmapuri in the center.
This is enhanced by the close similarity between the eight Loka-palas and the eight Padadevatas situated at the cardinal and intermediate directions.

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Table 2.11 The 32 Padadevatas and the Loka-palas

For the 9x9 grid, the Padadevatas are listed in the table below. Different sources give small variants in the list of Padadevatas, and in the first three columns we give three lists from (1) (Kramrisch, 1946, p. 32), (2) (Tarkhedkar, 1995, p. 31), and (3) (Sthapati, 1997, p. 205).

The eight Loka-palas are listed for comparison in the fourth column of the table. The demigods are listed in groups of nine for each side of the 9x9 square, and each corner demigod therefore comes at the end of one list and the beginning of the next one. The corner demigods should be compared with the Loka-palas for the intermediate directions, and the demigods in the center squares of the sides should be compared with the Loka-palas for the cardinal directions. The similarity is close enough to indicate a strong connection between the Vastu Sastras and the Puranic lords of the directions. Note that the Padadevata for the center of the northern side is listed as Soma. This disagrees with the Loka-pala list, which has Kuvera, but it agrees with 5.21.7.

There is a connection between the Vastupurusamandala and the ecliptic. The ecliptic is the path of the sun against the background of stars, and in Indian astronomy it is marked by 27 or 28 constellations called naksatras. The Vistupurusamandala, which is situated on the earth, is linked with the ecliptic in the heavens by identifying the four cardinal directions with the solstices and equinoxes and by identifying 28 intermediate directions with the naksatras.

The Indian art historian Stella Kramrisch described this connection as follows for the 9x9 Vastupurusamandala with 32 squares in its border:

The 27 and 28 divisions of the Ecliptic become fixed in position like a great, fixed, square dial with the numbers ranging not along the equator, but along the Ecliptic itself. The square, cycle of the Ecliptic, would thus have to be sub-divided into 27 or 28 compartments. Instead of this, the number of Naksatras is augmented to 32, so that each field of the border represents a lunar mansion or Naksatra. In the Vastumandala their number is thus adjusted to the helio-planetary cosmogram of the Prthivimandala. There, the four cardinal points, with reference to the Ecliptic are the equinoxial and solstitial points in the annual cycle. The soIar cycles of the days and years are shown in the Vastumandala together with the lunations, the monthly revolutions of the moon around the earth. The soIar-spatial symbolism is primary and the lunar symbolism is accommodated within the Vastu-diagram (Kramrisch, 1946. p. 31).


According to Kramrisch, the Vastumandala represents a composite of different traditions, and she also mentions a different scheme in which naksatras and their presiding demigod are linked to the cardinal directions (Kramrisch, 1946, p. 34). These demigods are said to rule over positions of entrances to the planned building, and they differ from the 32 Padadevatas.

The ecliptic/Vastumandala link represents a scheme in which part of the earth (where a building is to be erected) is identified with the ecliptic in the sky. There is a similar identification in the Bhagavatam, where the earth-disk, Bhu-mandala, represents the ecliptic plane. It may therefore be significant that the Puranic Loka-palas on Mount Meru are connected with the Vastupurusamandala of Vastu Sastra.[???!!!]

Adrian Snodgrass describes the symbolism of the Vastupurusamandala, and he also relates it to a cosmological account in which the Trayastrimsa Heaven of lndra is situated on Mount Meru, along with 32 directional demigods representing the equinoxes and solstices and the 28 naksatra divisions of the ecliptic. He points out that this symbolism was reflected in the medieval Burmese kingdom of Pegu, in which 32 provinces surrounding the capital city represented the ecliptic and the Loka-palas (Snodgrass, 1990, pp. 210-11 ).

Snodgrass also points out that elaborate astronomical symbolism was built into the temple of Angkor Wat in Cambodia. Thus
Angkor Wat "incorporates at least twenty-two significant alignments to equinoctial and solstitial solar risings" (Snodgrass, 1990, p. 216). This implies that Hindu temple builders in Indochina must have been interested in making quantitative astronomical observations, and it may indicate some of the practical astronomy lying behind the Vastumandala concept.


Snodgrass also listed over thirteen different astronomical quantities that were built into the temple of Angkor Wat in multiples of a unit of length called the hat (Sanskrit hasta). For example, "the interior axial lengths of the nine chambers in the central tower are 27 on the east-west axis and 28 on the north-south axis, referring to the 27 or 28 lunar mansions (naksatra) and to the 28 days on which the moon is visible each month" (Snodgrass, 1990, p. 217).

An interesting feature is the latitude of Angkor Wat, which equals the local elevation of the polar axis. This is expressed in the building by several lengths of 13.43 hat, where one hat represents one degree of latitude. This is accurate to 60-90 seconds of arc (Snodgrass, 1990, p. 221). Also, several lengths of 432, 864, 1,296, and 1,728 hat in different parts of the building express the four yugas -- time periods which endure for corresponding numbers of millennia (Snodgrass, 1990, p. 223). (The yuga system is discussed in Section 8.4.)

The hat itself is 0.43454 meters, which is very close to the 0.432 meter hasta discussed in Section 4.5 on the length of the yojana (Snodgrass, 1990, p. 217). This unit, in turn, emerges independently in the study of the correlation between planetary orbits and Bhu-mandala reported in Section 4.4.


-- The Cosmology of the Bhagavata Purana: Mysteries of the Sacred Universe, by Richard L. Thompson [For Sale in Asia Only], 2000


It was composed or revised c. 800 CE from an earlier text also called the Surya Siddhanta.[5] The Surya Siddhanta text is composed of verses made up of two lines, each broken into two halves, or pãds, of eight syllables each.[9]

As described by al-Biruni, the 11th-century Persian scholar and polymath, a text named the Surya Siddhanta was written by one Lāta.[8] The second verse of the first chapter of the Surya Siddhanta attributes the words to an emissary of the solar deity of Hindu mythology, Surya, as recounted to an asura called Maya at the end of Satya Yuga, the first golden age from Hindu texts, around two million years ago.[8][10]

The text asserts, according to Markanday and Srivatsava, that the earth is of a spherical shape.[4] It treats Sun as stationary globe around which earth and other planets orbit. It calculates the earth's diameter to be 8,000 miles (modern: 7,928 miles),[6] the diameter of the moon as 2,400 miles (actual ~2,160)[6] and the distance between the moon and the earth to be 258,000 miles[6] (now known to vary: 221,500–252,700 miles (356,500–406,700 kilometres).[11] The text is known for some of earliest known discussion of sexagesimal fractions and trigonometric functions.[1][2][12]

The Surya Siddhanta is one of several astronomy-related Hindu texts. It represents a functional system that made reasonably accurate predictions.
[13][14][15] The text was influential on the solar year computations of the luni-solar Hindu calendar.[16] The text was translated into Arabic and was influential in medieval Islamic geography.[17] The Surya Siddhanta has the largest number of commentators among all the astronomical texts written in India. It includes information about the orbital parameters of the planets, such as the number of revolutions per Mahayuga, the longitudinal changes of the orbits, and also includes supporting evidence and calculation methods.[9]
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Part 2 of 2

Textual history

Further information: Jyotisha

In a work called the Pañca-siddhāntikā composed in the sixth century by Varāhamihira, five astronomical treatises are named and summarised: Paulīśa-siddhānta, Romaka-siddhānta, Vasiṣṭha-siddhānta, Sūrya-siddhānta, and Paitāmaha-siddhānta.: 50  Most scholars place the surviving version of the text variously from the 4th-century to 5th-century CE,[18][19] although it is dated to about the 6th-century BC by Markandaya and Srivastava.[20]

1 Introduction

Anthropologists and archaeologists agree that the beginning of civilization in India was around 4000 B.C. in the northwestern and central areas. Not much is known about the early period, but it is generally believed that by early in the 3ed millennium B.C. this civilization had developed a primitive village culture. Then, in a still unexplained great advance, these people developed one of the world's earliest civilizations.

Until recently little work has been done to collect and collate information on the contributions of the ancient Indians in the field of oceanography; this is because scientists are generally not familiar with the original sources, while classical scholars pass by the most valuable work as of no literary merit. In this article a survey has been made of the contribution by Indians to physical oceanography from the Harappan times (about 3000 B.C.) to 1947. The study has been classified into seven historical periods, viz.: Indo-Aryan (3000-600 B.C.), Jain and Buddhist (600·325 B.C.), Mauryan and Kushan (322 B.C.-320 A.D.), Gupta and Harsha (320-650 A.D.), Rajput (650-1200 A.D.), Muslim (1200-1757 A.D.), and British (1757-1947 A.D.). It may be noted here that certain events, not specifically oceanographic, have also been discussed to project a comprehensive picture of the intellectual thinking of the ancient Indians.

[pgs. 552 missing]

6 m. Hence, to effectively operate the dock it was essential for the Harappans to have a good knowledge of the tides in the area. A close study of the Lothal dock reveals that the Harappan ocean-engineers had also solved the problems of desilting in the dock and the maintenance of a constant water level in the channel (Rao 1956-1957,1970, 1973). Three perforated stone anchors and a Persian Gulf seal have been found at Lothal.

An Indus type of seal found in Mesopotamia has been dated from 2950-2220 B.C. (Wheeler 1964). Indian teak has been found in the Babylonian remains of the 3rd millennium (Sircar 1967).
The above finds give positive evidence that trade with west Asian ports had been well established in the Bronze Age.[???!!!] The outstanding feature of the wind system over the Arabian Sea is a seasonal reversal of its direction, associated with the northeast and southwest monsoon seasons. Without the knowledge of these changing winds the Harappan vessels could not have made their voyages; thus the Harappan sailors must have had at least a conceptual knowledge of the monsoon winds.
“Assumptions are the mother of all f***-ups” -- Anon
"Necessity is the mother of invention" -- Proverb

Trade at Lethal seems to have declined around 1500 B.C., followed by the decline (or migration) of the Harappan civilization.

Vedic Period (1500 8.C.-600 B.C.)

Image
Figure 1b. An Artist's concept of the Lothal dock (after Rao 1973).

The end of Harappan civilization caused much turmoil in the Indian sub-continent, and until 600 B.C. little archaeological evidence of maritime activity is available. However, a survey of the Hindu epics has been made to gather information on maritime activity during the Vedic period.[???!!!] Prabasa (Somnath), the place of Hindu holy rites in the epic Mahabharata, has been identified as a Vedic port on the Kathiawar coast. Mula-Dwarka, an estuarine port in the village of

[pgs. 554-555 missing]

of the maritime activity of the Indians. It seems that the Indians established colonies in west Asia, and it is believed that an Indian colony in the region of the upper Euphrates River west of Lake Van was established as early as the 2nd century B.C. Socotra Island (Sukhatara Davipa in Sanskrit) was also colonized.

In the Periplus the name of the sea goddess of Gujarat, Sikotari-mata, is mentioned. A number of Indian ports are also cited in Periplus: Hastabra (Hatab on the Kathiawar coast); Colliena (Kalyana); Mandager (Mandad); Palaeputmae (Pal) near Bombay. Muziris (Fig. 1c) near Cranganore, in South Canara, is also referred to in Periplus; this site has been excavated and the evidence should shows that it was in operation during the 1st to 2nd century A.D. (Ramachandran 1970, Rao 1970).

Though Greek writers mention ports on the eastern coast of India, evidence from the Tamil literature, viz. Chilappathikaram seems to be more accurate. It describes the ports of Poompohar (Kaveripattinam in Tamil Nadu); Poduke or Paduca (Arikamedu near Pondicherry); and Kaimapara (Konark in Orissa). Excavations at Kaveripattinam have exposed a brick jetty dateable to 300 B.C. Excavations conducted at Paduca have identified a warehouse of the 1st century A.D.; Paduca was a Roman trade-treaty port, and Roman pottery of the 1st century A.D. has been unearthed there (Ramachandran 1970, Rao 1970). At Dhanyakatka near Amaravati in Guntur, Andhra Pradesh, an embarkment with wharf and a navigational channel, with rouletted ware, dated as about 200 B.C., have been discovered. At Tamlik or Tamralipti on the mouth of the Ganga, an estuarine port dating from the 2nd to 3rd century A.D. has been unearthed (Ramachandran 1970, Rao 1970). The tidal bore in the river Ganga and its tributaries is an important oceanographic feature in the area; navigators for the above period must have had knowledge of these tidal bores, otherwise they would not have been able to operate their boats.

Image
Figure 1c. Ancient sea routes connecting India with the Arabian and south-east Asian countries (after Ramachandran 1970)

Literature on ship building is lacking in the earlier Indian writings. The only book that discusses ship building is Yuktikalpatara, written by Bhoja, King of Dhara (4th century A.D.). Details on the type of wood to be used, dimensions of ships, decorations, furnishings, mast size, cabin size, etc., are presented, including a list of a few selected metals to be used for construction. The use of iron nails for joining the bottom planks was prohibited because it was supposed that they would be attracted by magnetic reefs, exposing ships to danger; the concept of magnetic reefs was widespread up to the 14th century A.D. (Gopal 1970, Ramachandran 1970).

There are five important Hindu astronomical books known as Siddhantas. Surya Siddhanta is the oldest (about the 6th century B.C.). According to Al-Biruni it was written by Lata. The book is divided into 14 chapters (Table 1). According to Surya Siddhanta the earth is a sphere. Five planets and their ascending and descending modes are mentioned, noting that planets do not describe perfect circles, but move in epicycles (Filliozat 1963). The Paitamaha Siddhanta (second half of the 1st century A.D.) provides a method of locating moving celestial bodies relative to a fixed point and expresses angular distances in degrees and minutes. It uses the 12 rasi (zodiac) signs dividing the sky into 12 parts, each of 30°, thus giving a precise method for the determination of angular distance (Filliozat 1963). The Paulisa Siddhanta also includes methods for calculating the exact length of a day and predicting eclipses. Vasistha Siddhanta gives a method for determining the exact length of the day, a rough means for predicting eclipses, a method of locating moving celestial bodies by fixed points of reference and expressing angular distances in degrees and minutes (Filliozat 1963).

The Romaka Siddhanta (sometime between the 2nd and the 6th centuries A.D.) gives a lunar-solar cycle and a method for evaluating the length of the year, which agrees with the techniques of Ptolemy and Hipparchos. Romaka Siddhanta is more accurate than Paitamaha Siddhanta. Romaka Siddhanta also gives 150 tables of equations of anomaly (Filliozat 1963). Pancha Siddhanta, written by Varahamihira, summarizes the concepts of earlier Siddhantas. In addition it describes the conjunctions and motions of celestial bodies and various meteorological phenomena (Filliozat 1963).
Table 1. Chapters of Surya Siddhanta

Chapter no. / Subject of discussion


1 / Measurement of time
2 / Sine tables*
3 / Meridians, cardinal points, equinoxes and solstices
4 & 5 / Eclipses of moon and sun
6 / Graphical projection of eclipses
7 / Planetary motions
8 / Inclination of the nakshatras (constellations) to the eliptic
9 / Helical rising and setting of stars
10 / Relative motions of sun and moon
11 / Evil conjunctions
12 / Cosmography
13 / Elementary astronomical instruments
14 / Computations of the calendar

5 Gupta and Harsha Period (320 A.D.-650 A.D.)

The Gupta period (320 A.D,-A76 A.D.) is known as the golden age of Indian history. Indian science and arts reached their creative peaks.

Aryabhatiya, a comprehensive astronomical text written by Aryabhata (late 5th or early 6th century A.D.), introduced the principles of epicycles and the rotation of the earth (Filliozat 1963).
Aryabhata mentions in the Aryabhatiya that he was 23 years old 3,600 years into the Kali Yuga, but this is not to mean that the text was composed at that time. This mentioned year corresponds to 499 CE, and implies that he was born in 476....

It is fairly certain that, at some point, he went to Kusumapura for advanced studies and lived there for some time. Both Hindu and Buddhist tradition, as well as Bhāskara I (CE 629), identify Kusumapura as Pāṭaliputra, modern Patna. A verse[???] mentions that Aryabhata was the head of an institution (kulapa) at Kusumapura, and, because the university of Nalanda[???] was near Pataliputra at the time and had an astronomical observatory, it is speculated that Aryabhata might have been the head of the Nalanda university as well. [Taranatha also connects Aryadeva, a philosopher of the Madhyamika school of Buddhism of the early fourth century AD, with Nalanda.4 (History of Buddhism in India, Calcutta, by Chattopadhyay, D.P.) -- Nalanda Mahavihara: Victim of a Myth regarding its Decline and Destruction, by O.P. Jaiswal] Aryabhata is also reputed to have set up an observatory at the Sun temple in Taregana, Bihar....

The Arya-siddhanta, a lost work on astronomical computations, is known through the writings of Aryabhata's contemporary, Varahamihira [c. 505 – c. 587], and later mathematicians and commentators, including Brahmagupta and Bhaskara I....

Direct details of Aryabhata's work are known only from the Aryabhatiya. The name "Aryabhatiya" is due to later commentators. Aryabhata himself may not have given it a name....

The extreme brevity of the text was elaborated in commentaries by his disciple Bhaskara I (Bhashya, c. 600 CE) and by Nilakantha Somayaji in his Aryabhatiya Bhasya, (1465 CE).

-- Aryabhata, by Wikipedia

Brahmasphuta Siddhanta and Khandakhadyaka (6th or early 7th century A.D.) written by Brahmagupta, describe the mean and true planetary motions and conjunctions of planets (Filliozat 1963). Mahabhaskariya (7th century A.D.), written by Bhaskara I, records the longitudes of planets, and their connection with time, place and directions.

6 Rajput Period (650 A.D.-1200 A.D.)

This period of history has been well documented. Dhanapala's Tilakamajari gives a good account of the ships and shipping industry of the period. It tells about the regulations of sails and masts, types of anchors, naval expeditions, and the importance of astronomical knowledge for navigation (Gopal 1970, Ramachandran 1970).

The Tamil book, Permapanarrupadai, mentions important naval battles of the period. Raja Raja in 983 A.D. led successful expeditions against Sri Lanka. Rajendra conquered Kadarma (Kedah of the Malay Peninsula) (Gopal 1970). It may be pointed out here that in those days naval victory was closely associated with a knowledge of wind and waves, and that there is every likelihood that Indians of those days had a good knowledge of these oceanographic parameters. The navigation of Indian ships was facilitated by the presence of the compass, which had been discovered by ancient Indians.

An important treatise on astronomy and mathematics, Siromani Siddhanta, was compiled by Bhaskar II. This deals with arithmetic, algebra, motion of planets, etc.

7 Muslim Period (1200 A.D.-1757 A.D.)

During this period Indian astronomers and mathematicians came in close contact with their counterparts from Arabia and China. Jacques Devitry, in his book History of Jerusalem (1218 A.D.), mentions the use of compass by ancient Indian navigators. Abu Hanifa Dainuri, the Arab pilot (12th century A.D.), included 12 of the 16 types of winds in his work on nautical science from the Jain book Avasyakacurni (Ral 1970). Din Ahmed Ibra Majid, an Arab navigator, prepared a map of the Indian Ocean based on ancient literature; this map is presented in his book Mohit (1554 A.D.), and he also discusses monsoon winds. Dampier, the 17th century buccaneer, published a detailed chart of winds over the Indian Ocean; he also mentioned the cyclonic storms in the Indian seas.

Europeans started coming to India by the end of the 15th century A.D. However, the Indians retained their supremacy in the seas around India until the mid- 18th century A.D. The Russian voyager, Afaniasing Nikitia, came to India in 1469 A.D. on an Indian ship. A good description of the Indian shipping activities of the Muslim period was presented by Marco Polo, who visited India in the 13th century A.D.

8 British Period (1757 A.D.-1947 A.D.)

The late Muslim and early British periods are the history of battles for naval supremacy among the various European nations that came to India for trade. During this period the Indian sub-continent was in great turmoil. It was only after the British established themselves in India that they contributed significantly to the knowledge of physical oceanography. The Madras Meteorological Observatory was established in 1792. James Copper published the first climatological atlas on the winds and cyclones in the Indian seas in 1801, based on the reports of the ships plying the Indian Ocean. The tidal observations in the Hooghly (at Calcutta) were started in 1767 (Wadia 1938).

The establishment of the Trigonometrical Survey and Pratt's work, with other evidence from Bongner and Maryrertuis, led to the theory of isostasy (Chapin 1952. Glass 1955. Pratt 1855. Wadia 1938).

The hydrographic surveys in the Indian coastal areas were begun in 1832 by the Indian Navy. The marine survey department of the Indian Navy was established in 1874, and RIMS Investigator I was commissioned in 1881. In 1908 Investigator I was replaced by Investigator 11 (Rao 1938). The systematic collection of physical oceanographic data started after Sewell took over as Surgeon-Naturalist (Sewell 1925, 1929, 1952). Raman (1921, 1922) made some of the earliest observations on the optical properties of the sea. Some work was also done on coastal dynamics and harbor engineering during the last quarter of the 19th century and the first quarter of the 20th century (Ash 1938). The various oceanographic ships which passed through the Indian Ocean also contributed to the knowledge of physical oceanography.

Acknowledgments

The authors thank Mr. K. Satyanarayana, editor, Indian Journal of Marine Sciences, and Dr. A. K. Malhotra, Manager of Projects, E. I. L., for their keen interest and valuable suggestions.

-- Physical Oceanography in India: An Historical Sketch, by Sucharit Markanday and P.S. Srivastava


According to John Bowman, the version of the text existed between 350 and 400 CE wherein it referenced sexagesimal fractions and trigonometric functions, but the text was a living document and revised through about the 10th-century.[18] One of the evidence for the Surya Siddhanta being a living text is the work of medieval Indian scholar Utpala, who cites and then quotes ten verses from a version of Surya Siddhanta, but these ten verses are not found in any surviving manuscripts of the text.[21] According to Kim Plofker, large portions of the more ancient Sūrya-siddhānta was incorporated into the Panca siddhantika text, and a new version of the Surya Siddhanta was likely revised and composed around 800 CE.[5] Some scholars refer to Panca siddhantika as the old Surya Siddhanta and date it to 505 CE.[22]

Vedic influence

The Surya Siddhanta is a text on astronomy and time keeping, an idea that appears much earlier as the field of Jyotisha (Vedanga) of the Vedic period. The field of Jyotisha deals with ascertaining time, particularly forecasting auspicious dates and times for Vedic rituals.[23] Vedic sacrifices state that the ancient Vedic texts describe four measures of time – savana, solar, lunar and sidereal, as well as twenty seven constellations using Taras (stars).[24] According to mathematician and classicist David Pingree, in the Hindu text Atharvaveda (~1000 BCE or older) the idea already appears of twenty eight constellations and movement of astronomical bodies.[13]

According to Pingree, the influence may have flowed the other way initially, then flowed into India after the arrival of Darius and the Achaemenid conquest of the Indus Valley about 500 BCE. The mathematics and devices for time keeping mentioned in these ancient Sanskrit texts, proposes Pingree, such as the water clock may also have thereafter arrived in India from Mesopotamia. However, Yukio Ohashi considers this proposal as incorrect,[25] suggesting instead that the Vedic timekeeping efforts, for forecasting appropriate time for rituals, must have begun much earlier and the influence may have flowed from India to Mesopotamia.[26]Ohashi states that it is incorrect to assume that the number of civil days in a year equal 365 in both Indian(Hindu) and Egyptian–Persian year.[27] Further, adds Ohashi, the Mesopotamian formula is different than Indian formula for calculating time, each can only work for their respective latitude, and either would make major errors in predicting time and calendar in the other region.[28]

Kim Plofker states that while a flow of timekeeping ideas from either side is plausible, each may have instead developed independently, because the loan-words typically seen when ideas migrate are missing on both sides as far as words for various time intervals and techniques.[29][30]

Greek influence

It is hypothesized that contacts between the ancient Indian scholarly tradition and Hellenistic Greece via the Indo-Greek Kingdom after the Indian campaign of Alexander the Great, specifically regarding the work of Hipparchus (2nd-century BCE), explain some similarities between Surya Siddhanta and Greek astronomy in the Hellenistic period. For example, Surya Siddhanta provides table of sines function which parallel the Hipparchian table of chords, though the Indian calculations are more accurate and detailed.[31] According to Alan Cromer, the knowledge exchange with the Greeks may have occurred by about 100 BCE.[32] According to Alan Cromer, the Greek influence most likely arrived in India by about 100 BCE.[32] The Indians adopted the Hipparchus system, according to Cromer, and it remained that simpler system rather than those made by Ptolemy in the 2nd century.[33]

The influence of Greek ideas on early medieval era Indian astronomical theories, particularly zodiac symbols (astrology), is broadly accepted by the Western scholars.[31] According to Pingree, the 2nd-century CE cave inscriptions of Nasik mention sun, moon and five planets in the same order as found in Babylon, but "there is no hint, however, that the Indian had learned a method of computing planetary positions in this period".[34] In the 2nd-century CE, a scholar named Yavanesvara translated a Greek astrological text, and another unknown individual translated a second Greek text into Sanskrit. Thereafter started the diffusion of Greek and Babylonian ideas on astronomy and astrology into India.[34] The other evidence of European influential on the Indian thought is Romaka Siddhanta, a title of one of the Siddhanta texts contemporary to Surya Siddhanta, a name that betrays its origin and probably was derived from a translation of a European text by Indian scholars in Ujjain, then the capital of an influential central Indian large kingdom.[34]

According to mathematician and historian of measurement John Roche, the astronomical and mathematical methods developed by Greeks related arcs to chords of spherical trigonometry.[35] The Indian mathematical astronomers, in their texts such as the Surya Siddhanta, developed other linear measures of angles, made their calculations differently, "introduced the versine, which is the difference between the radius and cosine, and discovered various trigonometrical identities".[35] For instance "where the Greeks had adopted 60 relative units for the radius, and 360 for circumference", the Indians chose 3,438 units and 60x360 for the circumference thereby calculating the "ratio of circumference to diameter [pi, π] of about 3.1414".[35] The Surya Siddhanta was one of the two books in Sanskrit that were translated into Arabic in the later half of the eighth century during the reign of Abbasid caliph Al-Mansur.[citation needed]

Importance in history of science

Astronomical calculations: Estimated time per sidereal revolution[36]

Planet / Surya Siddhanta / Ptolemy / 20th-century


Mangala (Mars) 686 days, 23 hours, 56 mins, 23.5 secs 686 days, 23 hours, 31 mins, 56.1 secs 686 days, 23 hours, 30 mins, 41.4 secs
Budha (Mercury) 87 days, 23 hours, 16 mins, 22.3 secs 87 days, 23 hours, 16 mins, 42.9 secs 87 days, 23 hours, 15 mins, 43.9 secs
Bṛhaspati (Jupiter) 4,332 days, 7 hours, 41 mins, 44.4 secs 4,332 days, 18 hours, 9 mins, 10.5 secs 4,332 days, 14 hours, 2 mins, 8.6 secs
Shukra (Venus) 224 days, 16 hours, 45 mins, 56.2 secs 224 days, 16 hours, 51 mins, 56.8 secs 224 days, 16 hours, 49 mins, 8.0 secs
Shani (Saturn) 10,765 days, 18 hours, 33 mins, 13.6 secs 10,758 days, 17 hours, 48 mins, 14.9 secs 10,759 days, 5 hours, 16 mins, 32.2 secs


The tradition of Hellenistic astronomy ended in the West after Late Antiquity. According to Cromer, the Surya Siddhanta and other Indian texts reflect the primitive state of Greek science, nevertheless played an important part in the history of science, through its translation in Arabic and stimulating the Arabic sciences.[37][38] According to a study by Dennis Duke that compares Greek models with Indian models based on the oldest Indian manuscripts such as the Surya Siddhanta with fully described models, the Greek influence on Indian astronomy is strongly likely to be pre-Ptolemaic.[14]

The Surya Siddhanta was one of the two books in Sanskrit translated into Arabic in the later half of the eighth century during the reign of Abbasid caliph Al-Mansur. According to Muzaffar Iqbal, this translation and that of Aryabhatta was of considerable influence on geographic, astronomy and related Islamic scholarship.[39]

Contents

The contents of the Surya Siddhanta is written in classical Indian poetry tradition, where complex ideas are expressed lyrically with a rhyming meter in the form of a terse shloka.[40] This method of expressing and sharing knowledge made it easier to remember, recall, transmit and preserve knowledge. However, this method also meant secondary rules of interpretation, because numbers don't have rhyming synonyms. The creative approach adopted in the Surya Siddhanta was to use symbolic language with double meanings. For example, instead of one, the text uses a word that means moon because there is one moon. To the skilled reader, the word moon means the number one.[40] The entire table of trigonometric functions, sine tables, steps to calculate complex orbits, predict eclipses and keep time are thus provided by the text in a poetic form. This cryptic approach offers greater flexibility for poetic construction.[40][41]

The Surya Siddhanta thus consists of cryptic rules in Sanskrit verse. It is a compendium of astronomy that is easier to remember, transmit and use as reference or aid for the experienced, but does not aim to offer commentary, explanation or proof.[19] The text has 14 chapters and 500 shlokas. It is one of the eighteen astronomical siddhanta (treatises), but thirteen of the eighteen are believed to be lost to history. The Surya Siddhanta text has survived since the ancient times, has been the best known and the most referred astronomical text in the Indian tradition.[7]

The fourteen chapters of the Surya Siddhanta are as follows, per the much cited Burgess translation:[4][42]

Chapters of Surya Siddhanta

Chapter # / Title / Reference


1 Of the Mean Motions of the Planets [43]
2 On the True Places of the Planets [44]
3 Of Direction, Place and Time [45]
4 Of Eclipses, and Especially of Lunar Eclipses [46]
5 Of Parallax in a Solar Eclipse [47]
6 The Projection of Eclipses [43]
7 Of Planetary Conjunctions [48]
8 Of the Asterisms [49]
9 Of Heliacal (Sun) Risings and Settings [50]
10 The Moon's Risings and Settings, Her Cusps [51]
11 On Certain Malignant Aspects of the Sun and Moon [52]
12 Cosmogony, Geography, and Dimensions of the Creation [53]
13 Of the Armillary Sphere and other Instruments [54]
14 Of the Different Modes of Reckoning Time [55]


The methods for computing time using the shadow cast by a gnomon are discussed in both Chapters 3 and 13.

Description of Time

The author of Surya Siddhanta defines time as of two types: the first which is continuous and endless, destroys all animate and inanimate objects and second is time which can be known. This latter type is further defined as having two types: the first is Murta (Measureable) and Amurta (immeasureable because it is too small or too big). The time Amurta is a time that begins with an infinitesimal portion of time (Truti) and Murta is a time that begins with 4-second time pulses called Prana as described in the table below. The further description of Amurta time is found in Puranas where as Surya Siddhanta sticks with measurable time.[56]

Time described in Surya Siddhanta[56]

Type / Surya Siddhanta Units / Description / Value in modern units of time


Amurta Truti 1/33750 seconds 29.6296 micro seconds
Murta Prana - 4 seconds
Murta Pala 6 Pranas 24 seconds
Murta Ghatika 60 Palas 24 minutes
Murta Nakshatra Ahotra 60 Ghatikas One Sidereal day


The text measures a savana day from sunrise to sunrise. Thirty of these savana days make a savana month. A solar (saura) month starts with the entrance of the sun into a zodiac sign, thus twelve months make a year.[56]

North pole star and South pole star

Surya Siddhanta asserts that there are two pole stars, one each at north and south celestial pole. Surya Siddhanta chapter 12 verse 43 description is as following:

मेरोरुभयतो मध्ये ध्रुवतारे नभ:स्थिते। निरक्षदेशसंस्थानामुभये क्षितिजाश्रिये॥१२:४३॥

This translates as "On both sides of the Meru (i.e. the north and south poles of the earth) the two polar stars are situated in the heaven at their zenith. These two stars are in the horizon of the cities situated on the equinoctial regions".[57]

The Sine table

The Surya Siddhanta provides methods of calculating the sine values in chapter 2. It divides the quadrant of a circle with radius 3438 into 24 equal segments or sines as described in the table. In modern-day terms, each of these 24 segments has angle of 3.75°.[58]

Table of Sines [59]

No. / Sine / 1st order differences / 2nd order differences / No. / Sine/ 1st order differences / 2nd order differences


0 0 - - 13 2585 154 10
1 225 225 1 14 2728 143 11
2 449 224 2 15 2859 131 12
3 671 222 3 16 2978 119 12
4 890 219 4 17 3084 106 13
5 1105 215 5 18 3177 93 13
6 1315 210 5 19 3256 79 14
7 1520 205 6 20 3321 65 14
8 1719 199 8 21 3372 51 14
9 1910 191 8 22 3409 37 14
10 2093 183 9 23 3431 22 15
11 2267 174 10 24 3438 7 15
12 2431 164 10


The 1st order difference is the value by which each successive sine increases from the previous and similarly the 2nd order difference is the increment in the 1st order difference values. Burgess says, it is remarkable to see that the 2nd order differences increase as the sines and each, in fact, is about 1/225th part of the corresponding sine.[59]

Calculation of tilt of Earth's axis (Obliquity)

The tilt of the ecliptic varies between 22.1° to 24.5° and is currently 23.5°.[60] Following the sine tables and methods of calculating the sines, Surya Siddhanta also attempts to calculate the Earth's tilt of contemporary times as described in chapter 2 and verse 28, the obliquity of the Earth's axis, the verse says "The sine of greatest declination is 1397; by this multiply any sine, and divide by radius; the arc corresponding to the result is said to be the declination".[61] The greatest declination is the inclination of the plane of the ecliptic. With radius of 3438 and sine of 1397, the corresponding angle is 23.975° or 23° 58' 30.65" which is approximated to be 24°.[62]

Planets and their characteristics

Question: How Can the Earth Be a Sphere?

Thus everywhere on the terrestrial globe (bhūgola),
people suppose their own place higher,
yet this globe (gola) is in space where there is no above nor below.

—Surya Siddhanta, XII.53
Translator: Scott L. Montgomery, Alok Kumar[7][63]


The text treats earth as a stationary globe around which sun, moon and five planets orbit. It makes no mention of Uranus, Neptune and Pluto.[64] It presents mathematical formulae to calculate the orbits, diameters, predict their future locations and cautions that the minor corrections are necessary over time to the formulae for the various astronomical bodies.[9]

The text describes some of its formulae with the use of very large numbers for "divya-yuga", stating that at the end of this yuga, Earth and all astronomical bodies return to the same starting point and the cycle of existence repeats again.[65] These very large numbers based on divya-yuga, when divided and converted into decimal numbers for each planet, give reasonably accurate sidereal periods when compared to modern era western calculations.[65]

Sidereal Periods[65]

-- / Surya Siddhanta / Modern Values


Moon 27.322 days 27.32166 days
Mercury 87.97 days 87.969 days
Mars 687 days 686.98 days
Venus 224.7 days 224.701 days
Jupiter 4,332.3 days 4,332.587 days
Saturn 10,765.77 days 10,759.202 days


Calendar

See also: Astronomical basis of the Hindu calendar

The solar part of the luni-solar Hindu calendar is based on the Surya Siddhanta.[66] The various old and new versions of Surya Siddhanta manuscripts yield the same solar calendar.[67] According to J. Gordon Melton, both the Hindu and Buddhist calendars that are in use in South and Southeast Asia are rooted in this text, but the regional calendars adapted and modified them over time.[68][69]

The Surya Siddhanta calculates the solar year to be 365 days 6 hours 12 minutes and 36.56 seconds.[70][71] On average, according to the text, the lunar month equals 27 days 7 hours 39 minutes 12.63 seconds. It states that the lunar month varies over time, and this needs to be factored in for accurate time keeping.[72]

According to Whitney, the Surya Siddhanta calculations were tolerably accurate and achieved predictive usefulness. In Chapter 1 of Surya Siddhanta, "the Hindu year is too long by nearly three minutes and a half; but the moon's revolution is right within a second; those of Mercury, Venus and Mars within a few minutes; that of Jupiter within six or seven hours; that of Saturn within six days and a half".[73]

The Surya Siddhanta was one of the two books in Sanskrit translated into Arabic during the reign of 'Abbasid caliph al-Mansur (r. 754–775 AD). According to Muzaffar Iqbal, this translation and that of Aryabhata was of considerable influence on geographic, astronomy and related Islamic scholarship.[39]

Editions

• The Súrya-Siddhánta, an antient system of Hindu astronomy ed. FitzEdward Hall and Bápú Deva Śástrin (1859).
• Translation of the Sûrya-Siddhânta: A text-book of Hindu astronomy, with notes and an appendix by Ebenezer Burgess Originally published: Journal of the American Oriental Society 6 (1860) 141–498. Commentary by Burgess is much larger than his translation.
• Surya-Siddhanta: A Text Book of Hindu Astronomy translated by Ebenezer Burgess, ed. Phanindralal Gangooly (1989/1997) with a 45-page commentary by P. C. Sengupta (1935).
• Translation of the Surya Siddhanta by Bapu Deva Sastri (1861) ISBN 3-7648-1334-2, ISBN 978-3-7648-1334-5. Only a few notes. Translation of Surya Siddhanta occupies first 100 pages; rest is a translation of the Siddhanta Siromani by Lancelot Wilkinson.

See also

• Hindu units of measurement
• Indian science and technology

References

1. Menso Folkerts, Craig G. Fraser, Jeremy John Gray, John L. Berggren, Wilbur R. Knorr (2017), Mathematics, Encyclopaedia Britannica, Quote: "(...) its Hindu inventors as discoverers of things more ingenious than those of the Greeks. Earlier, in the late 4th or early 5th century, the anonymous Hindu author of an astronomical handbook, the Surya Siddhanta, had tabulated the sine function (...)"
2. John Bowman (2000). Columbia Chronologies of Asian History and Culture. Columbia University Press. p. 596. ISBN 978-0-231-50004-3., Quote: "c. 350-400: The Surya Siddhanta, an Indian work on astronomy, now uses sexagesimal fractions. It includes references to trigonometric functions. The work is revised during succeeding centuries, taking its final form in the tenth century."
3. Gangooly, Phanindralal, ed. (1935) [1st ed. 1860]. Translation of the Surya-Siddhanta, A Text-Book of Hindu Astronomy; With notes and an appendix. Translated by Burgess, Rev. Ebenezer. University of Calcutta.
4. Markanday, Sucharit; Srivastava, P. S. (1980). "Physical Oceanography in India: An Historical Sketch". Oceanography: The Past. Springer New York. pp. 551–561. doi:10.1007/978-1-4613-8090-0_50. ISBN 978-1-4613-8092-4., Quote: "According to Surya Siddhanta the earth is a sphere."
5. Plofker, pp. 71–72.
6. Richard L. Thompson (2007). The Cosmology of the Bhagavata Purana. Motilal Banarsidass. pp. 16, 76–77, 285–294. ISBN 978-81-208-1919-1.
7. Scott L. Montgomery; Alok Kumar (2015). A History of Science in World Cultures: Voices of Knowledge. Routledge. pp. 104–105. ISBN 978-1-317-43906-6.
8. Thompson, Richard L. (2007). The Cosmology of the Bhāgavata Purāṇa: Mysteries of the Sacred Universe. Motilal Banarsidass. pp. 15–18. ISBN 978-81-208-1919-1.
9. Burgess, Ebenezer (1935). Translation of the Surya Siddhanta. University of Calcutta.
10. Gangooly 1935, p. ix (Introduction): Calculated date of 2163102 B.C. for "the end of the Golden Age (Krta yuga)" mentioned in Surya Siddhanta 1.57.
11. Murphy, T W (1 July 2013). "Lunar laser ranging: the millimeter challenge" (PDF). Reports on Progress in Physics. 76 (7): 2. arXiv:1309.6294. Bibcode:2013RPPh...76g6901M. doi:10.1088/0034-4885/76/7/076901. PMID 23764926. S2CID 15744316.
12. Brian Evans (2014). The Development of Mathematics Throughout the Centuries: A Brief History in a Cultural Context. Wiley. p. 60. ISBN 978-1-118-85397-9.
13. David Pingree (1963), Astronomy and Astrology in India and Iran, Isis, Volume 54, Part 2, No. 176, pages 229-235 with footnotes
14. Duke, Dennis (2005). "The Equant in India: The Mathematical Basis of Ancient Indian Planetary Models". Archive for History of Exact Sciences. Springer Nature. 59 (6): 563–576. Bibcode:2005AHES...59..563D. doi:10.1007/s00407-005-0096-y. S2CID 120416134.
15. Pingree, David (1971). "On the Greek Origin of the Indian Planetary Model Employing a Double Epicycle". Journal for the History of Astronomy. SAGE Publications. 2 (2): 80–85. Bibcode:1971JHA.....2...80P. doi:10.1177/002182867100200202. S2CID 118053453.
16. Roshen Dalal (2010). Hinduism: An Alphabetical Guide. Penguin Books. p. 89. ISBN 978-0-14-341421-6., Quote: "The solar calendar is based on the Surya Siddhanta, a text of around 400 CE."
17. Canavas, Constantin (2014), "Geography and Cartography", The Oxford Encyclopedia of Philosophy, Science, and Technology in Islam, Oxford University Press, doi:10.1093/acref:oiso/9780199812578.001.0001, ISBN 978-0-19-981257-8, retrieved 2020-07-19
18. John Bowman (2005). Columbia Chronologies of Asian History and Culture. Columbia University Press. p. 596. ISBN 978-0-231-50004-3., Quote: "c. 350-400: The Surya Siddhanta, an Indian work on astronomy, now uses sexagesimal fractions. It includes references to trigonometric functions. The work is revised during succeeding centuries, taking its final form in the tenth century."
19. Carl B. Boyer; Uta C. Merzbach (2011). A History of Mathematics. John Wiley & Sons. p. 188. ISBN 978-0-470-63056-3.
20. Markanday, Sucharit; Srivastava, P. S. (1980). "Physical Oceanography in India: An Historical Sketch". Oceanography: The Past. Springer New York. pp. 551–561. doi:10.1007/978-1-4613-8090-0_50. ISBN 978-1-4613-8092-4., Quote: "According to Surya Siddhanta the earth is a sphere."
21. Romesh Chunder Dutt, A History of Civilization in Ancient India, Based on Sanscrit Literature, vol. 3, ISBN 0-543-92939-6 p. 208.
22. George Abraham (2008). Helaine Selin (ed.). Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Springer Science. pp. 1035–1037, 1806, 1937–1938. ISBN 978-1-4020-4559-2.
23. James Lochtefeld (2002), "Jyotisha" in The Illustrated Encyclopedia of Hinduism, Vol. 1: A–M, Rosen Publishing, ISBN 0-8239-2287-1, pages 326–327
24. Friedrich Max Müller (1862). On Ancient Hindu Astronomy and Chronology. Oxford University Press. pp. 37–60 with footnotes. Bibcode:1862ahac.book.....M.
25. Yukio Ohashi 1999, pp. 719–721.
26. Yukio Ohashi 1993, pp. 185–251.
27. Yukio Ohashi 1999, pp. 719–720.
28. Yukio Ohashi (2013). S.M. Ansari (ed.). History of Oriental Astronomy. Springer Science. pp. 75–82. ISBN 978-94-015-9862-0.
29. Plofker 2009, pp. 41–42.
30. Sarma, Nataraja (2000). "Diffusion of astronomy in the ancient world". Endeavour. Elsevier. 24 (4): 157–164. doi:10.1016/s0160-9327(00)01327-2. PMID 11196987.
31. "There are many evident indications of a direct contact of Hindu astronomy with Hellenistic tradition, e.g. the use of epicycles or the use of tables of chords which were transformed by the Hindus into tables of sines. The same mixture of elliptic arcs and declination circles is found with Hipparchus and in the early Siddhantas (note: [...] In the Surya Siddhanta, the zodiacal signs are used in similar fashion to denote arcs on any great circle." Otto Neugebauer, The Exact Sciences in Antiquity, vol. 9 of Acta historica scientiarum naturalium et medicinalium, Courier Dover Publications, 1969, p. 186.
32. "The table must be of Greek origin, though written in the Indian number system and in Indian units. It was probably calculated around 100 B.C. by an Indian mathematicisn familiar with the work of Hipparchus." Alan Cromer, Uncommon Sense : The Heretical Nature of Science, Oxford University Press, 1993, p. 111.
33. "The epicyclic model in the Siddnahta Surya is much simpler than Ptolemy's and supports the hypothesis that the Indians learned the original system of Hipparchus when they had contact with the West." Alan Cromer, Uncommon Sense : The Heretical Nature of Science, Oxford University Press, 1993, p. 111.
34. David Pingree (1963), Astronomy and Astrology in India and Iran, Isis, Volume 54, Part 2, No. 176, pages 233-238 with footnotes
35. John J. Roche (1998). The Mathematics of Measurement: A Critical History. Springer Science. p. 48. ISBN 978-0-387-91581-4.
36. Ebenezer Burgess (1989). P Ganguly, P Sengupta (ed.). Sûrya-Siddhânta: A Text-book of Hindu Astronomy. Motilal Banarsidass (Reprint), Original: Yale University Press, American Oriental Society. pp. 26–27. ISBN 978-81-208-0612-2.
37. "Surya Siddhanta the basis of space studies, says Governor". The Hindu. Special Correspondent. 2020-01-24. ISSN 0971-751X. Retrieved 2021-09-02.
38. Alan Cromer (1993), Uncommon Sense : The Heretical Nature of Science, Oxford University Press, pp. 111-112.
39. Muzaffar Iqbal (2007). Science and Islam. Greenwood Publishing. pp. 36–38. ISBN 978-0-313-33576-1.
40. Arthur Gittleman (1975). History of mathematics. Merrill. pp. 104–105. ISBN 978-0-675-08784-1.
41. Raymond Mercier (2004). Studies on the Transmission of Medieval Mathematical Astronomy. Ashgate. p. 53. ISBN 978-0-86078-949-9.
42. Enrique A. González-Velasco (2011). Journey through Mathematics: Creative Episodes in Its History. Springer Science. pp. 27–28 footnote 24. ISBN 978-0-387-92154-9.
43. P Gangooly (1935, Editor), Translator: Ebenezzer Burgess, Translation of Surya Siddhanta: A Textbook of Hindu Astronomy, University of Calcutta, page 1
44. P Gangooly (1935, Editor), Translator: Ebenezzer Burgess, Translation of Surya Siddhanta: A Textbook of Hindu Astronomy, University of Calcutta, page 54
45. P Gangooly (1935, Editor), Translator: Ebenezzer Burgess, Translation of Surya Siddhanta: A Textbook of Hindu Astronomy, University of Calcutta, page 108
46. P Gangooly (1935, Editor), Translator: Ebenezzer Burgess, Translation of Surya Siddhanta: A Textbook of Hindu Astronomy, University of Calcutta, page 143
47. P Gangooly (1935, Editor), Translator: Ebenezzer Burgess, Translation of Surya Siddhanta: A Textbook of Hindu Astronomy, University of Calcutta, page 161
48. P Gangooly (1935, Editor), Translator: Ebenezzer Burgess, Translation of Surya Siddhanta: A Textbook of Hindu Astronomy, University of Calcutta, page 187
49. P Gangooly (1935, Editor), Translator: Ebenezzer Burgess, Translation of Surya Siddhanta: A Textbook of Hindu Astronomy, University of Calcutta, page 202
50. P Gangooly (1935, Editor), Translator: Ebenezzer Burgess, Translation of Surya Siddhanta: A Textbook of Hindu Astronomy, University of Calcutta, page 255
51. P Gangooly (1935, Editor), Translator: Ebenezzer Burgess, Translation of Surya Siddhanta: A Textbook of Hindu Astronomy, University of Calcutta, page 262
52. P Gangooly (1935, Editor), Translator: Ebenezzer Burgess, Translation of Surya Siddhanta: A Textbook of Hindu Astronomy, University of Calcutta, page 273
53. P Gangooly (1935, Editor), Translator: Ebenezzer Burgess, Translation of Surya Siddhanta: A Textbook of Hindu Astronomy, University of Calcutta, page 281
54. P Gangooly (1935, Editor), Translator: Ebenezzer Burgess, Translation of Surya Siddhanta: A Textbook of Hindu Astronomy, University of Calcutta, page 298
55. P Gangooly (1935, Editor), Translator: Ebenezzer Burgess, Translation of Surya Siddhanta: A Textbook of Hindu Astronomy, University of Calcutta, page 310
56. Deva Shastri, Pandit Bapu. Translation of the Surya Siddhanta. pp. 2–3.
57. Deva Sastri, Pundit Bapu (1861). The Translation of Surya Siddhanta (PDF). Calcutta: Baptist Mission Press. pp. 80–81.
58. Deva Shastri, Pundit Bapu (1861). Translation of the Surya Siddhanta. pp. 15–16.
59. Burgess, Rev. Ebenezer (1860). Translation of the Surya Siddhanta. p. 115.
60. "Milutin Milankovitch". earthobservatory.nasa.gov. 2000-03-24. Retrieved 2020-08-15.
61. Ebenezer Burgess (1989). P Ganguly, P Sengupta (ed.). Sûrya-Siddhânta: A Text-book of Hindu Astronomy. Motilal Banarsidass (Reprint), Original: Yale University Press, American Oriental Society. p. 65. ISBN 978-81-208-0612-2.
62. Burgess, Rev. Ebenezer (1860). Translation of the Surya Siddhanta. p. 118.
63. P Gangooly (1935, Editor), Translator: Ebenezzer Burgess, Translation of Surya Siddhanta: A Textbook of Hindu Astronomy, University of Calcutta, page 289 verse 53
64. Richard L. Thompson (2004). Vedic Cosmography and Astronomy. Motilal Banarsidass. pp. 10–11. ISBN 978-81-208-1954-2.
65. Richard L. Thompson (2004). Vedic Cosmography and Astronomy. Motilal Banarsidass. pp. 12–14 with Table 3. ISBN 978-81-208-1954-2.
66. Roshen Dalal (2010). The Religions of India: A Concise Guide to Nine Major Faiths. Penguin Books. p. 145. ISBN 978-0-14-341517-6.
67. Robert Sewell; Śaṅkara Bālakr̥shṇa Dīkshita (1896). The Indian Calendar. S. Sonnenschein & Company. pp. 53–54.
68. J. Gordon Melton (2011). Religious Celebrations: An Encyclopedia of Holidays, Festivals, Solemn Observances, and Spiritual Commemorations. ABC-CLIO. pp. 161–162. ISBN 978-1-59884-205-0.
69. Yukio Ohashi (2008). Helaine Selin (ed.). Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Springer Science. pp. 354–356. ISBN 978-1-4020-4559-2.
70. Lionel D. Barnett (1999). Antiquities of India. Atlantic. p. 193. ISBN 978-81-7156-442-2.
71. V. Lakshmikantham; S. Leela; J. Vasundhara Devi (2005). The Origin and History of Mathematics. Cambridge Scientific Publishers. pp. 41–42. ISBN 978-1-904868-47-7.
72. Robert Sewell; Śaṅkara Bālakr̥shṇa Dīkshita (1995). The Indian Calendar. Motilal Banarsidass. pp. 21 with footnote, cxii–cxv. ISBN 9788120812079.
73. William Dwight Whitney (1874). Oriental and Linguistic Studies. Scribner, Armstrong. p. 368.

Bibliography

• Pingree, David (1973). "The Mesopotamian Origin of Early Indian Mathematical Astronomy". Journal for the History of Astronomy. SAGE. 4 (1): 1–12. Bibcode:1973JHA.....4....1P. doi:10.1177/002182867300400102. S2CID 125228353.
• Plofker, Kim (2009). Mathematics in India. Princeton University Press. ISBN 978-0-691-12067-6.
• Pingree, David (1981). Jyotihśāstra : Astral and Mathematical Literature. Otto Harrassowitz. ISBN 978-3447021654.
• K. V. Sarma (1997), "Suryasiddhanta", Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures edited by Helaine Selin, Springer, ISBN 978-0-7923-4066-9
• Yukio Ôhashi (1999). "The Legends of Vasiṣṭha – A Note on the Vedāṅga Astronomy". In Johannes Andersen (ed.). Highlights of Astronomy, Volume 11B. Springer Science. ISBN 978-0-7923-5556-4.
• Yukio Ôhashi (1993). "Development of Astronomical Observations in Vedic and post-Vedic India". Indian Journal of History of Science. 28 (3).
• Maurice Winternitz (1963). History of Indian Literature, Volume 1. Motilal Banarsidass. ISBN 978-81-208-0056-4.

Further reading

• Victor J. Katz. A History of Mathematics: An Introduction, 1998.

External links

Sanskrit Wikisource has original text related to this article:
Surya Siddhanta (सूर्यसिद्धान्त): Sanskrit text

• Surya Siddhantha Planetary Model
• Surya Siddhanta Sanskrit text in Devanagari
• Remarks on the Astronomy of the Brahmins, John Playfair (Archive)
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Simon de la Loubère
by Wikipedia
Accessed: 5/15/22

Simon de la Loubère (21 April 1642 – 26 March 1729)[1] was a French diplomat to Siam (Thailand), writer, mathematician and poet. He is credited with bringing back a document which introduced Europe to Indian astronomy, the "Siamese method" of making magic squares, as well as one of the earliest description of parachutes.

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The Siamese method, or De la Loubère method, is a simple method to construct any size of n-odd magic squares (i.e. number squares in which the sums of all rows, columns and diagonals are identical). The method was brought to France in 1688 by the French mathematician and diplomat Simon de la Loubère, as he was returning from his 1687 embassy to the kingdom of Siam. The Siamese method makes the creation of magic squares straightforward.

De la Loubère published his findings in his book A new historical relation of the kingdom of Siam (Du Royaume de Siam, 1693), under the chapter entitled The problem of the magical square according to the Indians. Although the method is generally qualified as "Siamese", which refers to de la Loubère's travel to the country of Siam, de la Loubère himself learnt it from a Frenchman named M.Vincent (a doctor, who had first travelled to Persia and then to Siam, and was returning to France with the de la Loubère embassy), who himself had learnt it in the city of Surat in India...

The method

The method was surprising in its effectiveness and simplicity...

First, an arithmetic progression has to be chosen (such as the simple progression 1,2,3,4,5,6,7,8,9 for a square with three rows and columns (the Lo Shu square)).

Then, starting from the central box of the first row with the number 1 (or the first number of any arithmetic progression), the fundamental movement for filling the boxes is diagonally up and right (↗), one step at a time. When a move would leave the square, it is wrapped around to the last row or first column, respectively.

If a filled box is encountered, one moves vertically down one box (↓) instead, then continuing as before.

Order-3 magic squares

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Order-5 magic squares

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Other sizes

Any n-odd square ("odd-order square") can be thus built into a magic square. The Siamese method does not work however for n-even squares ("even-order squares", such as 2 rows/ 2 columns, 4 rows/ 4 columns etc...).

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Other values

Any sequence of numbers can be used, provided they form an arithmetic progression (i.e. the difference of any two successive members of the sequence is a constant). Also, any starting number is possible. For example the following sequence can be used to form an order 3 magic square according to the Siamese method (9 boxes): 5, 10, 15, 20, 25, 30, 35, 40, 45 (the magic sum gives 75, for all rows, columns and diagonals).

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Other starting points

It is possible not to start the arithmetic progression from the middle of the top row, but then only the row and column sums will be identical and result in a magic sum, whereas the diagonal sums will differ. The result will thus not be a true magic square:

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Rotations and reflections

Numerous other magic squares can be deduced from the above by simple rotations and reflections.

Variations

A slightly more complicated variation of this method exists in which the first number is placed in the box just above the center box. The fundamental movement for filling the boxes remains up and right (↗), one step at a time. However, if a filled box is encountered, one moves vertically up two boxes instead, then continuing as before.

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Numerous variants can be obtained by simple rotations and reflections. The next square is equivalent to the above (a simple reflexion): the first number is placed in the box just below the center box. The fundamental movement for filling the boxes then becomes diagonally down and right (↘), one step at a time. If a filled box is encountered, one moves vertically down two boxes instead, then continuing as before.[6]

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These variations, although not quite as simple as the basic Siamese method, are equivalent to the methods developed by earlier Arab and European scholars, such as Manuel Moschopoulos (1315), Johann Faulhaber (1580–1635) and Claude Gaspard Bachet de Méziriac (1581–1638), and allowed to create magic squares similar to theirs.

-- Siamese method, by Wikipedia

Chinese geomantic figures, the Pu-Kwa (Par-k'a) and the Me- wa, enter largely into the calculations of the Lama astrologer, and these are usually figured on the belly of a spread tortoise, as in the above figure, whose paws sometimes grasp a pole surmounted by or transfixing a frog.

The Pu-Kwa or Par-k'a symbolize the great productive and antagonistic powers of nature, as summarized in a most interesting manner by Dr. Legge.
The first character, pu, is the Chinese symbol for divining by the lines produced through a certain process on the back of a tortoise-shell. It consists of two lines,10 which may possibly, says Dr. Legge, have been intended to represent the lines appearing on the shell. The second character, Kwa, was the symbol for divining by means of the eight famous trigrams of Fu-hsi, themselves called "the eight Kwa." They are not characters, but lineal figures composed of whole and divided lines, on which was built up the mysterious book called the Yi-Kin, or "Book of Changes," with its sixty-four hexagrams. The eight trigrams are here shown: —

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The whole lines in the figures are styled "the strong," and the divided lines "the weak." The two represent the two forms of the subtle matter, whether eternal or created is not said, of which all things are composed. Under one form the matter is active and is called Yang; under the other it is passive, and is called Yin. Whatever is strong and active is of the Yang nature; whatever is weak and passive is of the Yin. Heaven and earth, sun and moon, light and darkness, male and female, ruler and minister, are examples of these antinomies.

The aggregate of them makes up the totality of being, and the Yi is supposed to give in its diagram a complete picture of the phenomena of that totality. It does not give us a sexual system of nature, though of course the antinomy of sex is in it; but the lines on which it is constructed embrace other antinomies as well. Authority and power on one side; inferiority and docility on the other.

Further, the hidden operation in and through which the change takes place in nature is said to be that of the Kwei shan,11 usually meaning "spirits," but here held to be technical. "Shan is Yang, and indicates the process of expanding; Kwei is yin, and indicates the process of contracting." The fashion of the world is continually being altered. We have action and reaction, flux and reflux, and these changes are indicated in the diagrams, which are worked in divination by manipulating a fixed number of stalks of a plant called shih (Ptarmica Sibirica), and, indeed, the form of the trigrams themselves is suggestive of divination by twigs.

The usual geomantic arrangement of the Par-k'a is given in figure. Individually they are named Heaven, Earth, Fire, Thunder, Mountains, Celestial Water, Terrestrial Water, though the fourth and eighth are sometimes called Iron and Tree. And Mountain, Iron, and Water are said to be sons of the Earth and Heaven, while Wind, Fire, and Tree are their daughters.

It is remarkable, however, that while the Chinese use only the hexagrams for divination purposes, the Tibetans use only the trigrams in this way.

The Nine Mewa are arranged in the form of a quadratic square or circle, and the figures usually, as in a magic square, so disposed as to give the same total in all directions.

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The spirits of the seasons also powerfully influence the luckiness or unluckiness of the days. It is necessary to know which spirit has arrived at the particular place and time when an event has happened or an undertaking is entertained. And the very frequent and complicated migrations of these aerial spirits, good and bad, can only be ascertained by the Lamas. The most malignant of these evil spirits are a black dog, a monster with a dragon-tail, a man on horseback, and the fabulous Phoenix; and the seasons are specially assigned to these in the order of spring, summer, autumn, and winter respectively.

The almanac which the Lamaist astrologer uses, gives for each day the six presiding influences. Thus the page of the almanack for the first day of the third month of 1891 (Iron-horse) gives: —

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And the general record for the particular month is: This month's star is moderate and the celestial Mansion is the sheep. Nidana, Avidya. Element is mid-summer, and named Great Fire-Horse. It is time for plants budding and marshes, thunder and birds. The empty vase is in the east (... do not go E.). On the 15th day the Teacher taught the Kalacakra; it is a holiday. Thursday, Sunday, and Tuesday are good. Friday, Saturday, Monday, and Wednesday are bad. The "Yas" road (i.e., the road on which cake and the devil's image are to be thrown) is N.W. The "Zin-p'un" (a kind of genius loci) in the Ox and Sheep days at dawn passes from W. to E. (... at that time be careful).

-- The Buddhism of Tibet, or Lamaism With Its Mystic Cults, Symbolism and Mythology, and in its Relation to Indian Buddhism, by Laurence Austine Waddell, M.B., F.L.S., F.R.G.S., Member of the Royal Asiatic Society, Anthropological Institute, etc., Surgeon-Major H.M. Bengal Army, 1895

Mission to Siam

Simon de la Loubère led an embassy to Siam (modern Thailand) in 1687 (the "La Loubère-Céberet mission").[2]: 2  The embassy, composed of five warships, arrived in Bangkok in October 1687 and was received by Ok-khun Chamnan. La Loubère returned to France on board the Gaillard on 3 January 1688, accompanied by the Jesuit Guy Tachard, and a Siamese embassy led by Ok-khun Chamnan.[2]: 3 

Upon his return, La Loubère wrote a description of his travels, as had been requested by Louis XIV, published under the title Du Royaume de Siam: "It was by the orders, which I had the honours to receive from the King upon leaving for my voyage to Siam, that I observed in that country, as exactly as possible, all that appeared to be the most singular.[3]

Loubère also brought back with him an obscure manuscript relating to the astronomical traditions of Siam, which he passed on to the famous French-Italian astronomer Jean Dominique Cassini. The Siamese Manuscript, as it is now called, intrigued Cassini enough so that he spent a couple years deciphering its cryptic contents, determining on the way that the document originated in India.[4] His explication of the manuscript appeared in La Loubere's book on the Kingdom of Siam in 1691,[5]: 64–65  which laid the first foundation of European scholarship on Indian astronomy.[6]

French career

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A description of the Siamese method for creating magic squares, in the English translation of Simon de la Loubère's book

La Loubère was elected member of the Académie française (1693–1729), where he received Seat 16, following the 1691 publication of his book Du Royaume de Siam.[2]: 59 

La Loubère was a friend of the German scientist Gottfried Leibniz, and once wrote that he had "no greater joy than (to discuss) philosophy and mathematics" with him (22 January 1681 correspondence).[3]

Magic square

La Loubère brought to France from his Siamese travels a very simple method for creating n-odd magic squares, known as the "Siamese method" or the "La Loubère method",[7][8][9] which apparently was initially brought from Surat, India, by another Frenchman by the surname of Vincent, who was sailing on the return ship with La Loubère.[5]: 238 

Siamese parachute

La Loubère is also famous for making one of the earliest account of a parachute following his embassy to Siam.[???] He reported in his 1691 book that a man would jump from a high place with two large umbrellas to entertain the king of Siam, landing into trees, rooftops, and sometimes rivers.[!!!][5]: 47–48 [10]

Works

• Du Royaume de Siam, 1691 Full text in French or English translation
• Traité de l'origine des jeux floraux de Toulouse (1715)
• De la Résolution des équations, ou de l'Extraction de leurs racines, 1732 Full text

See also

• France-Thailand relations

References

1. BNF 12101988k
2. Tachard, Guy (1999). Smithies, Michael (ed.). A Siamese Embassy Lost in Africa, 1686: The Odyssey of Ok-khun Chamnan. Bangkok: Silkworm Books. ISBN 9747100959. Retrieved 15 October 2017.
3. de la Loubere, Simon (2003). Ames, Glenn J; Love, Ronald S (eds.). Distant Lands and Diverse Cultures: The French Experience in Asia, 1600-1700. Westport CT: Praeger. ISBN 0313308640. Retrieved 15 October 2017.
4. Burgess, James (1893). "Notes on Hindu Astronomy and the History of Our Knowledge of It". Journal of the Royal Asiatic Society of Great Britain & Ireland: 722–723.
5. de La Loubère, Simon (1693). A New Historical Relation of the Kingdom of Siam. Translated by A.P. Retrieved 16 October 2017.
6. Hands, Joseph (1879). New Views of Matter, Life, Motion, and Resistance. E.W. Allen. p. 466.
7. Eves, Howard W.; Johnson, Phillip E. (1972). Mathematical Circles Squared. Boston: Prindle, Weber & Schmidt. pp. 22. ISBN 0-87150-154-6. OCLC 448077.
8. Weisstein, Eric W. (12 December 2002). CRC Concise Encyclopedia of Mathematics. CRC Press. p. 1839. ISBN 978-1-4200-3522-3.
9. Pickover, Clifford A. (2002). The Zen of Magic Squares, Circles, and Stars: An Exhibition of Surprising Structures Across Dimensions. Princeton University Press. p. 38. ISBN 978-0-691-07041-4.
10. Bull, Stephen (2004). Encyclopedia of Military Technology and Innovation. Greenwood Publishing Group. p. 200. ISBN 978-1-57356-557-8.
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CHAP. XI. What the Siameses do know of the Mathematics. Excerpt from "A New Historical Relation of the Kingdom of Siam"
Tome II
by Monsieur De La Loubere
Envoy Extraordinary from the French King, to the King of Siam, in the years 1687 and 1688. Wherein a full and curious Account is given of the Chinese Way of Arithmetick, and Mathematick Learning. In Two Tomes, Illustrated with Sculptures. Done out of French, by A.P. Gen. R.S.S.
1693



Cassini is also credited with introducing Indian Astronomy to Europe. In 1688, the French envoy to Siam (Thailand), Simon de la Loubère, returned to Paris with an obscure manuscript relating to the astronomical traditions of that country, along with a French translation. The Siamese Manuscript, as it is now called, somehow fell into Cassini's hands. He was intrigued enough by it to spend considerable time and effort deciphering its cryptic contents, also determining on the way that the document originated in India. His explication of the manuscript appeared in La Loubère's book on the Kingdom of Siam in 1691.

-- Giovanni Domenico Cassini, by Wikipedia


Tome II, Pg. 64-67

CHAP. XI. What the Siameses do know of the Mathematics.

The great Heat of Siam, repugnant to all application of Mind.

The quick and clear Imagination of the Siamese should seem more proper for the Mathematics, than the other Studies, if it did not soon weary them; but they cannot follow a long thread of Ratiocinations, of which they do foresee neither the end nor the profit. And it must be confessed for their Excuse, that all application of Mind is so laborious in a Climate so hot as theirs, that the very Europeans could hardly study there, what desire soever they might have thereunto.

The Ignorance of the Siameses touching the principal parts of Mathematics.

The Siameses do therefore know nothing in Geometry or Mechanics, because they can be absolutely without them: And Astronomy concerns them only as far as they conceive it may be assistant to Divination. They know only some Practical part thereof, the Reasons of which they disdain to penetrate; but of which they make use in the Horoscopes of particular Persons, and in the Composition of their almanac, which, as it were, is a general Horoscope.

Of the Siamese Calendar, and why they have two Epocha's.

It appears that they have twice caused their Calendar to be reformed by able Astronomers, who, to supply the Astronomical Tables, have taken two arbitrary Epocha's, but yet remarkable for some rare Conjunction of the Planets. Having once established certain Numbers upon these Observations, they by the means of several Additions, Subtractions, Multiplications and Divisions, have given for the following Years the secret of finding the place of the Planets, almost as we find the Epact of every Year, by adding eleven to the Epact of the Year foregoing.

The most Modern is evidently Arbitrary.

The most Modern of the two Siamese Epocha's, is referred to the Year of Grace 638. I gave to Mr. Cassini, Director of the Observatory at Paris, the Siamese Method of finding the place of the Sun and Moon by a Calculation, the ground of which is taken from this Epocha. And the singular Merit which Mr. Cassini has had of unfolding a thing so difficult, and penetrating the Reasons thereof, will doubtless be admired by all the Learned. Now as this Epocha is visibly the ground only of an Astronomical Calculation, and has been chosen rather than another, only because it appear'd more commodious to Calculation than another, it is evident that we must thence conclude nothing which respects the Siamese History; nor imagine that the Year 638, has been more Famous amongst them than another for any Event, from which they have thought fit to begin to compute their Years, as we compute ours, from the Birth of the Saviour of the World.

The most Ancient also appears Arbitrary.

By the same Reason I am persuaded, that their most Ancient Epocha, from which in this Year 1689, they compute 2233 Years, has not been remarkable at Siam for any thing worthy of Memory, and that it proves not that the Kingdom of Siam is of that Antiquity. It is purely Astronomical, and serves as a Foundation to another way of calculating the places of the Planets, which they have relinquished for that new Method which I have given to Mr. Cassini. Some person may discover to them the Mistakes, where in process of time this ancient Method must fall; as in time we have found out the Errors of the Reformation of the Calendar made by the Order of Julius Cesar.

And is not taken from the death of Sommona Codom [Buddha]

The Historical Memoirs of the Siameses reascending, as I have remark'd in the beginning, to 900 Years, or thereabouts, it is not necessary to seek the Foundation of their Kingdom in the 545th Year before the birth of Jesus Christ; nor to suppose that from this time they have enjoyed a Succession of Kings, which they themselves are absolutely ignorant of. And tho' the Siameses do vulgarly report, that this first Epocha, from which they compute, as I have said, 2233 Years is that of the death of their Sommona-Codom [Buddha]; and altho' it refers almost to the time in which Pythagoras liv'd, who has sowed in the West the Doctrine of the Metempsychosis, which he had learnt from the Egyptians, yet it is certain that the Siameses have not any Memoirs of the time in which their Sommona Codom [Buddha] might have lived: And I cannot persuade my self that their Sommona-Codom [Buddha] could be Pythagoras, who was not in the East, not that their ancient Epocha is other than Astronomical and Arbitrary, no more than their Modern Epocha.

Man, -- ennemi de Sommona-Codom. Les Siamois le representent comme une espece de monstre, avec une tete herissee de serpents, un visage fort large et des dents horriblement grandes.

Google translate: Man, -- enemy of Sommona-Codom. The Siamese represent him as a species of monster, with a head bristling with snakes, a very large face and horribly large teeth.
 
-- Dictionnaire Infernal, by Jacques Collin de Plancy, 1818

Butta, place par les Indiens au rang des Dieux. -- Ne d'une vierge par le cote. Memoires, Vol. XXVI, 771. Appele aussi Puti. -- Sommona-condom chez les Siamois, que M. De Guignes interprete le Semaneen-condom. Ibid. 774. Les Arabes l'appellent Boudasp ou Boudass. -- Les Persans, Schekmouniberkari. -- Les Chinois, Tche-kia ou Chekiameouni, Foteou ou Foto; mais son nom le mieux connu est Fo ou Foto. -- Les Siamois le nomment Prah-poadi-tchaou, Sammana-khutama & Phutta. -- Hyde le derive du persan Butt. -- Leibnitz veut que ce foit le Wodin du nord. -- Chez les Indiens Butta signifie Mercure, 776. Les fables des Indiens, & le peu de detail des historiens, empechent de fixer le temps de sa naissance. -- Masoudi le place fous des regnes inconnus. -- Les Arabes le font naitre dans le Kaschmir, d'ou il passe dans les Indes & fonde le Sabeisme. -- Les Chinois font naitre Fo aussi dans le Kaschmir. Mem. Volume XXVI, 777 & 778. L'accord des Chinois & des Arabes semble exclure le sentiment de ceux qui le font naitre a Siam ou a Ceilan. -- Deux epoques de sa naissance chez les Chinois, dont la difference est de trois cents quarante-quatre ans. Ibidiem, 778 & 779. M. De Guignes, pour les accorder, etablit que le system de cette religion etant fonde sur la metempsycose, ils auront adopte les fondateurs des autres religions, comme de nouvelles apparitions de leur Dieu. -- Les Bonzes trouvent, en consequence, sept Fo, 779. Soutiennent que Vischnou a reparu fous le nom de Krischtenou, & y joignent toutes les circonstances qui indigent J.C. 780. M. De Guignes pense qu'ils ont adopte de meme Zoroastre, & fait voir que l'epoque de Fo, la moins ancienne, quadre avec le temps ou a paru Zoroastre, 780, 781 & 785. Que les Indiens ont connu Zoroastre, 783. Que Darius, roi de Perse, transporte un pyree dans le Kaschmir, & oblige les Rois qui lui etoient foumis a y veniradorer un cypres, 784. D'ou ceux qui venoient au pyree auront pu croire que Zoroastre etoit une nouvelle apparition de Butta. -- Ils conservent des traces du manisine, dans le respect qu'ils portent au feu & a l'arbre casta. -- M. De Guignes conclut que la vraie epoque de Fo fera la plus ancienne des deux, & soutient que ce qu'on troube de Christianisme dans la religion des Indes, provient du commerce des Occidentaux; car on y troube des mots Romains consacres a la religion. -- Naissance de Fo. -- Conformite de ce qu'en disent les historiens Chinois & S. Jerome, 785. Fables que debitent les Chinois a ce sujet. -- Ses differentes renaissances. -- Est le meme que Vischnou, dont la dixieme apparition est sous la figure de Boudha. -- Son mariage. -- A un fils. -- Se retire dans les deserts avec cinque Philosophes. -- Sa mort. -- Devient Dieu, 786. Enseigne a sa mort que tout ce qu'il avoit dit etoit figure. -- Que son veritable sentiment etoit que tout fortoit du neant & y retournoit. -- Son principe favori, suivant les Missionaires, est l'atheisme. -- Ses dernieres paroles produisent deux sectes, l'une suit la doctrine exterieure, l'autre la doctrine interieure. -- Les sectateurs de la doctrine exterieure connus sous les noms de Brahmes, Bonzes, Lamas, Talapoins. -- Leurs principes. -- Nombre de leurs divinites. -- Leur veneration pour l'eau du Gange. -- Leur ame se perfectionne a force de transmigrations, jusqu'a ce qu'elle occupe le corps d'un Samaneen. Memoires, Vol. XXVI, 787 & 788.

Google translate: Butta, placed by the Indians in the rank of the Gods. -- Not of a virgin by the side. Memoirs, Vol. XXVI, 771. Also called Puti. -- Sommona-condom among the Siamese, which M. De Guignes interprets as Semaneen-condom. Ibid. 774. The Arabs call it Boudasp or Boudass. -- The Persians, Schekmuniberkari. -- The Chinese, Tche-kia or Chekiameouni, Foteou or Foto; but its better known name is Fo or Foto. -- The Siamese call it Prah-poadi-tchaou, Sammana-khutama & Phutta. -- Hyde the derivative of the Persian Butt. -- Leibnitz wants it to be the Wodin of the north. -- Among the Indians Butta means Mercury, 776. The fables of the Indians, and the lack of detail of historians, prevent us from fixing the time of his birth. -- Masoudi places him in the realms of the unknown. -- The Arabs give birth to him in Kaschmir, from where he goes to India & founds Sabeism. -- The Chinese are also having Fo born in Kaschmir. Same. Volume XXVI, 777 & 778. The agreement of the Chinese and the Arabs seems to exclude the feeling of those who cause it to be born in Siam or Ceilan. -- Two epochs of his birth among the Chinese, the difference between which is three hundred and forty-four years. Ibidiem, 778 & 779. M. De Guignes, to agree with them, establishes that the system of this religion being founded on metempsychosis, they will have adopted the founders of other religions, as new apparitions of their God. -- The Bonzes find, consequently, seven Fo, 779. Maintain that Vischnou has reappeared in the name of Krischtenou, & add to it all the circumstances which indigate J.C. 780. M. De Guignes thinks that they adopted Zoroaster in the same way, & shows that the time of Fo, the least ancient, squares with time where Zoroaster appeared, 780, 781 & 785. That the Indians knew Zoroaster, 783. That Darius, king of Persia, transports a pyreus in the Kaschmir, and obliges the Kings who were furnished to him to come there to adore a cypress, 784. From where those who came to the pyres could have believed that Zoroaster was a new appearance of Butta. -- They retain traces of the manisine, in the respect they have for fire & the casta tree. -- M. De Guignes concludes that the true period of Fo will be the oldest of the two, & maintains that what is disturbed by Christianity in the religion of the Indies, comes from the trade of Westerners; for there are found Roman words devoted to religion. -- Birth of Fo. -- Conformity with what Chinese historians say & S. Jerome, 785. Fables the Chinese utter on this subject. -- Its different revivals. -- Is the same as Vishnu, whose tenth appearance is under the figure of Buddha. -- His wedding. -- Has a son. -- Withdrew into the deserts with five Philosophers. -- His death. -- Becomes God, 786. Teach at his death that all he had said was a figure. -- That his real feeling was that everything was coming out of nothingness and returning to it. -- His favorite principle, according to the Missionaries, is atheism. -- His last words produce two sects, one following the outer doctrine, the other the inner doctrine. -- The followers of the exterior doctrine known under the names of Brahmes, Bonzes, Lamas, Talapoins. -- Their principles. -- Number of their divinities. -- Their reverence for the water of the Ganges. -- Their soul is perfected by dint of transmigrations, until it occupies the body of a Samaneen. Memoirs, Vol. XXVI, 787 & 788.

-- Table Des Matieres: Contenues dans l'Histoire & dans les Memoires de l'Academie Royale Des Inscriptions Et Belles-Lettres, depuis le Volume XXIII, jusques & compris le Volume XXXII. Tome Trente-troisieme. A Paris, De L'Imprimerie Royale. LM. DCCLXX. [Google translate: Table Of Contents: Contained in the History & in the Memoirs of the Royal Academy of Inscriptions and Belles-Lettres, from Volume XXIII, up to & including Volume XXXII. Volume Thirty-Third. In Paris, From the Royal Printing. LM. 1770.]

The Variety of Style in their Dates.

But if the Siameses do still make use thereof in their Dates, after having relinquish'd it in their Astronomical Calculations, it is because that in things of Style they do not easily alter the Usages unto which they are accustomed; and yet they cease not to date sometimes with respect to that modern Epocha which they have taken, as I have said, from the Year of our Lord 638. But their first Month is always the Moon of November or December, in which they depart not from the ancient Style, even then when they date the Year according to their new Style; tho' the first Month of the Year, according to this new Style, be the fifth or sixth of the old Style.

What the Siameses do think of the System of the Worlds

This, in few words, is the whole Skill of the Siameses in Astronomy. Moreover, they understand nothing of the true System of the World, because they know nothing by Reason. They believe therefore, like all the East, that the Eclipses are caused by some Dragon, which devours the Sun and Moon (perhaps by reason of the Astronomer's metaphorical way of speaking, that the Eclipses are made in the Head and Tail of the Dragon:) And they make a great noise, with Fire-shovels and Kettles, to scare and drive away this pernicious Animal, and to deliver those beauteous Planets. They believe the Earth Four-square, and of vast Extent, on which the Arch of Heaven rests at its extremities, as if it was one of our Glass-Bells with which we cover some of our Plants in our Gardens. They assert, that the Earth is divided into four habitable parts of the World, so separated one from the other by Seas, that they are, as it were, four different Worlds. In the middle of these four Worlds, they suppose an exceeding high Pyramidal Mountain with four equal sides, called, Aon pra Sommene (Caon signifies, a Mountain, and to Mount:) and from the Surface of the Earth, or the Sea, to the top of this Mountain, which, as they say, touches the Stars, they compute 85,000 lods, and every lod contains about 8,000 Fathoms. They reckon as many lods from the Surface of the Sea to the Foundations of the Mountain; and they likewise reckon 84,000 lods extent of Sea from each of the four sides of this Mountain to every of the four Worlds which I have mentioned. Now our World, which they call Tchiampion, lies, as they report, to the South of this Mountain, and the Sun, Moon and Stars do incessantly turn round it; and it is that, which according to them, makes the Day and Night. At the top of this Mountain is a Heaven, which they call Intratiracha, which is surmounted by the Heaven of Angels. This Sample, which is all I know thereof, will suffice to demonstrate their Gtossness; and if it does not exactly accord to what others have writ before me concerning this matter, we must not more admire the variety of the Siamese Opinions in a thing they understand not, than the contrariety of our Systems in Astronomy, which we pretend to understand.

The Indians are Superstitious proportionably to their extream Ignorance.

The extream Superstition of the Indians is therefore a very natural Consequence of their profound Ignorance; but for their Excuse, some People, more illuminated than them, have not been less Superstitious. Have not the Greeks, and after them the Romans, believed in Judiciary Astrology, Augurs, Presages, and all sorts of Arts invented under pretence of Divining and Predicting? They thought that it was the goodness of the Gods, to bestow on Men some Succors to penetrate Futurities; and the words Divination and Divine are the same word in their Origine, because that according to the ancient Pagans, the Art of Divining was only an Art to consult the Deities. The Siameses are also of opinion, that there is an Art of Prophecying, as there is one of restoring Health to the Sick: And when the King of Siam's Soothsayers are mistaken, he causes them to be bastinado'd, [Bastinado: A form of torture in which the soles of the feet are beaten with whips or cudgels.] not as Impostors, but as negligent persons; as he commands his Physicians to be cudgell'd, when the Remedies they give him, perform not the Effect which is thereby promised.

The Authority of Soothsayers over the Siameses.

This Prince, no more than his Subjects, undertakes no Affair, nor Expedition, till his Diviners, which are all Brames or Peguins, have fix'd him an hour prosperously to set upon it. He stirs not out of his House, or if he be gone, he enters not again, so long as his Diviners prohibit him. Sunday seems to him more lucky than the other days, because that in his Tongue he has preserv'd the name of the Sun's-day. He believes the Increase of the Moon more lucky than the Decrease; and besides this, the Almanac which he causes Annually to be made by a Brame Astrologer, denotes to him and his Subjects, the lucky or unlucky days for most of the things they used to do: A Folly which is perhaps too much tolerated amongst the Christians, witness the Almanac of Milan, to which so many persons do now give such a blind Belief.

And Presages.

The Siameses do take the Howlings of wild Beasts, and the Cryes of Stags and Apes, for an ill Omen; as several persons amongst us are frightened with the Barking of the Dogs in the Night. A Serpent which crosses the way, the Thunderbolt which falls on a House, any thing that falls as it were of itself, and without any apparent Cause, are Subjects of dread to the Siameses, and the reasons of laying aside or setting upon an Affair, how important and pressing soever it be. One of the ways they make use of to foretel things to come, and which is common to all the Orientals, is to perform some superstitious Ceremonies, then to go into the City, and to take for an Oracle about what they desire to know, the first words which they hear accidentally spoken in the Streets, or in the Houses. I could learn no more thereof, by reason that the Christian Interpreters, which I made use of, look'd upon these things with Horror, as Witchcraft and Compacts with the Daemon, altho' it be very possible that they are only Fooleries full of Credulity and Ignorance. The ancient Francs, by a like Superstition, consulted in their Wars the first words which they heard sung in the Church, at their entering thereinto. At this very day several persons have a Superstitious Belief in certain Herbs which they gather the Evening of St. John, from whence is risen this Proverb, To use or employ all the Herbs of St. John, that is, the utmost skill in an Affair: And amongst the Italians, there are some, who, after having wash'd their Feet in Wine on St. John's Eve, do throw the Wine out at Window, and so stand afterwards to hear those that pass along the Street, taking for a certain Augury on what they desire to know, the first word they hear spoken.

The Indians accused of Sorcery, and why.

But that which has rais'd the Reputation of great Sorcerers amongst the Indians, is principally the continual Conjurations which they use to drive away the evil Spirits with, and attract the good. They pretend to have some Talismans, or Characters which they call Cata, to accomplish whatever they please; as to kill, or to render invulnerable; and to impose Silence on Persons and Dogs, when they would commit a wicked Action, and not be discovered. If they prepare a Medicine, they will fasten to the brim of the Vessel several Papers, wherein they will write some mysterious words, to hinder the Petpayatons from carrying away the vertue of the Remedy with the steem. These Petpayatons are in their Opinion some Spirits diffused in the Air, of whom they believe, amongst other things, that they do first enjoy all the Maidens; and that they do them that pretended hurt, which is renewed every Month. In a Storm at Sea, they will fasten to all the Tackle such like written Papers, which they believe proper to assuage the Winds.

But the commonest use of sacred symbols is as talismans to ward off the evils of those malignant planets and demons who cause disease and disaster, as well as for inflicting harm on one's enemy. The symbols here are used in a mystical and magic sense as spells and as fetishes, and usually consist of formulas in corrupt and often unintelligible Sanskrit, extracted from the Mahayana and Tantrik scriptures, and called dharani, as they are believed to "hold" divine powers, and are also used as incantations. Shorter forms of these, consisting often of a single letter, are also used as representing the essence or "germ" of these spells or mantras, and hence named vija. And the mystic diagram in which they are often arranged is named Yantra, as in Hindu Tantrism.

The forms of these talismans and amulets are innumerable. The majority are luck-compelling, but different diseases, accidents and misfortune have each their special kinds.

The eating of the paper on which a charm has been written is an ordinary way of curing disease, as indeed it had been in Europe till not so many centuries ago, for the mystic Rx heading our prescriptions is generally admitted to have had its origin in the symbol of Saturn, whom it invoked, and the paper on which the symbol and several other mystic signs were inscribed constituted the medicine, and was itself actually eaten by the patient. The spells which the Lamas use in this way as medicine are shown in the annexed print, and are called "the edible letters" (za-yig).

A still more mystical way of applying these remedies is by the washings of the reflection of the writing in a mirror, a practice not without its parallels in other quarters of the globe. Thus to cure the evil eye as shown by symptoms of mind-wandering and dementia condition — called "byad-'grol" — it is ordered as follows: Write with Chinese ink on a piece of wood the particular letters and smear the writing over with myrobalams and saffron as varnish, and every twenty-nine days reflect this inscribed wood in a mirror, and during reflection wash the face of the mirror with beer, and collect a cupful of such beer and drink it in nine sips.

But most of the charms are worn on the person as amulets. Every individual always wears around the neck one or more of these amulets, which are folded up into little cloth-covered packets, bound with coloured threads in a geometrical pattern. Others are kept in small metallic cases of brass, silver, or gold, set with turquoise stones as amulets, and called "Ga-u." These amulets are fastened to the girdle or sash, and the smaller ones are worn as lockets, and with each are put relics of holy men — a few threads or fragments of cast-off robes of saints or idols, peacock feathers, sacred Kusa grass, and occasionally images and holy pills. Other large charms are affixed overhead in the house or tent to ward off lightning, hail, etc., and for cattle special charms are chanted, or sometimes pasted on the walls of the stalls, etc.

Most of these charms against accident, disease, and ill-fortune are in the form figured on the opposite page, which is called "The Assembly of all the Lamas' Hearts," as it is believed to contain the essence of all that is most powerful in the Lamaist spells.

It consists of a series of concentric circles of spells surrounded by flames, amid which in the four corners are the symbols of the Buddhist trinity symbolized as three gems, a lotus-flower, a thunder-bolt sceptre, and a flaming dagger with a vajra-hilt. In the interior is an eight-petalled lotus-flower, each petal of which bears mystic syllables, and in the centre of the flower is a circular space of about an inch in diameter, in which is placed the especial mystic charm...

As most of these specific charms are of the nature of sympathetic magic, and evidently derived from very ancient Indian sources, probably dating back to Vedic times when the ritual consisted largely of sympathetic magic,49 I give here a few examples: —

Thus to make the

Charm against Bullets and Weapons. — The directions are as these: With the blood of a wounded man draw the annexed monogram (D (upside-down D) and insert in the vacant space in the centre of the aforesaid print of "The Assembly of the Hearts of the Lamas." The sheet should then be folded and wrapped in a piece of red silk, and tie up with a piece of string and wear around the neck or an unexposed part of your breast immediately next the skin, and never remove it.

Charm for Clawing Animals (i.e., tigers, cats, bears, etc.). — On a miniature knife write with a mixture of myrobalans and musk-water the monogram (? ZAH) and tie up, etc. (Here the knife seems to represent the animal's claw.)

For Domestic Broils. — Write the monogram (? RE) and insert in print and fold up and bind with a thread made of the mixed hairs of a dog, goat, sheep, and enclose in a mouse-skin, and tie, etc. (This seems to represent union of domestic elements.)

For Kitchen Cooking Smells offensive to the House-Gods. — With the blood of a hybrid bull-calf write the monogram GAU ( = cow), and insert it in the print, and fold up in a piece of hedge- hog-skin. (Compare with the western Aryan myth of the Greek hearth-god Vulcan, whose mother Hera as Io is represented as a cow.)

For Cholera (or "the vomiting, purging, and cramps" ). — With the dung of a black horse and black sulphur and musk-water write the monogram (? ZA), and insert in the print, and fold up in a piece of snake-skin, and wear, etc. (Here the dung seems to represent the purging, the horse the galloping course, the black colour the deadly character, and the snake the virulence of the disease.)

-- The Buddhism of Tibet, or Lamaism With Its Mystic Cults, Symbolism and Mythology, and in its Relation to Indian Buddhism, by Laurence Austine Waddell, M.B., F.L.S., F.R.G.S., Member of the Royal Asiatic Society, Anthropological Institute, etc., Surgeon-Major H.M. Bengal Army, 1895

Superstitions for Women in Child-bed.

The superstitions which they use towards Women in Child-bed, appear not less ridiculous, although they be founded perhaps on some benefit for health. They believe that Women in Child-bed have need of being purified: whether that the Jews, spread throughout the Earth, have sowed this Tradition amongst several Nations, or that the people of hot Countries are more easily prejudiced than those of cold Countries with the natural impurities of Women. The Siameses keep the Women in Child-bed before a continual and great fire for a month, where they turn them sometimes on one side, sometimes on the other. The smoak does greatly incommode them, and passes slowly through an Aperture, which they make in the roof of their houses. The Peguins do put their Wives on a kind of Bambou-grate, very nigh, with fire underneath; but they keep them thus no more than four or five days. At the up-rising, the one and the other return thanks to the Fire for having purified their Wives; and in the Entertainment which they give on this occasion to their Friends, they eat nothing which they have not first offered to the Fire, leaving it some time near it. During the whole time of lying in Child-bed, the Women neither eat nor drink anything that is not hot: and I understand that our Midwives, forbid their Women also to drink anything cold.

Philtres look'd upon as the effect of Magick.

But the most speedy and most sensible effects of the pretended Divinations of the Indians are in the use of certain Philtres, which are only natural drinks. The Indies do produce some Simples, the kinds, force, or use of which we understand not. The Amorous Philtres, or Love potions, are those which debilitate the Imagination, and make a Man to become a Child; so that after this it is easie to govern him. My domesticks assur'd me that they had seen a man at Batavia, of whom it was reported that his wife had render'd him senseless after this manner. Other drinks do cause other effects. The Relations are full of those which the women of Goa frequently give their Husbands: and which render them so stupid for 24 hours, that they can then be unfaithful to them in their presence. Opium, or the quintessence of Poppies, causes such different effects, that it procures sleep, or watchfulness, as it is variously prepared. The Indians going to Battel, do take thereof to inspire them with courage, or rather with fury. They then run headlong upon the Enemy like wild Boars: It is dangerous to attend them, but one may avoid them by turning out of the way, for they go forwards. Moreover, the effect of Opium lasts only some hours, after which they relapse not only into their natural cowardice, but into a faintness, which leaves them but little action for their defence. And such were those Macassers, which had conspired against the King of Siam, some months before the Kings Ambassadors arrived there.

Distempers considered as the Effects of Magick.

The Siameses have likewise some Distempers, the symptoms of which are sometimes so strange, that they think the cause thereof can be attributed only to Witchcraft. But besides these extraordinary cases, their Physicians do almost continually accuse the greater Energy of the Spirits, with the inefficaciousness of their Remedies; and they do herein play such subtile juggling tricks, or rather they deal with persons so credulous, that whilst we were at Siam, they made a sick man believe, that he had voided a Deers skin with a Medicine, and that he must have swallowed this deerskin by a Magical effect, and without perceiving it. This is what I judged necessary to relate concerning the Siameses Superstititions, of which every one may judge as he pleases: for if on the one hand I have seen nothing which obliges me to accuse them of Sorcery, on the other hand I am not concern'd to justifie them entirely.

Superstition or Vanity touching the walls of Cities.

But before we quit this subject I will here add one thing, which may be attributed at your pleasure, to Superstition or Vanity: One day when the King's Ambassadors were saluted by the real or supposed Ambassaders, from Patana, Camboya, and some other neighbouring Courts, the Ambassadors of some of the several Nations which are at Siam, were also at this Visit: and among the rest there were two, who said that the City of their Origine, the name of which I have forgot, remained no more: but that it had been so considerable, that it was impossible to go round it in three Months. I smil'd thereat as at a groundless folly: and in a few days after Mr. de la Mare the Ingineer, whom Mr. de Chanmont had left at Siam, informed me, that when by the King of Siam's order he had been at Liger to take the draught thereof, the Governour would not permit him to go round it under two days, though he could have done it in less than an hour. Let us proceed to the study of the last part of the Mathematicks.

CHAP. XII. Concerning Musick, and the Exercises of the Body.

The Siameses have no Art in Singing.

Musick is not better understood at Siam, than Geometry and Astronomy. They make Airs by Fancy, and know not how to prick them by Notes. They have neither Cadence, nor quaver no more than the Castisians: but they sometimes sing like us without words, which the Castitians thing very strange; and in the stead of words, they only say noi, noi, as we do say lan-la-lari. I have not remark'd one single Air, whose measure was triple, whereas those are without comparison the most familiar to the Spaniards. The King of Siam, without shewing himself, heard several Airs of our Opera on the Violin, and it was told us that he did not think them of a movement grave enough: Nevertheless the Siameses have nothing very grave in their Songs; and whatever they play on their Instruments, even in their Kings march, is very brisk.....
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Part 1 of 2

The Problem of the Magical Squares according to the Indians, Excerpt from "A New Historical Relation of the Kingdom of Siam"
Tome II
by Monsieur De La Loubere
Envoy Extraordinary from the French King, to the King of Siam, in the years 1687 and 1688. Wherein a full and curious Account is given of the Chinese Way of Arithmetick, and Mathematick Learning. In Two Tomes, Illustrated with Sculptures. Done out of French, by A.P. Gen. R.S.S.
1693



Cassini is also credited with introducing Indian Astronomy to Europe. In 1688, the French envoy to Siam (Thailand), Simon de la Loubère, returned to Paris with an obscure manuscript relating to the astronomical traditions of that country, along with a French translation. The Siamese Manuscript, as it is now called, somehow fell into Cassini's hands. He was intrigued enough by it to spend considerable time and effort deciphering its cryptic contents, also determining on the way that the document originated in India. His explication of the manuscript appeared in La Loubère's book on the Kingdom of Siam in 1691.

-- Giovanni Domenico Cassini, by Wikipedia


Curiously enough the first definite information respecting the Hindu system of astronomy, came to Europe from Siam, where, in the early centuries of our era, there was a flourishing Hindu state. In 1687 Louis XIV sent M. de la Loubere on an embassy to Siam, and he brought back with him a portion of a manuscript containing rules for computing the places of the sun and moon. This was submitted to the celebrated John Dominic Cassini, the Italian astronomer, whom Louis had brought to Paris to take charge of his observatory. In his hands the calculations described, without indication of the meaning of the constants employed, were lucidly explained.

-- Burgess, James (1893). "Notes on Hindu Astronomy and the History of Our Knowledge of It". Journal of the Royal Asiatic Society of Great Britain & Ireland: 722–723.


I gave to Mr. Cassini, Director of the Observatory at Paris, the Siamese Method of finding the place of the Sun and Moon by a Calculation, the ground of which is taken from this Epocha. And the singular Merit which Mr. Cassini has had of unfolding a thing so difficult, and penetrating the Reasons thereof, will doubtless be admired by all the Learned. Now as this Epocha is visibly the ground only of an Astronomical Calculation, and has been chosen rather than another, only because it appear'd more commodious to Calculation than another, it is evident that we must thence conclude nothing which respects the Siamese History; nor imagine that the Year 638, has been more Famous amongst them than another for any Event, from which they have thought fit to begin to compute their Years, as we compute ours, from the Birth of the Saviour of the World.

-- CHAP. XI. What the Siameses do know of the Mathematics. Excerpt from "A New Historical Relation of the Kingdom of Siam", Tome II, by Monsieur De La Loubere, Envoy Extraordinary from the French King, to the King of Siam, in the years 1687 and 1688. Wherein a full and curious Account is given of the Chinese Way of Arithmetick, and Mathematick Learning. In Two Tomes, Illustrated with Sculptures. Done out of French, by A.P. Gen. R.S.S., 1693


Tome II, p. 227-247

The Problem of the Magical Squares according to the Indians.

This Problem is thus:

A square being divided into as many little equal figures as shall be desired, it is necessary to fill the little squares with as many numbers given in Arithmetical progression, in such a manner that the numbers of the little squares of each rank, whether from top to bottom, or from right to left, and those of the Diagonals do always make the same sum.

Now to the end that a square might be divided into little equal squares, it is necessary that there are as many ranks of little squares, as there shall be little squares to each rank.

The little squares I will case the cases, and the rows from top to bottom upright, and those from right to left transverse; and the word rank shall equally denote the upright and transverse.

I have said that the Cases must be filled with numbers in Arithmetical progression, and because that all Arithmetical Progression is indifferent for this Problem, I will take the natural for example, and will take the Unite for the first number of the progression.

Behold then the two first examples, viz. the square of nine Cases, and that of 16, filled, the one with the nine first numbers from the unite to nine, and the other with the sixteen first numbers from the unite to 16: So that in the square of 9 Cases, the summ of every upright, and that of every Transverse is 15, and that of each Diagonal 15 also: and that in that of 16 Cases, the summ of every upright, and that of every Transverse is 34, and that of each Diagonal 34 also.

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This Problem is called Magical Squares, because that Agrippa in his second Book De Occulta Philosophia, cap. 22. informs us that "they were used as Talismans, after having engraved them on plates of diverse metals: the cunning that there is in ranging the numbers after this manner, having appear'd so marvellous to the ignorant, as to attribute the Invention thereof to Spirits superior to man. Agrippa has not only given the two preceding Squares, but five successively, which are those of 25, 36, 49, 64, and 81 Cases; and he reports that these seven squares were consecrated to the seven Planets. The Arithmeticians of these times have looked upon them as an Arithmetical sport, and not as a mystery of Magic. And they have sought out general methods to range them.

The first that I know who laboured therein, was Gaspar Bachet de Meziriac, a Mathematician famous for his learned Commentaries on Diophantus. He found out an ingenious method for the unequal squares, that is to say, for those that have a number of unequal cases: but for the equal squares he could find none. 'Tis in a Book in Octave, which he has entitled, Pleasant Problems by numbers.

Mr. Vincent, whom I have so often mentioned in my Relation, seeing me one day in the Ship, during our return, studiously to range the Magical squares after the manner of Bachet, informed me that the Indians of Suratte ranged them with much more facility, and taught me their method for the unequal squares only, having, he said, forgot that of the equal.

The first square, which is that of 9 cases, return'd to the square of Agrippa, it was only subverted: but the other unequal squares were essentially different from those of Agrippa. He ranged the numbers in the cases immediately, and without hesitation; and I hope that it will not be unacceptable that I give the Rules, and the demonstration of this method, which is surprizing for its extream facility to execute a thing, which has appeared difficult to all our Mathematicians.

1. After having divided the total square into its little squares, they place the numbers according to their natural order, I would say by beginning with the unite, and continuing with 2, 3, 4, and all the other numbers successively, and they place the unite, or the first number of the Arithmetical Progression given, in the middle case of the upper transverse.

2. When they have put a number into the highest case of an upright, they place the following number in the lowest case of the upright, which follows towards the right: that is to say, that from the upper transverse they descend immediately to that below.

3. When they have placed a number in the last case of a transverse, the following is put in the first case of the transverse immediately superior, that is to say, that from the last upright, they return immediately to the first upright on the left.

4. In every other occurrence, after having placed a number, they place the following in the cases which follow diametrically or slantingly from the bottom to the top, and from the left to the right, until they come to one of the cases of the upper transverse, or of the last upright to the right.

5. When they find the way stopp'd by any case already filled with any number, then they take the case immediately under that which they have filled, and they continue it as before, diametrically from the bottom to the top, and from the left to the right.

These few Rules, easie to retain, are sufficient to range all the unequal squares in general. An example tenders them more intelligible.

Image

This square is essentially different from that of Agrippa; and the method of Bachet is not easily accommodated thereto; and on the contrary, the Indian method may easily give the squares of Agrippa, by changing it in something.

1. They place the unite in the Case, which is immediately under that of the Center, and they pursue it diametrically from top to bottom, and from the left to the right.

2. From the lowest case of an upright, they pass to the highest case of the upright which follows on the right; and from the last case of a Transverse they return to the left to the first case of the Transverse immediately inferior.

3. When the way is interrupted, they re-assume two cases underneath that which they filled; and if there remains no case underneath, or that there remains but one, the first case of the upright is thought to return in order after the last; as if it was indeed underneath the lowest.

An Example taken from Agrippa.

Image

As Bachet has not given the demonstration of his method, I have search'd it out, not doubting but it would give me also that of the Indian method: But to make my demonstration understood, it is necessary that I give the method of Bachet.

1. The square being divided by cases, to be filled with numbers in the Magical order, he augments it before all things by the square sides in this manner. To the upper part of the first transverse, he adds another transverse, but contracted by two cases, viz. one at each end. Over this first transverse contracted he adds a second contracted by two new cases. To the second he adds a third more contracted than the former, to the third a fourth, and so on, if it is necessary, until that the last transverse have but one case. Underneath the last transverse he adds likewise as many transverses more contracted one than the other. And in fine, to the first upright on the left, to the last upright on the right, he adds also as many uprights thus contracted.

EXAMPLES.

Image

aa are the squares of 9 and 25 cases, bb are the cases of Augmentation.

The square being thus augmented, Bachet there places the numbers according to the natural order, as well of the numbers as the cases, in the following manner.

Image

In this disposition it is evident that the cases of the true square are alternately full, and alternately empty, and that its two Diameters are entirely full. Now the full cases receive not any change in the sequel of the operation, and the Diameters remain always such as they are by position in the square augmented: but for the cases of the true square, which are likewise void, they must be filled with the numbers which are in the cases of Augmentation, by transporting the high ones lower, and the low ones higher, each into its upright; those of the right to the left, and those of the left to the right, each into its transverse, and all to as many cases, as there are in the side of the real square. Thus in the square of 9 cases, which has only three in its side, the unite, which is in the case of Augmentation at the top, is removed to the third case below in the same upright; 9, which is in the case of Augmentation below, is removed to the third case above in the same upright, [illegible], which is in the case of Augmentation on the right, is remov'd toward the left, to the third case in the same transverse; and in sine, 7, which is in the case of Augmentation on the left, is removed towards the right, to the third case in the same transverse.

After the same manner, in the square of 25 cases, which has 5 in its side, the numbers, which are in the cases of Augmentation above, do descend 5 cases below each in its upright. Those of the cases of Augmentation below do ascend five cases above each in its upright. Those of the cases of Augmentation on the right do pass 5 cases to the left, each in its transverse; and those of the cases of Augmentation on the left do pass 5 cases to the right, each also in its transverse. It ought to be the same in all the other squares proportionably, and thereby they will become all Magical.


Definitions.

In the augmented square of Bachet, the ranks of Augmentation shall be called Complements of the ranks of the true square, into which the numbers of the ranks of Augmentation must be removed: and the ranks which must receive the Complements, shall be called defective ranks. Now as by Bachet's method every number of the cases of Augmentation must be removed to as many cases as there are in the side of the true square, it follows that every defective rank is as far distant from its Complements, as there are cases in the side of the true square.

2. Because that the true square, that is to say, that which it is necessary to fill with numbers according to the Magical Order, is always comprehended in the square augmented, I will consider it in the square augmented, and I will call its ranks and its diameters, the ranks and diameters of the true square; but its ranks, whether transverse or upright, shall comprehend the cases, which they have at both ends; because that the numbers which are in the cases of Augmentation, proceed neither from their transverse nor from their upright, when removed into the cases of the true square, according to Bachet's method.

3. The diameters of the square augmented are the middle upright, and middle transverse of the true square, and they are the sole ranks which are not defective, and which receive no complement. They neither acquire, nor lose any number in Bachet's operation: they suffer only the removal of their numbers from some of their cases into others.

4. As the augmented square has ranks of another construction than are the ranks of the true square, I will call them Bands and Bars. The Bands descend from the left to the right, as that wherein are the numbers 1, 2, 3, 4, 5, in the preceding example, the Bars descend from the right to the left, as that, wherein are the numbers 1, 6, 11, 16, 11, in the same example.

Preparation to the Demonstration

The Problems of the Magical squares consists in two things.

The first is that every transverse and every upright make the same sum, and the second that ever diameter make likewise that same sum. I shall not speak at present of this last condition, no more than if I sought it not. And because that to arrive at the first, it is not necessary that all the numbers, which ought to fill a Magical square, be in Arithmetical proportion continued, but that it suffices that the numbers of a Band be Arithmetically proportional to those of every other Band, I will denote the first numbers of every Band by the letters of the Latin Alphabet, and the differences between the numbers of the same Band by the letters of the Greek Alphabet; and to the end that the numbers of a Band be Arithmetically proportional to the numbers of every other Band, I will set down:

Image

the differences of the numbers of each band by the same Greek Letters.

1. Nothing hinders why the Sign -, may not be placed instead of the Sign +, either before all the differences, or before some, provided that the same Sign be before the same difference in each band: for so the Arithmetical proportion will not be altered.

2. The greater a square shall be, the more Latin and Greek Letters it will have; but every band will never have but one Latin Letter, and all the Greek Letters; and the Latin Letter shall be different in each band. Every bar on the contrary shall have all the Latin Letters, and all except the first shall have a Greek Letter, which shall be different in every bar.

Demonstration.

From hence it follows. 1. That the diameters of the augmented square have each all of the Latin and all the Greek Letters, because that they have each a case of every band, and a case of every bar, and that the cases of every band do give them all the Latin Letters, and the cases of each bar all the Greek. The sum then of these two diameters is the same, viz. that of all the Letters, as well Greek as Latin, taken at once. Now these two diameters do make an upright and a transverse in the Magical square, because that in the operation of Bachet, their sum changes not by the loss or acquisition of any number, as I have already remarked.

2. As the ranks of the true square, whether transverse or upright, are as distant from their complements, as there are cases in the side of the true square, it follows that the bands, and the bars, which begin with a complement, or above this complement, touch not, that is to say, have no case at the defective rank of this complement; and that the bands and the bars which begin with a defective rank or above, have no case in its complement: the Letters then of the defective rank, are all different from those of the complements; because that different bands have different Latin Letters, and that different bars have different Greek Letters. But because that all the bands, and all the bars, have each a case in all the defective ranks, or in their complements: then every defective rank whatever, will have all the Letters, when it shall have received its complement; it will have all the Latin, because that all the bands, passing through every defective rank, or through its complement, do there leave all the Latin Letters; and it will have all the Greek, because that all the bars, passing also through every defective rank, or through its complement, do there leave all the Greek Letters. And thus all the defective ranks will make the same sum in the Magical square, and the same sum as the diameters of the square augmented, which are the two sole ranks not defective of the true square.

That this Method cannot agree to even Squares.

The Demonstration which I have given, agrees to the equal squares, as well as to the unequal, in this that in the augmented equal square, every defective rank and its complement do make the sum, which a range of the Magical square ought to make: But there is this inconvenience to the equal squares, that the numbers of the cases of Augmentation, do find the cases of the true square filled with other numbers, which they ought to fill; because that every case is full, which goes in an equal rank after a full case, and that in the equal squares, the cases of the defective ranks do come in an equal rank, after those of the complements, the defective ranks being as remote from the complements, as the side of the square has cases, and the side of every equal square having its cases in equal number.

Of the Diameters of the unequal Magical Squares.

By Bachet's operation it is clear, that he understands that the diameters are such as they ought to be, by the sole position of the numbers in the augmented square: and this will be always true, provided only that it is supposed, that the number of the case of the middle of each band, be a mean Arithmetic proportion between the other numbers of the same band, taken two by two: a condition, which is naturally included in the ordinary Problem of the Magical squares, wherein it is demanded that all the numbers be in Arithmetical proportion continued. Alternato the mean number of each bar, will be also a mean Arithmetical proportional between all the numbers of the same bar taken two by two: and hereby every mean, taken as many times as there are cases in the band, or in the bar, which is all one, will be equal to the total sum of the band, or of the bar. Therefore all the means of the bands, taken as many times as there are cases in every band, or which is all one, in the side of the square, will be equal to the total sum of the square: then taken once only, they will be equal to the sum of one of the ranks of the Magical square; and it will be the same of the means of the bars: and because that the means of the bands do make one diameter, and the means of the bars the other, it is proved that the diameters will be exact by the sole position of the numbers in the augmented square, provided that every mean of a band, be a mean Arithmetic proportional between all the numbers of its band, taken two by two.

In a word, as in the squares there are no augmented pairs, nor true square nor diameters of the true square, because that the bands of the equal squires have not a mean number, 'tis likewise a reason, which evinces that this method, cannot be accommodated to the equal squares.

Methods of varying the Magical Squares by Bachet's Square augmented.

1. By varying the order of the numbers in the bands, or in the bars, provided that the order which shall be taken, be the same in all the bands, or the same in all the bars, to the end that in this order the numbers of a band or of a bar, be Arithmetically proportioned to those of every other band or bar: but it is necessary that not any of the diameters loses any of its numbers.

2. Or rather (which will amount to the same) by varying the order of the bars amongst them in the augmented square: for this troubles not the Arithmetical proportion, which is the ground of the preceding demonstration: but it is necessary to remember to leave always in their place the band and the bar, which do make the two diameters.

3. By not putting the first number of each band, in the first case of each band: As for example

Image

d, a, e, c, b, are the five letters of the first band, the order of which is arbitrary, and the letter d, which is in the first case of this first band, is not found in the first case of any other band 2 + but in the fourth case of the second band, in the second of the third, in the fifth of the fourth, and in the third of the fifth. Besides the succession or other of the Letters must be the same in every band. But because that in the bands where the Letter d is in a case lower than the first, there remains not case enough underneath, to put all the other Letters successively, the first cases of the bands do return in order after the last, and are in this case thought the last cases of their bands. A circumstance which it is necessary carefully to observe.

If then in an augmented square the numbers are disposed in each band, as in the bands of this square I have disposed the Letters a, b, c, d, e, and which one continues to operate like Bachet, that is to say, to remove as he does, the numbers of the cases of Augmentation into the void cases of the real square, the true square will be Magical, at least as to the ranks, whether transverse or upright, for I speak not as yet of the Diameters.

I shall call those capital cases, wherein are found the Letters like to the Letter which is put in the first case of the first band, which I will call the first capital case.

Preparation to the Demonstration.

1. It is necessary to observe in disposing these Letters, that after having chosen the capital case of the second band, near a Letter of the first band, which I will call the Letter of Indication, so that this second capital case be also the second case of the bar which begins with this Letter of Indication, one may chuse the capital case of the third band, near the Letter of the second band, like to the first Letter of Indication, so that this third capital case be the third of the bar, wherein shall be the second Letter of Indication. After the same manner shall be determin'd the capital case of every band, near the Letter of Indication of the precedent band. From whence it follows, that there are as many capital cases as bands, and no more.

It follows also, that not only the Letter d is always under the Letter c in the same bar, but that all the other Letters are always under the same Letters in the same bars, and that the Letters have likewise the same order in all the bars, as they have the same in all the bands, though the orders of the Letters in the bars, is not the same as the order of the Letters in the bands.

1. The choice of the capital case of the second band, which determines that of the rest, is not entirely arbitrary. To regulate it 'tis necessary to have regard to the number of the ranks of the true square, which is the number 5 in the preceding example, and which is always the square root of the number, which expresses the multitude of the cases of the true square, and so I will call it the root of the square.

Take then a number at your own choice, provided nevertheless that it be less than the root of the square, and first to this very root, and that by adding two points, it be still first at the same root of the square: 'Twill be by this number that we shall determine the choice of the second capital case: and we call it the number determining.

The second capital case must not be the second case of the second band, because that this second case is found in the upright diameter of the augmented square, and that there must not be two Letters alike in any of the diameters of the augmented square: and so as the first capital case is already in the upright diameter, the second cannot be there. It is necessary on the contrary, that the case which you shall chuse in the second band, for the second capital, be as far distant from the second case of the upright diameter, as your determining number shall have Unites, and at the same time your second capital shall be removed from the first capital case as many transverses, as your determining number + 2 shall have Unites. Thus in the preceding example, the second capital case, viz. the case of the second band, where is the Letter d, is the second case after that, which is in the upright diameter, and it is in the fourth transverse underneath the first capital case, which alone is looked upon as a transverse, and the number 2, which determines this second capital case, is first to 5, which is the root of the square, and 2 + 2 that is to say 4, is likewise first to 5, the third case of the second band is therefore the first, which removes from the upright diameter, and it is with this that it is necessary to begin to compute the distance of the rest: so that the first case of this second band is in this sense the remotest of the second case, though to reckon after a contrary sense it touches it.

You may then in the preceding example, where the root of the square is 5, take either 1 or 2, or 4, which do give you three different cases, of which you may make your second capital case, 1 is first to 5, and 1 will give you the case wherein is b, three transverses distant from the first capital case. a is first to 5, and 2 + 2 that is to say 4, is also first to 5, and 2 will give you the case wherein is d, 4 transverses distant from the first capital case., 3 is also first to 5, but because that 3 + 2, that is to say 5, is not first to 5, 3 can give you in this example only a false capital case. 4 is first to 5, and 4 + 2 that is to say 6, is also first to 5, but from 6 it is necessary to deduct 5 which is the root, and there will remain 1. And 4 will give you the case wherein is e, the fourth in distance from the case of the diameter rising, and has a transverse near the first capital. The number 4 will give you then Bachet's disposition, who has placed all the capital cases in the first bar: and as often as for a determining number you shall take a less number by an Unite, than the root of the square, you will fall into Bachet's disposition.

3. From hence it follows, that the diameter ascending will not have any other capital case than the first, which it has already, and that so it will not have twice the Letter, which shall be in the capital cases. To prove it let us suppose that our bands be sufficiently extended towards the right, to make as many new uprights as we desire; and let us mark the first upright, which shall be as distant from the diameter ascending, as the root of the square has Unites: that is to say, which shall be the fifth on the right of the diameter ascending, if the root of the square is 5. And at a like distance from this first upright marked, let us mark a second, and then a third, and a fourth, always at an equal distance one from the other, until that there are as many uprights marked, as the determining number has Unites. In this case as the determining number and the root of the square are first amongst them, the last upright marked will be the sole one, whose distance to take it from the diameter ascending, would be divisible by the determinating number.

Suppose also, that now the bands are long enough, the capital cases are marked all together, and without ever returning to the first cases of the bands, as it was necessary to do, before that the bands were extended, because that then they had not cases enough after the capital, to receive all the Letters successively. I say that in these suppositions, none of these marked uprights will have a capital cases except the last: because that it is the sole marked upright, whose distance from the diameter ascending unto it, is divisible by the determining number: for as the uprights, wherein are the capital cases, are as removed (viz. the first from the upright, the second from the first, the third from the second, and so successively) as the determining number has Unites, it follow that no upright has a capital case when the distance from the upright diameter unto it, is not divisible by the determining number. 'Tis proved then that no marked upright, except the last, will have a capital case: and the capital case which is shall have will be the first beyond the number of the cases necessary to your augmented square, because that in counting the first capital case, there will be as many others before this, as the root of the square has Unites.

Now when you mark the capital cases in a square augmented, according to the method which I have given, so that when you arrive at the last case of a band, you return to its first case, as if it was after the last, you do no other thing, than successively to place all the capital cases, in respect of the diameter ascending, as in the case of the extension of the bands, you will place one after the other in regard of all the uprights successively marked. And none of your capital cases, except a first supernumerary, can fall into your ascending diameter, as no other, except a first supernumerary, could fall into your last upright marked.

4. But if you consider the first capital case, as a transverse, and that you make the same suppositions as before, so that there are as many transverses marked, as the determining number + 2 shall have Unites, and as distant (viz. the first from the first capital case, the second from the first, the third from the second, and so successively) as the root of the square shall have Unites: From this that the root of the square and the determining number + 2 are first amongst them, and from this that the determining number + 2 expresses the distance of the transverses, wherein will be the capital cases, you will prove that there shall be only the last transverse marked, which has a capital case, which will be the first supernumerary: and consequently, that the defective rank, the first capital case of which is the complement, will have no capital case, because that it is the first transverse marked: and you will prove also that the first supernumerary capital case must return to the transverse of the first capital case, and as it must return likewise to the upright diameter, it follows that the first supernumerary case, that is to say, that which you would mark after the last of the necessary, is the first capital case, because there is only this which is common to its transverse, and to the upright diameter.

5. From the order of the letters, alike in all the bands and alike also in all the bars, you will prove that all the letters alike, are at the same distance one from the other, and in the same order amongst them, as the letters of the capital cases amongst them, and that so all the cases which contain letters alike may be considered as capital, so that two letters alike, are never found in the same upright, nor in the same transverse, nor in a defective rank, nor in its complement. Which needs no other demonstration.

Demonstration.

This supposed, the demonstration of the Problem is easie, for whereas no letter is twice in any of the diameters of the augmented square, nor in any defective rank and its complement, it follows that every of the two diameters, and every defective rank and its complement, have all the letters, and that consequently they make the same sumum.
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Re: Freda Bedi Cont'd (#3)

Postby admin » Wed May 18, 2022 4:58 am

Part 2 of 2

Of the Diameters.

The Band which makes one of the diameters being Magical by position, as it ought to be, continues Magical, because that it receives not any new Letter, nor loses any of its own. The bar which makes the other diameter is found Magical by the disposition, and the proof is this.

As far as the bar of the second capital case is removed from the first bar, so much the bar of the third capital case, is removed from the bar of the second, and so successively, the first bars to which you return, being reckon'd in this case as coming after the last. Now the bar of the second capital case is as far distant from the first as there are Unites in the determining number + 1. Therefore if the determining number + 1 is first to the root of the square, the preceding demonstration sufficeth to prove, that not any bar will have two Letters alike, wherefore the bar which shall serve as the diameter, will not have two Letters alike, and so it will have all the Letters once.

But if the determining number + 1 is an aliquot part of the root of the square, then each bar will have as many Letters alike, as there shall be Unites in the determining number + 1, and there will be as many different Letters, as there shall be Unites in the other aliquot part of the root of the square, which shall be the quotient of the division made from the root by the determining number + 1. These several Letters will be therefore in an odd number, because that this quotient can be only an odd number, being an aliquot of an odd number., Of these Letters in an odd number, the one will be the middle of the first band, the others, taken two by two, will be like to the Letters of the first band, which taken also two by two, will be equally remote from the middle, the one towards the head of the band, the other towards the tail: So that if the order of the Letters of the first band, is as the middle by its situation, or middle proportional between all the others, which, taken two by two, shall be equally remote from it, then the bar which shall serve as diameter will be Magical, because that if it has not the middle Letters of all the bands, it will have the power thereof; for the other Letters, which shall not be mean, if being taken two by two, the one is weaker than the middle of its band, the other will be stronger as much as the middle of its own; and thus the two together will countervail the middle of their bands. As for example, in the square of 81 cases, the root of which is 9, if the determining number is 2, as a 2 + 1, that is to say, 3 is the aliquot part of 9, the corresponding aliquot of which, that is to say that, which returns from the division of 9 by 3, is also 3, there will be in each bar three several Letters which will every one be there repeated three times. The first of the different will be the middle of the first band, the two others between the different, will be alike to two of the first band equally distant from the middle. After the same manner in the square of 225 cases, the root of which is 15, if the determining number is likewise 2, as 2 + 1, that is to say, 3 is the aliquot part of 15 (of which 5 is the aliquot corresponding) it will happen that in every bar there will be 5 several Letters repeated every one three times. The one will be the middle of the first band, the 4 others will be alike to 4 of the first band, which taken two by two will be equidistant from the middle.

The Conclusion is then, that when the determining number + 1, is first to the root of the square, the bars which serves as diameter can only be Magical: but that if the determining number + 1, is aliquot of the root of the square, the bar which serves as diameter cannot be Magical; that the middle Letter of the first band, cannot be the middle Arithmetic of all the other Letters of its first band two by two, and that it is not the letters of its band, which, taken two by two, are at equal distances from it, and the like of which ought to enter into the bar, which shall serve as diameter. After this the order of the Letters of the first band is arbitrary.

In a word, the nearest of these equidistant Letters, shall be each as distant from the middle, as the determining number + 1 shall have Unites, the following shall be as remote from these first, every one from its own, and so successively.

I have said that it is necessary to take the second capital case in the second band, tho it may be taken in such other band as one pleases, provided that the band of the third capital case be as distant from the band of the second case, as this shall be from the first, and that the band of the fourth capital case be at this very distance from the band of the third, and so successively, the first bands returning in order after the last. But besides this, it is necessary that this distance be expressed by a number first to the root of the square, and the thing will return to the same, that is to say, to put a capital case in each band. But if you put the second capital case in a band, whose distance from the first band, was not expressed by a number first to the root of the square, then several capital cases would fall in the first band, which being supposed full of all the different Letters, could not receive the like Letters, which fill the capital cases.

Another way of varying the Magical Squares.

You shall double the preceding variations, if you perform in the bars what you did in the bands, and in the bands what you performed in the bars; taking for one of the diameters, a bar which should be Magical by position, and rendring Magical by disposition the band which shall be the other diameter.

From these Principles it follows, that the square of o cases is always the same, without being able to receive essential varieties, because that it can have only two for the determining number: and because that the removing of the bands, or of the bars amongst them, makes only a simple subversion, by reason that there are only two bands and two bars subject to transposition, and that the band and the bar which serve as diameters cannot be displaced.

It follows also, that always one of the diameters at least must be Magical by position: and that the greatest and least of the number proposed to fill a Magical square, can never be at the center, because that the center is always filled by one of the numbers of the diameter by position, in which, be it band or bar, the greatest nor smallest number cannot be.

On the contrary, the middle number of the whole square, that is to say, that which by the position is at the center of the augmented square, will remain at the center of the Magical square, as often as the diameter by position shall have the capital case at one of its ends, but in every other case it will go out thence, and yet it will never depart from the diameter by position.

All which things must be understood according to the suppositions above explained. Besides I know that the uneven Magical squares may be varied into a surprising number of ways, unto which all that I have said would not agree.

In fine, one of the diverse methods, which result from the Principles which I have explained, is Indian, as may be proved, by removing into an augmented square the numbers of an Indian Magical square, in such a manner, that the cases of Augmentation be full of the Numbers, which they must render to the true square. It will be seen how the numbers shall be ranged in the augmented square, in one of the methods which I have explained.

An Illustration of the Indian Method.

As I had communicated to Mr. de Malezien, Intendant to the Duke of Mayne, the Indian unequal squares, without saying any thing to him of my Demonstration, which I had not as yet fully cleared, he found out one which has no relation to Bachet's augmented square, and which I will briefly explain, because that the things which I have spoken, will help to make me understood.

Let there be a square which we will call natural, in which the numbers should be placed in their natural order in this manner:

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The business is to dispose these numbers magically into another square of as many cases and empty.

1. In considering this square, I see that the two diameters, and the middle upright and transverse means do make the same summ: which Mr. de Malezien thought to have given ground to the Problem, out of a desire of rendering the other transverses and other uprights equal also, without destroying the equality of Diagnolas.

2. I see that the first transverse contains all the numbers, from the unite to the root of the square: that the second transverse contains these same numbers and in the same order, but augmented every one with a root: that the third contains also these very numbers in the same order, augmented every one with two roots: that it is the same in every transverse, save that the fourth has every one of these numbers augmented with three roots, that the fifth hath them augmented with four roots, and so in proportion of the other transverses, if there were more.

3. It therefore occurs naturally to my mind to consider another figure, where in every transverse I will place the same numbers, which are in the first, that is to say from the unite to the root of the square, without augmenting them with any root in any transverse; and I find presently that the transverses will be equal in their summs, having each the same numbers; and that the uprights of this new square, will have the same surplusage one over the other, as the uprights of the natural square, because that the difference of the uprights in the natural square, proceeds not from the roots affixt to the numbers, but from these numbers which are repeated in every transverse, as it is seen in this example, where the strokes annext to the numbers, do denote the roots wherewith each number is augmented in the natural square.

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4. It is evident that in this square all the transverses are equal, in that they have every one the same numbers, and that the uprights are only unequal because that they have not every one all those different numbers which are in every transverse, but on the contrary one alone of these numbers repeated as many times as there are squares in every upright. Therefore I shall render the uprights equal to one another, if I make that not one of these numbers be twice in every upright, but that all be there once. And because that these very numbers do bear every one the same number of roots in the same transverse, I shall also render the transverses equal, if I make that ever transverse have not all these several numbers of it self, but that it borrows one of every transverse. Thus the diameters are already equal, because that they have every one the several numbers that it is necessary to have, and that they take one from every transverse, that is to say, one without the root, the other augmented with a root, the other with 2, the other with 3, and so successively.

The true secret then is to dispose all the numbers of every transverse in a diametrical way, that is to say slanting, so that Having placed one number, the following will be in another transverse and another upright at the same time. Which cannot be better performed than after the Indian manner.

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These are the numbers of the first transverse placed slanting -- , so that there is not two in the same upright nor in the same transverse. I must therefore dispose the numbers of the second transverse after the same manner, and because that I must avoid placing the first number of this transverse, under the first of the other, I cannot do better than to place it under the last in this manner:

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With the same Oeconomy I dispose the other transverses, placing always the first number of the one under the last of the other; and for one of the diameters I put the middle transverse, because that naturally it is Magical.

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It is clear that in this disposition not any transverse, nor any upright have two numbers, neither from the same transverse, nor from the same upright of the natural square, and that the diameters which we have not made by position, has also only one number from every transverse, and every upright of the natural square. This is what M. de Malezien thought, without having had the leisure to fathom it further; and it is evidently the Principle, on which the Indian Method and that of Bachet are grounded, and all the others, of which I have shown, that it is possible to vary the Magical squares. And if care be taken that in a Magical square the ranks parallel to the diameters are defective, and that they have their complements, it will be seen that Bachet's augmented square, and the Magical square have opposite proprieties. In the augmented square, the bands which are the true ranks, are not Magical, and its defective ranks augmented with their complements are. On the contrary, in the Magical square the ranks are Magical, and the defective ranks and their complements do contain, every one, what a band of the augmented square contains.

To finish what M. de Malezien has thought, it is necessary only to accommodate what we have said concerning the choice of the capital cases: and because that this is easie to do, I will speak no more of it.

M. de Malezien thought likewise, that this principle might serve to the even squares, and this is true: but here likewise there is found difficulty in the execution, because that in the even squares, the defective ranks and their complements have every one a case in the same diameter, or have none at all, so that by dispersing the numbers from a transverse into a defective rank, and its complement, two numbers of this transverse are put into the same diameter, or else none at all, and the one and the other of these two things is equally bad. Besides there is no transverse in the even squares, which can furnish a diameter by position: and so it would be necessary to remove a little into the even squares, after the Indian manner of dispencing the numbers, and to put one into each rank and one into each diameter. But the Method presents not it self immediately. However, he is the first example thereof.

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Of the Indian Method of the Even Squares.

I thought to have divined it from the examples of the squares of 16, 36, and 64 cases, which Agrippa has given us.

1. As the ranks are in even number in the even squares, they may be considered two by two. Comparing then the first to the last, the second to the last save one, the third to the last but two, and so successively, by equally removing us from the first and the last ranks, we will call them opposite, be they transverse, or upright.

Now because that the numbers of one rank, are arithmetically proportional with those of another rank of the same way, it is clear to those who understand arithmetical proportion, that two opposite ranks do make the same total sum as two other opposite ranks, and that if this sum be divided into two equals, each half will be the sum that a Magical rank ought to make.

2. The opposite numbers are also the first and last of the whole square, the second and last save one, the third and last but two, and so successively, by removing as equally from the first and last numbers: so that the sum of two opposite numbers is always equal to the sum of other opposites.

From hence it is evident, that the numbers opposite to those of one rank, are the numbers which are in the opposite rank, and that to render the sums of two opposite ranks equal, it is necessary only to take the moity of the numbers of one of the ranks, and to exchange them for their opposites, which are in the other. As for Example:

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1, 2, 3, 4, do make the first natural rank of the square of 16 cases, and 13, 14, 15, 16, do make the last rank thereof. To render them equal, it is necessary only to take 2 and 3, which are the moity of the numbers of the first, and to exchange them for 14 and 15, their opposites; and so 1, 14, 15, 4, will make the same sum as 13, 2, 3, 16.

The transverses between them, and the uprights between them, may render themselves equal by this Method: but because that the choice of the opposite numbers may be made after several ways, the Indians have chosen one, that is easie to retain, which leaves the diameters such as they are in the natural square, because that they are such as they ought to be, and ranges the uprights, when it is intended only to range the transverses. The whole Method consists then in knowing how to range two opposite transverses, and the rules are these.

1. They take the half of the numbers of the upper transverse, and remove them to the lower: and they take their opposite numbers in the lower transverse, and remove them to the upper.

2. The numbers which remain in each rank, do remain there in their natural place, and in their natural order: the transposed do place themselves every one in the case of its opposite, and consequently in a subverted order.

3. The first and the last numbers of every rank do continue in their natural rank, the second and third are transposed, the fourth and the fifth remain, the sixth and the seventh are transposed, and so alternatively two are transposed, and two remain.

EXAMPLE.

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1, 2, 3, 4, 5, 6, 7, 8, do make the first natural rank of the square of 64 cases; 57, 58, 59, 60, 61, 62, 63, 64, do make the last thereof. 1 an d8 the first and last numbers of the first rank remain there, and in their natural place, 57 and 64 the first and last numbers of the last rank do remain there and in their place. Afterwards 2 and 3 are transposed, 4 and 5 remain, 6 and 7 are transposed: and after the same manner the numbers of the opposite rank 58 and 59 are removed, 60 and 61 do remain, 62 and 63 are removed. 1, 4, 5, 8, which remain in the first rank, are in their natural cases, and consequently in their natural order. 2, 3, 6, 7, which are removed, are in the cases of their opposites, and are in a subverted order. 58, 59, 62, 63, which are removed, are in the cases of their opposites, and in a subverted order.

All the opposite ranks must be ranged according to these few rules: but it is not always certain that it may be necessary to put the first number of the rank in the first case on the left; for after this manner the first and last uprights would keep all their natural numbers, and would not be equal. Therefore it is necessary to render them equal by the same rule as the transverses, by removing half of the numbers of the first upright into the cases of their opposites, leaving the first and the last in their upright, removing the second and the third, leaving the fourth and the fifth, removing the sixth and the seventh, and so successively according to the rules that we have given for the transverses. The head of every transverse will be then on the right, or on the left, according as its first number shall be continued or removed, to the first or to the last upright, to the right or to the left.

An Example of the Square of 64 Cases.

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But these rules suffice only to the squares equally even; and there is some particular observation for them unequally even.

Every square unequally even, if you thence deduct a compass (that is to say the first and the last transverses, the first and the last uprights) leaves a square equally even, which must be ranged according to the aforesaid rules with a little alteration, which we will declare. It is necessary therefore to see how the first and last transverses do range themselves, because that the first and last uprights do range themselves after the same manner.

1. The transverses, being of a square unequally even, have each a number of cases unequally even: but if care be not taken about the two middle cases of each transverse, then there will remain in every one a number of cases equally even, which we will call the cases equally even. The first rule is therefore to remove half of the numbers of the cases equally even, and to remove those, which should be chosen for this purpose, into a transverse of a square equally even. Thus the first and the last numbers do remain in their cases, the second and the third are removed, the fourth and the fifth continue, the sixth and the seventh are removed, and so successively: but I speak only of the numbers of the cases equally even, and I only comprehend those in the account which I make, no more than if the middle cases had no numbers.

2. The removed numbers pass not to the cases of their opposites, but into the cases which are against theirs, that is to say in their upright: and so they are not found in a subverted order in the transverse into which they pass.

An Example taken from the Square of 100 Cases.

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I have not set down the numbers 5 and 6 in this example, because that they are those of the two middle cases of the first transverse, and that the number of the two middle cases of the first transverse, in every square unequally even have a particular rule, which I will give. As to the eight other numbers, 1, 2, 3, 4, 7, 8, 9, 10, which are those of the cases equally even, they are ranged according to the rules which I have given. 1. The first and last are in their natural cases, then the second and third are removed, the fourth and the fifth remain in their natural cases, the sixth and the seventh are removed. 2. The removed, viz, 2, 3, 8, 9, are in the cases over against theirs, and in their natural order, and not in an inverted order.

3. As to the two middle numbers, the first continues, and the second is removed: but the first remains not in its natural case. It passes to the case of the second, and the second is not removed to the case which is over against its own, but into that of its opposite: because that it is not necessary that the first leaves its natural case to its opposite, which shall be transposed into this first transverse, and that the second leaves also to its opposite, the case which is over against its own.

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The numbers 5 and 6 are the middle. 5 remains in its transverse, but it passes to the case of 6, and 6 is removed to the case of its opposite, and not to that which is over against its own.

4. The numbers of the last transverse are ranged after this manner. The first and the last remain in their cases, the others fill the cases which are vacant, in the two transverses, and it is necessary to place them there successively, but in an inverted order. After this manner the two transverses become equal, because that they have given one to the other half of the numbers of the cases equally even, and that their middle numbers do make the like sum in every transverse, the opposites being together, and not in different transverses. It is possible if defined to range the second transverse as we have ranked the first, but then 'twould be necessary to rank the first as we have marked the second.

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The numbers 91 and 100, which are the first and the last of the last transverse, do remain in their natural places, the others which are 92, 93, 94, 95, 96, 97, 98, 99, do fill the cases, which remained vacant in the two transverses, and they are there places successively, but in an inverted order.

5. The first and the last uprights of the squares unequally even do rank themselves one in relation to the other, as the first and the last transverses: and by this means the whole square unequally even is found Magical, and by a Method easie to retain, and to execute by Memory.

The demonstration thereof is palpable. For to consider the numbers, as we have ranked them in the first and last transverses, it is evident that the opposite numbers, taken two by two, are there placed either diametrically in the first and last cases of every transverse, or directly opposite in the same upright, and because that the opposite numbers taken, thus two by two, do always make equal sums, it follows that these two transverses being at the top and at the bottom of the squares equally even, and interior already Magical, will add equal sums to the diameters and to the uprights of this interior square equally even; and that for the uprights and diameters of the square unequally, will be equal in their sums. It will be the same of the transverses of the square unequally even, because that its first and its last uprights will likewise add equal sums to the transverses of the interior square equally even. And our demonstration would be compleat, were not the two numbers mean as well of the first, and last transverses, as of the first and last uprights: for these numbers not being placed every right against its opposite, do add unequal sums to the middle transverses and uprights of the interior square equally even. Therefore to repair this inequality, which is only of two points, it is necessary to make a little alteration in the interior square equally even, which will be the last rule of this Method.

6. By ranging the interior square equally even, according to the rules of the Magical squares equally even; it is necessary to invert the order, which according to these rules of the squares equally even, the two middle numbers of the last transverse of the square of 16 cases, which is at the center of all, and the two middle numbers of the last upright of the same square of sixteen cases, ought to have, you will thus weaken the first middle upright, and the first middle transverse of the square equally even: forasmuch as in the first transverse of the square of 16 cases, the first middle number is always stronger than the second, and that in the last upright of the same square of 16 cases, the middle superior number is stronger than the inferior.

A Square of Thirty Six Cases.

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This square is that of Agrippa, save that I have placed on the right, what he has put on the left, because that he has taken the squares which he gives, after the Hebrew Talismans, where the natural order of the numbers is from the right to the left, according to the Hebrew's manner of writing.

A Square of 100 Cases.

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In the square of 36 cases the numbers 9 and 10, which are the middle of the last transverse of the square of 16 cases, which is at the center, are in an order contrary to that which they ought to have, according to the rules of the squares equally even. Thus 14 and 20, which are the middle of the last upright of the same square of 16 cases, are in a contrary number, to that which they ought to have by the same rules: for it would be necessary that 10 was before 9, and 14 under 20.

In the square of 100 cases at the seventh transverse, the middle numbers 35 and 36 are placed against the very rules of the squares equally even: 36 ought to precede 35 according to the rules: and 44 and 54 which are the middle of the seventh upright are also inverted, because that 44 ought to be under 54.

In every square equally even ranged Magically, according to the rules which I have given, it is infallible that in the transverse, which is immediately under the middle transverses, the two middle numbers should be in an inverted order, that is to say, the strongest precedes the weakest: for either these middle numbers are removed, and consequently in an inverted order, because that then their transverse begins at the right: forasmuch as if the middle numbers of each rank are not removed as it is supposed, the middle of the first upright are not, and so the middle transverses begin on the left, therefore the transverse underneath begins on the right. By a like ratiocination it will be proved that according to the rules of the squares equally even, the middle numbers of the upright, which is immediately after the middle uprights, are ranged in such a manner, that the strongest is always above the weakest.

This is Agrippa's Method of the even squares, which in my opinion are the Indian, the merit of which consists not in giving the sole possible manner of ranging the even squares, but the most easie to execute by memory: For it is to this principally that it seems, that the Indians should addict themselves. In a word, the Indian even squares are also Magical in the Geometrical Progression.

The Indians have two Principles for the Problem of the Magical squares, the one of which they have applied to the uneven squares, and the other to the even. The Mathematicians of this Country, which have laboured herein, have known only one of these two Principles, which is that of the even squares; but they have adapted it likewise to the uneven squares, and moreover they have added a singular condition to this Problem, which is that the Magical square be so ranged, that in deducting its first compass, that is to say its first and its last transverses, its first and its last uprights, the interior square which shall remain is found Magical, after this very kind, that is to say, being able to lose all it compasses one after the other, and to leave always for the rest a Magical square, provided that this residue have at least 9, or 16 cases; because that the square of 4 cases cannot be Magical.

Monsieur Arnoud has given the solution of this last Problem at the end of his Elements of Geometry, and before that he had printed it the first time, I had also resolved this Problem in its whole extent, having been proposed to me by the late Monsieur de Fermat, Counsellor in the Parliament of Thalouse, whose Memory is yet in Veneration amongst the learned: but then I divined not Agrippa's Principle of the unequal squares, nor the reason of Bachet's Method.

In fine, I am obliged to render this Testimony to Monsieur Sauveur, Professor of the Mathematics are Paris, that he found out a Demonstration of the Indian uneven squares, which Monsieur de Malezien communicated unto him: and that he has also invented a Method to range the even squares. I leave unto him the care of publishing this, and several other things of his own invention, because that this Chapter is already too long.
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Re: Freda Bedi Cont'd (#3)

Postby admin » Wed May 18, 2022 4:59 am

Rules of the Siamese Astronomy, for calculating the Motions of the Sun and Moon, translated from the Siamese, and since examined and explained by M. Cassini, a Member of the Royal Academy of Sciences, Excerpt from "A New Historical Relation of the Kingdom of Siam"
Tome II
by Monsieur De La Loubere
Envoy Extraordinary from the French King, to the King of Siam, in the years 1687 and 1688. Wherein a full and curious Account is given of the Chinese Way of Arithmetick, and Mathematick Learning. In Two Tomes, Illustrated with Sculptures. Done out of French, by A.P. Gen. R.S.S.
1693

Tome II, p. 186-199

Rules of the Siamese Astronomy, for calculating the Motions of the Sun and Moon, translated from the Siamese, and since examined and explained by M. Cassini, a Member of the Royal Academy of Sciences.

Monsieur de la Loubere, the King's Ambassador extraordinary at Siam brought back a Siamese Manuscript, which comprehends the Rules for calculating the motions of the Sun and Moon, according to the method of that Country, the Translation thereof he likewise brought from Siam, and communicated unto me.

This method is extraordinary. They make no use of Tables; but only the Addition, Subtraction, Multiplication, and Division of certain numbers, of which we do not presently discern the Ground, nor to what these numbers refer.

Under these numbers are conceal'd divers Periods of Solar Years, of Lunar Months, and other Revolutions, and the Relation of the one with the other. Under these numbers are likewise conceal'd several sorts of Epoches which are not distinguished, as the Civil Epoche, the Epoche of the Lunar Months, that of the Equinoxes, Apogaea, and Solar Cycle. The numbers in which the difference between these Epoches consists, are not ordinarily at the head of the Operations to which they serve, as they ought to be according to the Natural Order: they are often mixed with certain numbers, and the Sums or differences are multiplied or divided by others, for they are not always simple numbers, but frequently they are Fractions, sometimes Simple, sometimes Compound, without being ranged after the manner of Fractions, the Numerator being sometimes in one Article, and the Denominator in another; as if they had had a contrived design to conceal the Nature and Use of these numbers. In the Calculation of the Sun, they intermix some things which appertain only to the Moon, and others which are not necessary, either to the one or to the other, without making any distinction. They confound together the Solar and the Lunisolar Years, the Months of the Moon, and the Months of the Sun, the Civil and the Astronomical Months, the Days Natural and the Days Artificial. The Zodiack is divided sometimes into twelve Signs, according to the number of the Month of the Year, sometimes into 27 parts, according to the number of the Days that the Moon runs through the Zodiack, and sometimes in 30 parts, according to the number of the Days, that the Moon returns to the Sun. In the Division of the Day there is no discourse of Hours; but therein is found the 11th the 703d and the 800th parts of the Day, which result from the Arithmetical Operations which are prescribed.

This Method is ingenious; and being illustrated, rectified, and purged from Superfluities, it will be of some use, being practicable without books, by the means of divers Cycles, and of the difference of their Epoches. Wherefore it is that I have endeavoured to decypher it, what difficult soever I found at first, not only by reason of the confusion which everywhere appeared, and of the Names which are wanting in the supposed numbers; but likewise by reason of the extraordinary names, which are given to what results from the Operations, of which there are more than Twenty which have not been interpreted by the Translator, and of which I could never have found the Signification, if I had not first discover'd the method; which has likewise evinced to me, that the Interpretation, which the Translator has made of three or four other names, is not very exact.

In this research I have first distinguished, and separated from the other numbers, those which belong to the Epoches, having observed that these numbers, are those which were given to add or to subtract, either simply, or by dividing or multiplying them by certain other numbers.

Secondly, I have considered the Analogies which result from the Multiplications and Divisions of the other numbers, separated from the Epoches; and it is in the terms of these Analogies, that I have found the Periods of the Years, of the Months, and of the Days, and the differences of the one from the other, which the experience of things Astronomical, and the occasion of divers operations which I have made, has been me to understand.

I thought that the Missionaries, to whom Astronomy gives admittance amongst the great and learned throughout the East, might reap some advantage from this work, for the Understanding, and for the Explication of the Oriental Astronomy, which might easily be rectified and adapted to ours, with a little altering the Method, by correcting the numbers which it uses.

I thought also that it would not be useless to reduce the Astronomy of Europe to this form, to be able to supply the want of the Tables which greatly abridge the work. This method would be much more easie to practice in the form of the Julian and Gregorian year of which we make use, than in the form of the Lunisolar year, which the Orientals observe: for their principal difficulty consists in reducing the Lunisolar years and the Civil Lunary months to the years and months of the Sun, which the form of our Kalender immediately gives us; and what has given me the most trouble, has been to find out the method which they use to reduce them, in which the several sorts of Years, Months and Days, which are supposed and sought, are not distinguished. Wherefore the reason of the Explication which I give, and of the Determination of the Genus to the Species which I make in the beginning, will not presently be understood; but in the sequel it will be comprehended by the Connexion of things, and by what necessarily results therefrom.

The jurisprudence of the Hindus and Arabs being the field which I have chosen for my peculiar toil, you cannot expect that I should greatly enlarge your collection of historical knowledge; but I may be able to offer you some occasional tribute; and I cannot help mentioning a discovery which accident threw in my way, though my proofs must be reserved for an essay which I have destined for the fourth volume of your Transactions. To fix the situation of that Palibothra (for there may have been several of the name) which was visited and described by Megasthenes, had always appeared a very difficult problem, for though it could not have been Prayaga, where no ancient metropolis ever stood, nor Canyacubja, which has no epithet at all resembling the word used by the Greeks; nor Gaur, otherwise called Lacshmanavati, which all know to be a town comparatively modern, yet we could not confidently decide that it was Pataliputra, though names and most circumstances nearly correspond, because that renowned capital extended from the confluence of the Sone and the Ganges to the site of Patna, while Palibothra stood at the junction of the Ganges and Erannoboas, which the accurate M. D'Ancille had pronounced to be the Yamuna; but this only difficulty was removed, when I found in a classical Sanscrit [Sanskrit] book, near 2000 years old, that Hiranyabahu, or golden armed, which the Greeks changed into Erannoboas, or the river with a lovely murmur, was in fact another name for the Sona itself; though Megasthenes, from ignorance or inattention, has named them separately. This discovery led to another of greater moment, for Chandragupta, who, from a military adventurer, became like Sandracottus the sovereign of Upper Hindustan, actually fixed the seat of his empire at Pataliputra, where he received ambassadors from foreign princes; and was no other than that very Sandracottus who concluded a treaty with Seleucus Nicator; so that we have solved another problem, to which we before alluded, and may in round numbers consider the twelve and three hundredth years before Christ, as two certain epochs between Rama, who conquered Silan a few centuries after the flood, and Vicramaditya, who died at Ujjayini fifty-seven years before the beginning of our era.

-- Discourse X. Delivered February 28, 1793, P. 192, Excerpt from "Discourses Delivered Before the Asiatic Society: And Miscellaneous Papers, on The Religion, Poetry, Literature, Etc. of the Nations of India", by Sir William Jones


Concerning the Astronomical Epocha of this Method.

I have endeavoured to discover what is the Epoche, from whence they here begin to compute the Motions of the Sun and Moon; and to what year, what month, and what day of our Kalender it refers: for it is not treated of in this extract, which supposes it either known, or explained perhaps in the preceding Chapters from whence this extract has been taken, seeing that without the knowledge of the Epocha, it is absolutely impossible to practice this Method.

I have found that this Epoche is Astronomical, and that it is different from the Civil, which I have understood, because it is here prescribed to begin to compute the Months of the Year, current with the fifth Month in the Leap Year, which consists of 13 Months, and with the sixth Month in the common Year, which consists of 12 Months. For this would not be intelligible, if they supposed not two different Epoches of Years, the one whereof, which must be the Astronomical, begins sometimes in the fifth, and sometimes in the sixth Month of the other, which is the Civil. That which likewise evinc'd to me that the Astronomical Epoche, is different from the Civil Epocha, not only in the Months, but also in the Years, is the Operation which is here made to find the Year of ones Nativity, by subtracting his Age from the number of the Years elaps'd since the Epocha; for this Operation would be useless, if they demand only the Year of the Birth after the Civil Epocha, which is immediately known, and which is compared to the Year current, to know the Age of a Person.

This being supposed, I have first searched out the Age to which this Astronomical Epocha may refer; and having found in the Calculation of the Sun performed by this method, that two Signs and twenty Degrees which are therein employed, can only denote the place of the Zodiack, where was found the Apogaeum of the Sun in the Epocha, which Apogaeum must be in the twentieth Degree of Gemini; I judged that this Epocha must be about the seventh Age, where the Apogaeum of the Sun is found in the twentieth Degree of Gemini according to most Astronomical Tables.

Secondly, having found that the number 621, which is intermixed in the Calculation of the Sun, can only be the number of the days comprized, between the Astronomical Epocha, and the return of the Moon's Apogaeum, to the beginning of the Zodiack; and that the number 3232, which is afterwards employed therein, can be only the number of the Days, during which, this Apogaeum makes a Revolution; I have confirmed that the Apogaeum of the Moon which in 621 Days makes two Signs and nine Degrees, was in this Epocha, in the 21 Degrees of Capricorn: And because that the Moon's Apogaeum by the Revolution it makes in eight Years three quarters, returns to the same degree of the Zodiack twelve times in one Age; I have distinguished the Years of the Age, in which the Moon's Apogaeum is found in this Degree, and I have excluded the other Year.

Thirdly, having found by the method here used for Calculating the place of the Sun, that this Astronomical Epocha is very near the vernal AEquinox, which in the seventh Age fell on the 10th or 21st of March; Amongst these select Years I have found one in which the Moon's Apogaeum, arrived at this Degree of Capricorn, about the 21st of March, which is found but once in 62 Years, wanting some Degrees; and I have found that in the 638th Year of Jesus Christ, the Apogaeum of the Moon was at the 21st Degree of Capricorn the 21st of March.

Fourthly, I have remarked that this Astronomical Epocha must have begun at a new Moon; because the Lunar Months are reduced into Days, to find the number of the Days from the Epocha, and the value of the whole Months being deducted from the Sum of the Days, the test serves to find the Moon's distance from the Sun.

In the 638th Year of Jesus Christ, the AEquinoxial new Moon happened teh 21st of March at three a Clock in the Morning at Siam, when the Sun by its middle Motion ran through the first degree of Aries, the Sun's Apogaeum being in the 20th Degree of Gemini, and the Moon's in the 21st Degree of Capricorn. This Day was likewise remarkable for a great Eclipse of the Sun, which happened the same day, but 14. Hours after the mean Conjunction.

Fifthy, By the manner of find the day of the week, which is here observed, it appears that the day of the Epocha, was a Saturday, and th3 21st of March, in the Year 638 was also a Saturday. This likewise confirms the certainty of this Epocha, and demonstrates the Knowledge and Judgment of those that have established it, who contented not themselves with a Civil Epocha, as other astronomers have done: but who have chosen an Astronomical one, which was the Natural Principle of several Revolutions, which could not begin again, till after several Ages. This Epocha is 5 Years and 278 Days distant from the Persian Epocha of Jesdegerdes, the first year of which began on the 16th of June, in the Year of Jesus Christ, 632. Yet these Indian Rules are not taken from the Persian Tables related by Crosotoca; for these Tables do make the Sun's Apogaeum two degrees more backward, and the Moon's Apogaeum above six degrees forwarder; which agrees not so exactly with our modern Tables. The Persian Tables do also make the Sun's AEquation 12 Minutes less, and that of the Moon 4 Minutes greater; which agrees better with the Moderns.

These Indian Rules are not drawn neither from the Tables of Ptolemy, where the Sun's Apogaeum is fixed to the 5th degree and a half of Gemini; nor from the other Tables since made, which have all this moveable Apogaeum. It seems therefore that they have been invented by the Indians; or that perhaps they have been taken from the Chinese Astronomy, as may be conjectured from this, that in this extract the Numbers are written from the top downwards, after the manner of the Chineses: but it may be that this way of writing the numbers might be common to these two Nations.

Having found the Astronomical Epocha of this method, and the Relation is has with the Julian years; we may rectifie teh Epocha's of the motions of the Sun and Moon by the modern Tables, by adding about a Minute a Year to the Sun's apogaeum, and by correcting the other Periods. Thus there will be no difficulty, to reduce the Years and Months since the Epocha into days; and if the Equations are likewise corrected conformably to the modern Tables, we shall by the same Method, find the place of the Sun and Moon with a great deal more exactness. We will give this Correction, with the Supplement of what is wanting in these Rules, after that we have explained them.

Rules to find the place of the Sun and Moon at the time of any Person's Birth / Explication.

I. / I.

1st. Set down the AEra / 1st. The Aera in this place is the number of the years since the Astronomical Epocha from whence is take the motion of the Planets to the current year; which will appear in the sequel.

2nd. Subtract the Age of the Person from the AEra, you will have the Age of the Birth. / 2nd, The Age of the Person, is the number of the Years from his Birth to the Year current, which being deducted from the AEra, there remains the Age or time of the Birth, that is to say, the Year from the Astronomical Epoche in which the Nativity happened.

3rd. Multiply it by 12. / 3rd. By multiplying the years by 12 they are reduced into Months. These Months will be solar, each consisting of 30 days, 10 hours and a half, a little more or less, according to the several Hypotheses, if the years are solar; or near upon if they are lunisolar, and in so great number, that the excess of the one recompences the defect of the others.

4th. Add hereunto the number of the Months of the year current1 and for this purpose if the year current is Attikamaat, that is to say, if it has 13 Lunar months, you shall begin to compute with the 5th month; but if it is not Attikamaat, you shall begin to compute with the 6th month. / The Form of the Year here mentioned, is lunisolar, seeing there are some common of 12 lunar months, and abundant or Embolismal, called Attikmaas, of 13 lunar months. For that they begin to compute the months, not with the first month of the year, but with the fifth, if it is Leap year, and with the sixth if it is not: I have inferred that there are two Epocha's, and two forms of different Years, the one Astronomical and the other Civil: that the first Month of the Astronomical Year begins in the fifth Month of the Civil Leap year, which would be the sixth Month without the intercalation of the Leap month, which is not reckoned amongst the 12 Months, and which is supposed to be inserted before; and that in the Other Years, all the Months of which are successively computed without Intercalation, the first Month of the Astronomical Year, is computed only from the sixth Month of the Civil Year.

But as it is not expressly determined here, whether one ought to begin to compute an entire month at the beginning or end of the 5th or 6th month, it may be that for the first month of the Astronomical Year they take, that which ends at the beginning of the months whereof it is discourses in this Article. In this case, the Interval between the beginning of the Civil Year, and the beginning of the Astronomical Year, would be only of 3 or 4 entire months: whereas if an entire month is reckoned only at the end of the 5th or 6th month, and that the first month which is reckoned, according to this Rule, be the first of the Astronomical Year; the interval between the beginnings of these two sorts of years, will be 4 or 5 whole months. We shall see in the sequel, that the Indians have diverse sorts of Astronomical Years, the beginnings of which are different, and are not much distant from the Vernal AEquinox; whereas the Civil Year must begin before the Winter Solstice, sometimes in the month of November, sometimes in the month of December of the Gregorian Year.

They add the number of the months of the current year, which are lunar months, to those that they have found by the third Article, which are solar months; and they suppose that the sum, as heterogeneous as it is, should be equal to the number of the solar months elapsed from the Astronomical Epochs. They neglect the different that there may be, which in a year cannot amount to an entire month: but they might be deceived a month in the succession of the years, if they took not good heed to the Intercalations of the months, after which the number of the months which are computed in the Civil Year, is lesser than that which they would reckon without the precedent Intercalations.

5th. Multiply by 7 the number found Art. 4.

6th. Divide the sum by 228.

7th. Joyn the quotient of the division to the number found Art. 4. This will give you the Maasaken (that is to say, the number of the months) which you shall keep.

-- / 5th, 6th, 7th. They here seek the number of the lunar months from the Astronomical Epocha, discoursed of in the 1st Article, to the beginning of the current month: which is performed by reducing the solar months, which are supposed to have been found above, into lunar months, by the means of the difference, which is between the one and the other. In the operations which are made, it is supposed that as 228 is to 7, so the number of the solar months given, is to the difference which the number of the lunary months surpasses the number given of the solar months elapsed, during the same space of time; that thus in 228 solar months, which do make 19 years, there are 228 lunary months, and 7 months more, that is to say 235 lunary months. This therefore is a Period like to that of Numa and Mero, and to our Cycle of the golden number of 19 years, during which the Moon rejoyn'd it self 235 times to the Sun.

Yet in the sequel we shall see, that these Periods which accord together in the number of the lunar months and solar years, agree not in the number of the hours, by reason of the greatness of the solar year and of the lunar month, which is supposed various in these several Periods: and that the Indian is not subject to a fault so great, as the ancient Cycle of the Golden Number, which they have been obliged to expunge out of the Roman Kalender, in the Gregorian correction, because it gave the new Moons later than they are, almost a day in 312 years; whereas the New Moons determined by this Indian Period, agree with the true in this interval of time to near an hour, as will be found by comparing these Rules with the following.

II. / II.

1. Set down the Maasaken / --

2. Multiply it by 30 / --

3. Joyn thereunto the days of the current Month. / The months of the Moon are here reduced into days: but because they make all the months to consist of 30 days, there only will be some artificial months about 11 hours 16 minutes longer than the Astronomical, or some artificial days which begin at the New Moons, and are 22 minutes, 32 seconds shorter than the natural days of 24 hours, which begin always at the return of the Sun to the same Meridian.

4. Multiply the whole by 11. / --

5. Add thereunto also the number of 650. / They reduce the days into 11 parts, by multiplying them by 113 and they add thereto 650 elevenths, which do make 59 days and [illegible]. I find that these 59 days and 1/11 are the artificial days, which were elapsed to the day of the Epocha, since that an eleventh part of the natural day, and an eleventh of the artificial had began together under the meridian of the Indies, to which these Rules are accommodated.

6. Divide the whole by 703. / --

7. Keep the Numerator which you shall call Anamaan. / --

8. Take the quotient of the Fraction found Art. 6, and subtract it from the number found Art. 3. The remainder will be the Horoconne (that is to say, the number of the days of the AEra) which you shall keep. / Having laid apart what is always added by the 5th. Article, it appears by the 2d, 3d, 4th, 6th and 8th, operation, that as 703 is to 11, so the number of the artificial days, which results from the Operations of the 2d, and 3d. Art. is to the number of the days deducted to have the number of the natural days, which answers to this number of the artificial days: whence it appears, that by making the lunar month to consist of 30 artificial days, 703 of these days do surpass the number of the natural days, which equal them above eleven days.

One may find the greatness of the Lunar Month, which results from this Hypothesis: for if 703 Artificial Days do give an excess of 11 Days 30 of these Days which do make a Lunar Month, do give an excess of 163/303? in the Day; and as 703 is to 330, so 24 Hours are to 11 Hours, 15 Minutes, 57 Seconds; and deducting this Overpins from 30 Days, there remains 29 Days, 12 Hours, 44 Minutes, 3 Seconds for the Lunar Month, which agrees within a Second to the Lunar Month determined by our Astronomers.

As to the value of 59 Days and 1/11 which is added before the Division, it appears that if 703 Days do give 11 to subtract, 59 Days and 1/11 do give [x] in the Day, which do make 22 Hours, 11 Minutes and a half, by which the end of the Artificial Day, must arrive before the end of the Natural Day, which is taken for the Epocha.

The anamsan is the number of 703 part of the Day, which remain from the end of the Artificial Day, to the end of the current Natural Day. Use is made hereof in the sequel to calculate the motion of the Moon, as shall be afterwards explained.

The Quotient which is taken from the number of the Days found by the third Art. is the difference of the entire Days, which is found between the number of the Artificial Days, and the number of the Natural Days from the Epocha.

The Herotonne is the number of the Natural Days elapsed from the Astronomical Epocha to the current Day. It should seem that in rigour the Addition of the Days of the current Month, prescribed by the third Article, should not be made till after the Multiplication and Division, which serves to find the difference of the Artificial Days from the Natural, because that the Days of the Current Month are Natural, and not Artificial of 30 per mensem: but by the sequel it appears that this is done more exactly to have the Anamaan which serves for the calculation of the motion of the Moon.

III. / IIII.

1. Set down the Horoconne.

2. Divide it by 7.

3. The Numerator of the Fraction is the day of the Week. / It follows from this Operation and Advertisement, that if after the Division there remains 1, the current day will be a Sunday; and if nothing remains, it will be a Saturday: The Astronomical Epocha of the Horoconne is therefore a Saturday.

Note, That the first day of the Week is Sunday.

If it be known likewise what day of the Week is the day current, it will be seen whether the Precedent Operations have been well made.

IV. / IV.

1. Set down the Horoconne.

2. Multiply it by 800.

3. Subtract it by 373.

4. Divide it by 292207.

5. The Quotient will be the AEra, and the Numerator of the Fraction will be the Krommethiapponne, which you shall keep. / The days are here reduced into 800 parts. The number 373 of the third Article makes [x] of the day, which do make 11 hours and 11 minutes. They can proceed only from the difference of the Epochas, or from some correction, seeing that it is always the same number that is subtracted. The Epocha of this fourth Section may therefore be 11 hours and 11 minutes after the former.

The AEra will be a number of Periods of Days from this new Epocha, 800 of which will make 292207. The Question is to know what these Periods will be? 800 Gregorian Years, which very nearly approach as many Tropical Solar Years, do make 292194 Days. If then we suppose that the AEra be the number of the Tropical Solar Years from the Epocha, 800 of these Years will be 13 Days too long, according to the Gregorian correction.

But if we suppose that they are Anomalous Years, during which the Sun returns to his Apogeum, or Astral Years during which the Sun returns to the same fixt Star; there will be almost no error: for in 13 Days, which is the overplus of 800 of these Periods above 800 Gregorian Years, the Sun by its middle motion makes 12d. 48'. 48" which the Apogeum of the Sun does in 800 Years by reason of 57". 39'". per annum. Albategnius makes the Annual motion of the Sun's Apogeum 59". 4'". and that of the fix'd Stars 54". 34'". and there are some modern Astronomers which do make this annual motion of the Sun's Apogaeum 57". and that of the fix'd Stars 51"3. Therefore if what is here called AEra, is the number of the Anomalous or Astral Years: these Years will be almost conformable to those which are established by the antient and modern Astronomers. Nevertheless it appears by the following Rules, that they use this form of Year as if it were Tropical, during which the Sun returns to the same place of the Zodiack, and that it is not distinguished from the other two sorts of Years.

The Krommethiapponne which remains after the preceeding Division, that is to say, after having taken all the entire Years from the Epocha, will therefore be the 800 parts of the Day, which remain after the Sun's return to the same place of the Zodiack: and it appears by the following Operations that this place was the beginning of Aries. Thus according to this Hypothesis the Vernal middle AEquinox will happen 11 Hours 11' after the Epocha of the preceeding Section.

V. / V.

1. Set down the Krommethiapponne.

2. Subtract from it the AEra.

3. Divide the remainder by 2.

4. Neglecting the Fraction, subtract 1 from the quotient.

5. Divide the remainder by 7, the Fraction will give you the day of the Week.

Note, That when I shall say the Fraction, I mean only of the Numerator. / Seeing that in the third Art. the day of the week is found by the Horoconne, after a very easie manner, it is needless to stay on this which is longer and more compounded.

VI. / VI.

1. Horoconne.

2. Subtract from it 621.

3. Divide the remainder by 3232. The Fraction is called Outhiapponne, which you shall keep. / This Subtraction of 628, which is always deducted from the Horoconne, what number soever the Horoconne contains, denotes an Epocha, which is 621 days after the Epocha of the Horoconne.

The number 3232 must be the number of the Days, which the Moon's Apogaeum employs in running through the Circle of the Zodiack: 3232 Days to make 8 Indian Years and 310 Days. During that time this Apogaeum finishes a Revolution after the rate of 6'. 41". which it performs in a Day, even according to the Astronomers of Europe. The Apogaeum of the Moon does consequently finish its Revolution 621 days after the Epocha of the Horoconne. 'Tis here performed then; as 3232 days are to a Revolution of the Apogaeum, so the number of the days is to the number of the Revolutions of the Apogaeum. They keep the remainder which is the number of the days called Onthiapponne. The Outhiapponite will therefore be the number of days elapsed from the return of the Moon's Apogaeum to the beginning of the Zodiac; which will more evidently appear in the sequel.

If you would have the day of the Week by the Outhiappone, take the Zuotient of the aforesaid Division; multiply it by 5, then joyn it to the Outhiapponne, then subtract thence two days, divide it by 7, the Fraction will show the day.

Whatever is before is called Poulasouriat, as if one should say the Force of the Sun. / Having already explained the true method of finding the day of the Week, it is needless to stay here. Leaving the care of examining it, and searching the ground thereof, to those that shall have the curiosity.

Notwithstanding the name of the Sun's Force which is here given to the precedent Operations, it is certain that what has hitherto been explained, belongs not only to the Sun, but likewise to the Moon.

VII. / VII.

1. Set down the Krommethiapponne.

2. Divide it by 24350.

3. Keep the quotient, which will be the Raasi, that is to say, the Sign where the Sun will be. / To find what the number 24350 is; it is necessary to consider, that the Krommethiapponne are the 800 parts of the day which remains after the Sun's return to the same place of the Zodiac, and that the solar year contains 292207 of these parts, as has been declared in the explication of the fourth Section. The twelfth part of a year will therefore contain 24350 and 7/180? of these 800 parts: wherefore the number 2435- denotes the twelfth part of a solar year; during which the Sun by its middle motion makes a Sign.

Seeing then that [illegible] of a day do give a Sign, the Krommethiapponne divided by 24350 will give to the Quotient the Signs which the Sun has run since his return by his middle motion to the same place; The Raasi then is the number of the Signs; run through by the middle motion of the Sun. They here neglect the Fraction, 7/23? so that the solar year remains here of 292 [illegible], that is to say of 365 days 1/4?, like the Julian year.

4. Lay down the Fraction of the aforesaid Division, and divide it by 811.

5. The Quotient of the Division will be the Ongsaa, that is to say, the degree wherein the Sun will be. / Seeing that by the preceding Article 24 [illegible] of a day do give a Sign of the Sun's middle Motion, the 30th part of 24 150/ooo will give a degree which is the 30th part of a Sign. The 30th part of 24330 is 811; which do make a degree: dividing the remainder by 811 [illegible], they will have the degree of the Sun's middle motion. Here they neglect that ; which can make no considerable difference.

6. Set down the Fraction of this last Division, and divide it by 14.

7. The Quotient will be the Libedaa, this is to say the Minute.

8. Subtract 3 from the Libedaa.

9. Place what belongs to the Libedaa, underneath the Ongsaa, and the Ongsaa underneath the Raasi: This will make a Figure which shall be called the Mettejomme of the sun, which you shall keep. I suppose it is locus medius Solis. / Seeing that in a degree there are [illegible] parts; in a minute, which is the 60th part of a degree, there will be 13!! of these parts. Neglecting the Fraction, they take the number 14, which dividing the remainder, will give the minutes. The Subtraction which is here made of three minutes is a reduction whereof we shall speak in the sequel.

It is here prescribed to put the Degrees under the Signs, and the Minutes under the Degrees in this manner.

Raasi, Signs.
Ongsaa, Degrees.
Libedaa, Minutes.

This Disposition of the Signs, Degrees, and Minutes one under the other is called a Figure, and it here denotes the middle place of the Sun.

VIII. / VIII.

To find the true place of the Sun,

1. Set down the Mettejomme of the Sun, that is to say, the figure which comprehends what is in the Raasi, Ongsaa and Libedaa.

2. Subtract 2 from the Raasi. But if this cannot be, add 12 to the Raasi, to be able to do it, then do it.

3. Subtract 20 from the Ongsaa. But if this cannot be, deduct 1 from the Raasi, which will amount to 30 in the Ongsaa, then you shall deduct the aforesaid 20. / The number 2[?], which is subtracted from the Raasi, in the second Article, and the number 20 in the third Article, are 2 Signs and 20 degrees, which doubtless denotes the place of the Suns Apogaeum according to this Hypothesis; in which there is not seen any number which answers to the motion of the Apogaeum. It appears then that this Apogaeum is supposed fix'd to the 20th degree of Gemini, which precedes the true place of the Apogaeum, 25 it is at present 17 degrees, which this Apogaeum performs not in less than 1000 years, or thereabouts: From whence it may be judged that the Epocha of this method is about a thousand years before the present age. But as the greatness of the year agrees better here with the Suns return to the Apogaeum and the fixed Stars, than with the Suns return to the Equinoxes; it may be that the beginning of the Signs here used, is not at present in the Equinoxial point, but that it is advanced 17 or 18 degrees, and so it will be necessary to be corrected by the Anticipation of the Equinoxes. Here then they subtract the Suns Apogaeum from its middle placed called Mattejomme, to have the Suns Anomalia: and the number of the signs of this Anomalia is that which they call Kenne.

4. What will afterwards remain, shall be called Kenne. / It appeareth by these Rules that the Kanne is the number of the half-signs of the distance of the Apogaeum or Periganat [?], taken according to the succession of the Signs, according as the Sun is nearer one term than the other: So than in the 5th Article is taken the distance of the Apogaeum according to the succession of the Signs; in Article 6th the distance of the Perigaum, against the succession of the Signs: in Article 7th the distance of the Perigaum according to the succession of the Signs; and in Article 8th the distance of the Apogaeum, contrary to the succession of the Signs. In the 6th, 7th, and 8th Articles it seems, that it must always be understood. Multiply the Raasi by 2, as it appears in the sequel.

In the 6th Article when the degrees of the Anomalia exceed 15, they add 1 to the Kanne; because that the Kanne, which is a half Sign, amounts to 15 degrees.

The degrees and minutes of the Kanne are here reduced into minutes, the number of which is called the Ponchalit.

It appears by these Operations, that the Chaajaa is the AEquation of the Sun calculated from 15 to 15 degrees, the first number of which is 35, the second 67, the third 94; and that they are minutes, which are to one another as the Sinns of 15, 30, and 45 degrees from whence

It follows that the Equation of 60, 75, and 90 degrees are 116, 129, 134. / 35-67-94-116-129-134

which are set apart in this form, and do answer in order to the number of the Kanne, 1, 2, 3, 4, 5, 6.

As for the other degrees they take the proportional part of the difference of one number to the other, which answers to 15 degrees, which do make 900 minutes, making: as 900, to the difference of two Equations; so the minutes which are in the overplus of the Kanne, to the proportional part of the Equation, which it is necessary to add to the minutes which answer to the Kanne to make the total Equation. They reduce these minutes of the Equation into degrees and minutes, dividing them by 60. The greatest Equation of the Sun is here of 2 degrees, 12 min. The Alphonsine Tables do make it 2 degrees, 10 minutes: We find it of 1 degree, 57 minutes. They apply the Equation to the middle place of the Sun, to have its true place which is called Sommepont.

5. If the Kenne is 0, 1, or 2, multiply it by 2, you will have the Kanne.

6. If the Kenne is 3, 4, or 5; you shall subtract the figure from this figure 5-29-60, which is called Attathiat, and amounts to 6 Signs.

7. If the Kenne is 6, 7, 8; subtract 6 from the Raasi, the remainder will be the Kanne.

8. If the Kenne is 9, 10, 11; subtract the figure from this figure 11-29-60 which is called Touataasamounetonne, and amounts to 12 Signs: the remainder in the Raasi will be the Kanne.

9. If you can deduct 15 from the Ongsaa, add 1 to the Kanne, if you cannot, add nothing.

10. Multiply the Ongsaa by 60.

11. Add thereunto the Libedaa, this will be the Pouchalit, which you shall keep.

12. Consider the Kanne. If the Kanne is 0, take the first number of the Chaajaa of the Sun, which is 35; and multiply it by the Pouchalit.

13. If the Kanne is some other number, take according to the number, the number of the Chajaa aattit, and subtract it from the number underneath. Then what shall remain in the lower number, multiply by it the Pouchalit. As for example, if the Kanne is 1, subtract 35 from 67, and by the rest multiply. If the Kanne is 2, subtract 67 from 94, and by the rest multiply the Pouchalit.

14. Divide the Sum of the Pouchalit multiplied by 900.

15. Add the Quotient to the superior number of the Chajaa, which you have made use of.

16. Divide the Sum by 60.

17. The quotient will be Ongsaa, the Fraction will be the Libedaa. Put an 0 in the place of the Raasi.

18. Set the figure found by the preceding Article over against the Mattejomme of the Sun.

19. Consider the Ken aforesaid. If the Ken is 0, 1, 2, 3, 4, 5; It is called Ken subtracting: Thus you shall subtract the figure found in the 17 Article from the Mattejomme of the Sun.

20. If the Ken is 6, 7, 8, 9, 10, 11, it is called Ken additional: So you shall joyn the said figure to the Mattejomme of the Sun: which will give out at last the Sommepont of the Sun, which you shall precisely keep.

19. [21?] This Equation, conformably to the rule of our Astronomers in the first demi-circle of the Anomalia, is subtractive; and in the second demi-circle, additional. Here they perform the Arithmetical operations placing one under the other, what we place side-ways; and on the contrary, placing side-ways what we place one under the other. As for Example:

-- / The Mattejomme / The Chajaa / The Sommepont / --

Raasi / 8 / 0 / 8 / Signs

Ongsaa / 25 / 2 / 27 / Degrees

Libedaa / 40 / 4 / 44 / Minutes

-- / Middle Place / Equation / True Place / --


IX. / IX.

1. Set down the Sommepont of the Sun.

2. Multiply by 30 what is in the Raagi.

3. Add thereto what is in the Ongsaa.

4. Multiply the whole by 60.

5. Add thereunto what is in the Libedaa.

6. Divide the whole by 800, the Quotient will be the Reuc of the Sun.

7. Divide the remaining Fraction by 13, the Quotient will be the Naati reuc, which you shall keep underneath the Reuc. / It appears by these Operations that the Indians divide the Zodiac into 17 equal parts, which are each of 13 degrees, 40 minutes. For by the six first Operations the signs are reduced into degrees, and the minutes of the true place of the Sun into minutes; an din dividing them afterwards by 800, they are reduced into 27 parts of a Circle; for 800 minutes are the 27th part of 21600 minutes which are in the Circle, the number of the 27 parts of the Zodiack are therefore called Reuc, each of which consists of 800 minutes, that is to say, of 13 degrees, 40 minutes. This division is grounded upon the diurnal motion of the Moon, which is about 13 Degrees, 40 Minutes; as the division of the Zodiack unto 360 Degrees has for foundation the diurnal motion of the Sun in the Zodiack, which is near a Degree.

The 60 of these parts is 13-1/3; as it appears in dividing 800 by 60, wherefore they divide the Remainder by 13, neglecting the fraction, to have what is here called Nati-reuc, which are the Minutes or 60 parts of a Reuc.

X. / X.

For the Moon. To find the Mattejomme of the Moon.

1. Set down the Anamaan.

2. Divide it by 25.

3. Neglect the Fraction, and joyn the Quotient with the Anamaan.

4. Divide the whole by 60, the Quotient will be Ongsaa, the Fraction will be Libedaa, and you shall put an 0 to the Raasi. / According to the 7th Article of the III Section, the Anamaan is the number of the 703 parts of the day, which remain from the end of the Artificial day to the end of the Natural day. Altho according to this rule, the Anamaan can never amount to 703: yet if 703 be set down for the Anamaan, and it be divided by 25, according to the 2d Article, they have 28 [illegible], for the Quotient. Adding 28 to 703, according to the third Article, the sum 731 will be a number of minutes of a degree. Dividing 731 by 60, according to the fourth Article, the Quotient which is 12d. 11', is the middle diurnal motion, by which the Moon removes from the Sun.

From what has been said in the II Section, it results that in 30 days the Anamaan augments 330. Dividing 330 by 24, there is in the Quotient 13 [illegible]. Adding this Quotient to the Anamaan, the summ is 343, that is to say, 5 d., 43'. which the Moon removes from the Sun in 30 days, besides the entire Circle.

The European Tables do make the diurnal motion of 12d, 11'. and middle motion in 39 days, of 5d. 43'., 21", besides the entire Circle.

5. Set down as many days as you have before put to the month current. Sect. II. n. 3.

6. Multiply this number by 12.

7. Divide the whole by 30 the Quotient, put it to the Raasi of the preceding figure which has an 0 at the Raasi, and joyn the fraction to the Ongsaa of the figure.

8. Joyn this whole figure to the Mattejomme of the Sun.

9. Subtract 40 from the Libedaa. But if this cannot be, you may deduct 1 from the Ongsaa, which will be 60 Libedaa.

10. What shall remain in the figure is the Mattejomme of the Moon sought. / After having found out the degrees and the minutes which agree to the Anamaan, they seek the signs and degrees which agree to the Artificial days of the current month. For to multiply them by 12, and to divide them by 30, is the same thing as to say, If thirty Artificial days do give 12 Signs, what will the Artificial days of the current month give? they will have the Signs in the Quotient. The Fractions are the 30ths of a Sign, that is to say, of the degrees. They joyn them therefore to the degrees found by the Anamaan, which is the surplusage of the Natural days above the Artificial.

The Figure here treated of is the Moons distance from the Sun, after they have deducted 40 minutes, which is either a Correction made to the Epocha, or the reduction of one Meridian to another: as shall be explain'd in the sequel. This distance of the Moon from the Sun being added to the middle place of the Sun, gives the middle-place of the Moon.

XI. / XI.

1. Set down the Outhiappone.

2. Multiply by 3.

3. Divide by 808.

4. Put the Quotient to the Raasi.

5. Multiply the fraction by 30.

6. Divide it by 808, the Quotient will be Ongsaa.

7. Take the remaining fraction, and multiply it by 60.

8. Divide the summ by 808, the Quotient will be Libedaa.

9. Add 2 to the Libedaa; the Raasi, the Ongsaa, and the Libedaa will be the Mattejomme of Louthia, which you shall keep. / Upon the VI. Section it is remarked that the Onthiapponne is the number of Days after the return of the Moon's Apogaeum, which is performed in 3232 Days: 808 Days are therefore the fourth part of the time of the Revolution of the Moon's Apogaeum, during which it makes 3 Signs, which are the fourth part of the Circle.

By these Operations therefore they find the motion of the Moon's Apogaeum, making as 808 Days are to 3 Signs; so the time passed from the return of the Moon's Apogaeum is to the motion of the same apogaeum during this time. It appears by the following Operation that this motion is taken from the same Principle of the Zodiack, from whence the motion of the Sun is taken.

The Mattepomme of Louthia, is the Place of the Moon's Apogaeum.

XII. / XII.

For the Sommepont of the Moon.

1. Set down the Mattejomme of the Moon.

2. Over against it set the Mattejomme of Louthia.

3. Subtract the Mattejomme of Louthia from the Mattejomme of the Moon.

4. What remains in the Raasi will be the Kenne.

5. If the Kenne is 0, 1, 2, multiply it by 2, and it will be the Kanne.

6. If the Ken is 3, 4, 5, subtract it from this figure: 5 / 29 / 60.

7. If the Ken is 6, 7, 8, subtract from it 6.

8. If the Ken is 9, 10, 11, subtract it from this figure: 11 / 29 / 60.

9. If the Kenne is 1 or 2, multiply it by 23 this will be the Kanne.

10. Deduct 15 from the Ongsaa, if possible; you shall add 1 to the Raasi; if not, you shall not do it.

11. Multiply the Ongsaa by 60, and add thereunto the Lebidaa, and it will be the Pouchalit, that you shall keep.

12. Take into the Moons Chajaa the number conformable to the Kanne, as it has been said of the Sun; subtract the upper number from the lower.

13. Take the remainder, and therewith multiply the Pouchalit.

14. Divide this by 900.

15. Add this Quotient to the upper number of the Moons Chajaa.

16. Divide this by 60, the Quotient will be Ongsaa, the Fraction Libedaa, and an 0 for the Raasi.

17. Opposite to this figure set the Mattejomme of the Moon.

18. Consider the Ken. If the Ken is 0, 1, 2, 3, 4, 5, subtract the figure of the Moons Mettejomme; if the Ken is 6, 7, 8, 9, 10, 11, join the two figures together, and you will have the Sommepont of the Moon, which you shall keep. / All these Rules are conformable to those of the VIII. Section, to find the place of the Sun, and are sufficiently illustrated, by the explication made of that Section.

The difference in the Chajaa of the Moon, discoursed of in the 14th and 15th Article. This Chajaa consists in these numbers: 77 / 1_8 / 209 / 256 / 286 / 296.

The greatest Equation of the Moon is therefore of 4 degrees 56 minutes, as some Modern Astronomers do make it, though the generality do make it of 5 degrees in the Conjunctions and Oppositions.

XIII. / XIII.

Set down the Sommepont of the Moon, and operating as you have done in the Sommepont of the Sun, you will find the Reuc and Nattireuc of the Moon. / This Operations has been made for the Sun in the IX Section. It is to find the position of the Moon in her Stations, which are the 27 parts of the Zodiac.

XIV. / XIV.

1. Set down the Sommepont of the Moon.

2. Over against it set the Sommepont of the Sun.

3. Subtract the Sommepont of the Sun from the Sommepont of the Moon, and the Pianne will remain, which you shall keep. / The Pianne is therefore the Moon's distance from the Sun.

XV. / XV.

1. Take the Pianne and set it down.

2. Multiply the Raasi by 30, add the Ongsaa thereunto.

3. Multiply the whole by 60, and thereunto add the Libedaa.

4. Divide the whole by 720, the Quotient is called Itti, which you shall keep.

5. Divide the Fraction by 12, the quotient will be Natti itti.

The end of the Souriat. / These three first Operations do serve to reduce the Moon's distance from the Sun into minutes; dividing it by 720, it is reduced to the 30 part of a Circle, for 720 minutes are the 30th part of 21600 minutes, which do make the whole circumference. The ground of this division is the Moons diurnal motion from the Sun, which is near the 30th part of the whole Circle. They consider then the Position of the Moon, not only in the Signs and in her stations, but also in the 30th parts of the Zodiack, which do each consist of 12 degrees, and are called itti; dividing the remainder by 12, they have the minutes, or sixtieth parths of an itti, which do each consist of 12 minutes of degrees, which the Moon removes from the Sun in the sixtieth part of a day; these sixtieth parts are called natti itti.
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Part 1 of 2

Nalanda Mahavihara: Victim of a Myth regarding its Decline and Destruction
by O.P. Jaiswal
Mainstream Weekly
Monday 18 June 2018

[T]he Shaman Hwui-li, took up his tablets and wrote the life of Hiuen-Tsiang. The Master had already written his immortal Si-yu-ki or Record of Western Countries... The Life is supplement to the Record. What is obscure or half told in the one is made clear in the other.

Hwui-li begins in the true Chinese manner with a grand pedigree of his hero, tracing his descent from the Emperor Hwang Ti, the mythical Heavenly Emperor....

And withal clear-sighted and intolerant of shams, he is still a child of his age and religion. With childish curiosity he tempts a bone to foretell the future, and with childish delight obtains the answer he most desires. In the town of Hiddha is Buddha's skull bone, one foot long, two inches round. "If anyone wishes to know the indications of his guilt or his religious merit he mixes some powdered incense into a paste, which he spreads upon a piece of silken stuff, and then presses it on the top of the bone: according to the resulting indications the good fortune or ill fortune of the man is determined." Hiuen obtains the impression of a Bodhi and is overjoyed, for, as the guardian Brahman of the bone explains, "it is a sure sign of your having a portion of true wisdom (Bodhi)." At another time he plays a kind of religious quoits by flinging garlands of flowers on the sacred image of Buddha, which, being caught on its hands and arms, show that his desires will be fulfilled. In simple faith he tells Hwui-li how Buddha once cleaned his teeth and flung the fragments of the wood with which he performed the act on the ground; how they took root forthwith, and how a tree seventy feet high was the consequence. And Hiuen saw that tree, therefore the story must be true....

He returned to his own country with no less than 657 volumes of the sacred books, seventy-four of which he translated into Chinese, while 150 relics of the Buddha, borne by twenty horses, formed the spoil reverently gathered from the many lands we call India....

The original from which the translation is made is styled "History of the Master of the Law of the three Pitakas of the 'Great Loving-Kindness' Temple." It was written, probably in five chapters, in the first instance by Hwui-li, one of Hiuen-Tsiang's disciples, and afterwards enlarged and completed in ten chapters by Yen-thsong, another of his followers. Yen-thsong was selected by the disciples of Hwui-li to re-arrange and correct the leaves which their master had written and hidden in a cave. ...

It will be found that Hwui-li's history often explains or elucidates the travels of Hiuen-Tsiang. Yen-thsong evidently consulted other texts or authorities. This is especially the case in reference to the history of the Temple of Nalanda...


-- The Life of Hiuen-Tsiang, by the Shaman Hwui Li, With an Introduction Containing an Account of the Works of I-Tsing, by Samuel Beal, B.A., D.C.L.


Nalanda1 has a very ancient history going back to the days of Mahavira and Buddha in the sixth and fifth centuries BC. According to the Jaina texts, it was a suburb (bahariya), situated to the north-west of the famous city of Rajagriha. Indeed, so important was the place that Mahavira spent as many as fourteen rainy seasons there. The Pali Buddhist literature too contains many references to Nalanda. It is said that in the course of his sojourns the Buddha often visited the place, which was mentioned as prosperous, swelling, teeming with population and containing a mango-grove called Pavarika. The distance from Rajagriha to Nalanda is given as a yojana.

This place is mentioned in the Maha-sudassana-Jataka2 as the birthplace of the Thera Sariputra, a chief disciple of the Buddha. In other texts the same place, under the name of Nalaka or Nalakagrama, appears as a centre of Sariputra’s activities.3 The Mahavastu, a Sanskrit Buddhist text, also gives Nalanda-gramaka, half a yojana distant from Rajagriha, as the place of birth of Sariputra and finds support in some Tibetan texts, including Taranatha’s History of Buddhism in India, a seventeenth-century Tibetan work.4

It is therefore reasonable to hold that Nala, Nalaka, Nalakagrama and Nalanda are all variants of the same place-name.
A yojana south-west from this place brought them to the village of Nala, [Or Nalanda; identified with the present Baragong. A grand monastery was subsequently built at it, famous by the residence for five years of Hsuan-chwang.] where Sariputtra [See chap. xvi, note 11. There is some doubt as to the statement that Nala was his birthplace.] was born, and to which also he returned, and attained here his pari-nirvâna. Over the spot (where his body was burned) there was built a tope, which is still in existence.

-- A Record of Buddhistic Kingdoms, Being an Account by the Chinese Monk Fa-Hien, Of His Travels in India and Ceylon (A.D. 399–414), Translated and Annotated with a Corean Recension of the Chinese Text by James Legge, M.A., LL.D.

Hiuen-Tsang, the renowned Chinese traveller of the seventh century AD, says that according to tradition the place owed its name to a naga of the same name who resided in a local tank. But he thinks it more probable that the Buddha, in one of his previous births as Bodhisattva, became a king with his capital at this place, and that his liberality won for him and his capital the name Nalanda or ‘charity without intermission’.5

According to Taranatha, Asoka, the great Mauryan emperor of the third century BC, gave offerings to the chaitya of Sariputra that existed at Nalanda and erected a temple here; Ashoka must therefore be regarded as the founder of the Nalanda-vihara [university] [mahavihara].[!!!]6 The same authority adds that Nagarjuna, the famous Mahayana philosopher and alchemist of about the second century AD, began his studies at Nalanda and later on became the high priest here. It is also added that Suvishnu, a Brahmana contemporary of Nagarjuna, built one hundred and eight temples at Nalanda to prevent the decline of both the Hinayana and Mahayana schools of Buddhism.7 Taranatha also connects Aryadeva, a philosopher of the Madhyamika school of Buddhism of the early fourth century AD, with Nalanda.4
Aryabhata mentions in the Aryabhatiya that he was 23 years old 3,600 years into the Kali Yuga, but this is not to mean that the text was composed at that time. This mentioned year corresponds to 499 CE, and implies that he was born in 476....

It is fairly certain that, at some point, he went to Kusumapura for advanced studies and lived there for some time. Both Hindu and Buddhist tradition, as well as Bhāskara I (CE 629), identify Kusumapura as Pāṭaliputra, modern Patna. A verse[???] mentions that Aryabhata was the head of an institution (kulapa) at Kusumapura, and, because the university of Nalanda was near Pataliputra at the time and had an astronomical observatory, it is speculated that Aryabhata might have been the head of the Nalanda university as well.

-- Aryabhata, by Wikipedia


Further, Asanga, a Buddhist philosopher of the Yogachara school, belonging to the fifth century AD,8 is said to have spent here twelve years of his later life and to have been succeeded by his still more famous brother, Vasubandhu, as the high priest of Nalanda.9
The German translation of Lama Taranatha's first book on India called The Mine of Previous Stones (Edelsteinmine) was made by Prof. Gruenwedel the reputed Orientalist and Archaeologist on Buddhist culture in Berlin. The translation came out in 1914 A.D. from Petrograd (Leningrad).

The German translator confessed his difficulty in translating the Tibetan words on matters relating to witchcraft and sorcery. So he has used the European terms from the literature of witchcraft and magic of the middle ages viz. 'Frozen' and 'Seven miles boots.'

He said that history in the modern sense could not be expected from Taranatha. The important matter with him was the reference to the traditional endorsement of certain teaching staff. Under the spiritual protection of his teacher Buddhaguptanatha, he wrote enthusiastically the biography of the predecessor of the same with all their extravagances, as well as the madness of the old Siddhas.

The book contains a rigmarole of miracles and magic….

-- Mystic Tales of Lama Taranatha: A Religio-Sociological History of Mahayana Buddhism, by Lama Taranatha, Translated into English by Bhupendranath Datta, A.M., Dr. Phil.

These statements of Taranatha would lead one to believe that Nalanda was a famous centre of Buddhism already at the time of Nagarjuna and continued to be so in the following centuries. But it may be clearly emphasised that the excavations have not revealed anything which suggests the occupation of the site before the Guptas, the earliest datable finds being a (forged) copper plate of Samudra-gupta and a coin of Kumaragupta. This is fully confirmed by the statement of Hiuen-Tsang (d. 664 CE) that ‘a former king of the country named Sakraditya built here a monastery and that his successors, Buddha-gupta, Tathagatagupta, Baladitya and Vajra built some monasteries nearby’.10
Kumaragupta I/Shakraditya (r. c. 415–455 CE)
Skandagupta (r. c. 455-467 CE)
Purugupta (r. c. 467–473 CE)
Kumaragupta II (r. c. 473-476 CE)
Budhagupta ( r. c. 476- 495 CE)
Narasimhagupta (r. c. 495-530 CE)
Kumaragupta III (r. c. 530-540 CE)
Vishnugupta (r. c. 540–550 CE) (Last king of the Gupta Empire)

-- by Wikipedia

As some of these names were borne by the Gupta emperors, it has been held that all of them refer to the Imperial Guptas of the fifth and sixth century AD.

The Chinese treatise known as the Hsi-yu-chi (or Si-yu- ki) is one of the classical Buddhist books of China, Korea, and Japan....

On the title-page of the Hsi-yu-chi it is represented as having been "translated" by Yuan-chuang and "redacted" or "compiled" by Pien-chi ([x]). But we are not to take the word for translate here in its literal sense, and all that it can be understood to convey is that the information given in the book was obtained by Yuan-chuang from foreign sources. One writer tells us that Yuan-chuang supplied the materials to Pien-chi who wrought these up into a literary treatise. Another states that Yuan-chuang communicated at intervals the facts to be recorded to Pien-chi who afterwards wove these into a connected narrative.

This Pien-chi was one of the learned Brethren appointed by T'ai Tsung to assist Yuan-chung in the work of translating the Indian books which Yuan-chuang had brought with him. It was the special duty of Pien-chi to give literary form to the translations. He was a monk of the Hui-chang ([x]) Monastery and apparently in favour at the court of the Emperor. But he became mixed up in an intrigue with one of T'ai Tsung's daughters and we cannot imagine a man of his bad character being on very intimate terms with the pilgrim. As to the Hsi-yu-chi we may doubt whether he really had much to do with its formation, and perhaps the utmost that can be claimed for him is that he may have strung together Yuan-chuang's descriptions into a connected narrative. The literary compositions of Yuan-chuang to be found in other places seem to justify us in regarding him as fully competent to write the treatise before us without any help from others...Some of the notes and comments may have been added by Pien-chi but several are evidently by a later hand....

The Hsi-yu-chi exists in several editions which present considerable variations both in the text and in the supplementary notes and explanations....

Under the guidance of the learned Doctors in Buddhism in these establishments he studied some of the great works of their religion, and soon became famous in China as a very learned and eloquent young monk. But he could not remain in China for he longed vehemently to visit the holy land of his religion, to see its far-famed shrines, and all the visible evidences of the Buddha's ministrations. He had learned, moreover, to be dissatisfied with the Chinese translations of the sacred books, and he was desirous to procure these books in their original language, and to learn the true meaning of their abstruse doctrines from orthodox pundits in India. After making enquiries and preparations he left the capital Ch'ang-an ([x]), the modern Hsi-an ([x])-foo, in the year 629, and set out secretly on his long pilgrimage....

After sixteen year's absence Yuan-chuang returned to China and arrived at Ch'ang-an in the beginning of 645, the nineteenth year of the reign of T'ang T'ai Tsung....

Now he had arrived whole and well, and had become a many days' wonder. He had been where no other had ever been, he had seen and heard what no other had ever seen and heard. Alone he had crossed trackless wastes tenanted only by fierce ghost-demons. Bravely he had climbed fabled mountains high beyond conjecture, rugged and barren, ever chilled by icy wind and cold with eternal snow. He had been to the edge of the world and had seen where all things end. Now he was safely back to his native land, and with so great a quantity of precious treasures. There were 657 sacred books of Buddhism, some of which were full of mystical charms able to put to flight the invisible powers of mischief. All these books were in strange Indian language and writing, and were made of trimmed leaves of palm or of birch-bark strung together in layers. Then there were lovely images of the Buddha and his saints in gold, and silver, and crystal, and sandalwood. There were also many curious pictures and, above all, 150 relics, true relics of the Buddha. All these relics were borne on twenty horses and escorted into the city with great pomp and ceremony.

The Emperor T'ai Tsung forgave the pilgrim for going abroad without permission, made his acquaintance and became his intimate friend. He received Yuan-chuang in an inner chamber of the palace, and there listened with unwearied interest from day to day to his stories about unknown lands and the wonders Buddha and his great disciples had wrought in them...On his petition the Emperor appointed several distinguished lay scholars and several learned monks to assist in the labour of translating, editing, and copying. In the meantime at the request of his Sovereign Yuan-chuang compiled the Records of his travels, the Hsi-yu-chi. The first draft of this work was presented to the Emperor in 646, but the book as we have it now was not actually completed until 648. It was apparently copied and circulated in Ms in its early form during the author's life and for some time after. When the Hsi-yu-chi was finished Yuan-chuang gave himself up to the task of translating, a task which was to him one of love and duty combined.... In the year 664 on the 6th day of the second month he underwent the great change.... he passed hence into Paradise....

His character as revealed to us in his Life and other books is interesting and attractive....Too prone at times to follow authority and accept ready-made conclusions he was yet self possessed and independent....

There were lengths, however, to which he could not go, and even his powerful friend the Emperor T'ai Tsung could not induce him to translate Lao-tzu's "Tao-Te-Ching" into Sanskrit or recognize Lao-tzu as in rank above the Buddha....His faith was simple and almost unquestioning, and he had an aptitude for belief which has been called credulity. But his was not that credulity which lightly believes the impossible and accepts any statement merely because it is on record and suits the convictions or prejudices of the individual. Yuan-chuang always wanted to have his own personal testimony, the witness of his own senses or at least his personal experience. It is true his faith helped his unbelief, and it was too easy to convince him where a Buddhist miracle was concerned. A hole in the ground without any natural history, a stain on a rock without any explanation apparent, any object held sacred by the old religion of the fathers, and any marvel professing to be substantiated by the narrator, was generally sufficient to drive away his doubts and bring comforting belief. But partly because our pilgrim was thus too ready to believe, though partly also for other reasons, he did not make the best use of his opportunities. He was not a good observer, a careful investigator, or a satisfactory recorder, and consequently he left very much untold which he would have done well to tell....

After Yuan-chuang's death great and marvellous things were said of him. His body, it was believed, did not see corruption and he appeared to some of his disciples in visions of the night. In his lifetime he had been called a "Present Sakyamuni", and when he was gone his followers raised him to the rank of a founder of Schools or Sects in Buddhism. In one treatise we find the establishment of three of these schools ascribed to him, and in another work he is given as the founder in China of a fourth school. This last is said to have been originated in India at Nalanda by Silabhadra one of the great Buddhist monks there with whom Yuan-chuang studied....

THE PREFACES TO THE HSI-YU-CHI.

There is only one Preface in the A, B, and C editions of the "Hsi-yu-chi", but the D edition gives two Prefaces.... This latter was apparently unknown to native editors and it was unknown to the foreign translators. This Preface is the work of Ching Po ([x]), a scholar, author, and official of the reigns of T'ang Kao Tsu and T'ai Tsung.... It is plain from this Preface that its author was an intimate friend of Yuan-chuang whose name he does not think it necessary to mention. He seems to have known or regarded Yuan-chuang as the sole author of the "Hsi-yu-chi", writing of him thus: — "he thought it no toil to reduce to order the notes which he had written down"....

The second Preface, which is in all editions except the Corean, is generally represented as having been written by one Chang Yueh ([x]). It has been translated fairly well by Julien, who has added numerous notes to explain the text and justify his renderings. He must have studied the Preface with great care and spent very many hours in his attempt to elucidate its obscurities. Yet it does not seem to have occurred to him to learn who Chang Yueh was and when he lived.

Now the Chang Yueh who bore the titles found at the head of the Preface above the name was born in 667 and died in 730, thus living in the reigns of Kao Tsung, Chung Tsung, Jui Tsung, and Hsuan Tsung. He is known in Chinese literature and history as a scholar, author, and official of good character and abilities. His Poems and Essays, especially the latter, have always been regarded as models of style, but they are not well known at present. In 689 Chang Yueh became qualified for the public service, and soon afterwards he obtained an appointment at the court of the Empress Wu Hou. But he did not prove acceptable to that ambitious, cruel and vindictive sovereign, and in 703 he was sent away to the Ling-nan Tao (the modern Kuangtung). Soon afterwards, however, he was recalled and again appointed to office at the capital. He served Hsuan Huang (Ming Huang) with acceptance, rising to high position and being ennobled as Yen kuo kung ([x]).

Now if, bearing in mind the facts of Chang Yueh's birth and career, we read with attention the Preface which bears his name we cannot fail to see that it could not have been composed by that official....according to the Chinese authorities and their translators Julien and Professor G. Schlegel, it was a schoolboy who composed this wonderful Preface, this "piece that offers a good specimen characterized by these pompous and empty praises, and presents, therefore the greatest difficulties, not only has a translator from the West, but still has every letter Chinese who would only know the ideas and the language of the school of Confucius." We may pronounce this impossible as the piece is evidently the work of a ripe scholar well read not only in Confucianism but also in Buddhism. Moreover the writer was apparently not only a contemporary but also a very intimate friend of Yuan-chuang.

In the A and C editions and in the old texts Chang Yueh's name does not appear on the title-page to this Preface. It is said to have been added by the editors of the Ming period when revising the Canon. Formerly there stood at the head of the Preface only the titles and rank of its author. We must now find a man who bore these titles in the Kao Tsung period, 650 to 683, and who was at the same time a scholar and author of distinction and a friend of the pilgrim. And precisely such a man we find in Yu Chih-ning ([x]), one of the brilliant scholars and statesmen who shed a glory on the reigns of the early T'ang sovereigns. ... On the death of T'ai Tsung his son and successor Kao Tsung retained Yu in favour at Court and rewarded him with well-earned honours. In 656 the Emperor appointed Yu along with some other high officials to help in the redaction of the translations which Yuan-chuang was then making from the Sanskrit books. Now about this time Yu, as we know from a letter addressed to him by Hui-li and from other sources, bore the titles which appear at the head of the Preface. He was also an Immortal of the Academy, a Wen-kuan Hsuo-shi ([x]). He was one of the scholars who had been appointed to compile the "Sui Shu" or Records of the Sui dynasty and his miscellaneous writings from forty chuan. Yu was probably a fellow-labourer with Yuan-chuang until the year 660. At that date the concubine of many charms had become all-powerful in the palace and she was the unscrupulous foe of all who even seemed to block her progress. Among these was Yu, who, accordingly, was this year sent away into official exile and apparently never returned.

We need have little hesitation then in setting down Yu Chih-ning as the author of this Preface. It was undoubtedly written while Yuan-chuang was alive, and no one except an intimate friend of Yuan-chuang could have learned all the circumstances about him, his genealogy and his intimacy with the sovereign mentioned or alluded to in the Preface. We need not suppose that this elegant composition was designed by its author to serve as a Preface to the Hsi- yu-chi. It was probably written as an independent eulogy of Yuan-chuang setting forth his praises as a man of old family, a record-beating traveller, a zealous Buddhist monk of great learning and extraordinary abilities, and a propagator of Buddhism by translations from the Sanskrit.

This Preface, according to all the translators, tells us that the pilgrim acting under Imperial orders translated 657 Sanskrit books, that is, all the Sanskrit books which he had brought home with him from the Western Lands. No one seems to have pointed out that this was an utterly impossible feat, and that Yuan-chuang did not attempt to do anything of the kind. The number of Sanskrit texts which he translated was seventy four, and these seventy four treatises (pu) made in all 1335 chuan. To accomplish this within seventeen years was a very great work for a delicate man with various calls on his time.

The translations made by Yuan-chuang are generally represented on the title-page as having been made by Imperial order and the title-page of the Hsi-yu-chi has the same intimation. We know also from the Life that it was at the special request of the Emperor T'ai Tsung that Yuan-chuang composed the latter treatise. So we should probably understand the passage in the Preface with which we are now concerned as intended to convey the following information. The pilgrim received Imperial orders to translate the 657 Sanskrit treatises, and to make the Ta-T'ang-Hsi-yu-chi in twelve chuan, giving his personal observation of the strange manners and customs of remote and isolated regions, their products and social arrangements, and the places to which the Chinese Calendar and the civilising influences of China reached....

At the beginning of Chuan I of the Records we have a long passage which, following Julien, we may call the Introduction. In a note Julien tells us that according to the editors of Pien-i-tien, this Introduction was composed by Tschang-choue (i.e. Chang Tue), author of the preface to Si-yu-ki". Another native writer ascribes the composition of this Introduction to Pien-chi. But a careful reading of the text shews us that it could not have been written by either of these and that it must be regarded as the work of the pilgrim himself. This Introduction may possibly be the missing Preface written by Yuan-chuang according to a native authority....

What our author here states to his reader is to this effect...
His Majesty ascended the throne" in accordance with Heaven, and taking advantage of the times it concentrated power to itself. [His Majesty] has made the six units of countries into one empire and this his glory fills; he is a fourth to the Three Huang and his light illumines the world. His subtle influence permeates widely and his auspicious example has a far-reaching stimulus....in founding an imperial inheritance for his posterity, in bringing order out of chaos and restoring settled government...and in raising men from mud and ashes, he had far transcended the achievements of the founders of the Chow and Han dynasties....

"In more than three-fifths of the places I traversed", all living creatures feel the genial influence [of H. Ms. reign] and every human being extols his merit. From Ch'ang-an to India the strange tribes of the sombre wastes, isolated lands and odd states, all accept the Chinese calendar and enjoy the benefits of H. Ms. fame and teaching. The praise of his great achievements in war is in everybody's mouth and the commendation of his abundant civil virtues has grown to be the highest theme... Were there not the facts here set forth I could not record the beneficial influences of His Majesty. The narrative which I have now composed is based on what I saw and heard."

This is an address well spiced with flattery in good oriental fashion.... The founder of the T'ang dynasty, it should be remembered, was neither a hero nor a man of extraordinary genius, and he came near being a prig and a hypocrite. His loyalty and honour were questioned in his lifetime, and history has given him several black marks. While sick of ambition, he was infirm of purpose, and wishing to do right he was easily swayed to do what was wrong.... But all his success in later life, and the fame of his reign were largely due to the son who succeeded him on the throne....

The splendour of T'ai Tsung's great achievements, the conspicuous merits of his administration, and the charm of his sociable affable manner made the people of his time forget his faults.... So it came that the historian, dazed by the spell and not seeing clearly, left untold some of the Emperor's misdeeds and told others without adding their due meed of blame. For this great ruler smutched his fair record by such crimes as murder and adultery. The shooting of his brothers was excusable and even justifiable, but his other murders admit of little palliation and cannot plead necessity. Though he yielded to his good impulses, again, in releasing thousands of women who had been forced into and kept in the harem of Sui Yang Ti, yet he also yielded to his bad impulses when he took his brother's widow and afterwards that maid of fourteen, Wu Chao, into his own harem. His love of wine and women in early life, his passion for war and his love of glory and empire, which possessed him to the end, were failings of which the eyes of contemporaries dazzled by the "fierce light" could not take notice....

It was during the reign of this sovereign, in the year 636, that Christianity was first introduced into China. The Nestorian missionaries, who brought it, were allowed to settle in peace and safety at the capital. This was the boon which called forth the gratitude of the Christian historian and enhanced in his view the merits of the heathen sovereign.

The author next proceeds to give a short summary of the Buddhistic teachings about this world and the system of which it forms a constituent. He begins —
Now the Saha world, the Three Thousand Great Chiliocosm, is the sphere of the spiritual influence of one Buddha. It is in the four continents (lit. "Under heavens") now illuminated by one sun and moon and within the Three Thousand Great Chiliocosm that the Buddhas, the World-honoured ones, produce their spiritual effects, are visibly born and visible enter Nirrvana, teach the way to saint and sinner...

The author next proceeds to make a few summary observations...
From the Black Range on this side (i.e. to China) all the people are Hu: and though Jungs are counted with these, yet the hordes and clans are distinct, and the boundaries of territories are defined....

"For the most part [these tribes] are settled peoples with walled cities, practising agriculture and rearing cattle. They prize the possession of property and slight humanity and public duty (lit. benevolence and righteousness). Their marriages are without ceremonies and there are no distinctions as to social position: the wife's word prevails and the husband has a subordinate position. They burn their corpses and have no fixed period of mourning. They flay (?) the face and cut off the ears: they clip their hair short and rend their garments. They slaughter the domestic animals and offer sacrifice to the manes of their dead. They wear white clothing on occasions of good luck and black clothing on unlucky occasions. This is a general summary of the manners and customs common to the tribes, but each state has its own political organization which will be described separately, and the manners and customs of India will be told in the subsequent Records."

This brief and terse account of the social characteristics common to the tribes and districts between China and India presents some rather puzzling difficulties. It is too summary, and is apparently to a large extent secondhand information obtained from rather superficial observers, not derived from the author's personal experience, and it does not quite agree with the accounts given by previous writers and travellers. Thus the pilgrim states that the tribes in question had no fixed period of mourning, that is, for deceased parents, but we learn that the people of Yenk'i observed a mourning of seven days for their parents. Nor was it the universal custom to burn the dead; for the T'ufan people, for example, buried their dead.

-- On Yuan Chwang's Travels in India, 629-645 A.D., by Thomas Watters M.R.A.S.

The assumption that the monasteries of Nalanda were the creation of the Gupta emperors beginning with Kumaragupta I receives confirmation from the fact that Fa-hien, the Chinese pilgrim of the early fifth century AD [337-422 CE], does not mention the monastic establishments of Nalanda. He speaks of the village of Nalo, the place of birth and death of Sariputra, and of a stupa existing here.11 As has been suggested above, this place is identical with Nalanda, but the absence of any other monument except a stupa at the time of Fa-hien is significant.

Hiuen-Tsang saw here an 80-ft. high copper image of the Buddha raised by Purnavarman,12 belonging to the early sixth century AD. And the illustrious Harshavardhana of Kanauj (606-647) no doubt greatly helped the institution by his munificence: he built a monastery of brass, which was under construction when Hiuen-Tsang visited the place. The biographer of Hiuen-Tsang says that Harsha remitted ‘the revenues of about a hundred villages as an endowment of the convent and two hundred householders in these villages contributed the required amount of rice, butter and milk’. ‘Hence,’ he adds, ‘the students here, being so abundantly supplied, do not require to ask for the four requisites. This is the source of the perfection of their studies, to which they have arrived.’ This statement makes it clear that the students did not have to beg for their daily food.

Harsha highly revered the Nalanda monks and called himself their servant.13 About a thousand monks of Nalanda were present at the royal congregation at Kanauj.[???] Royal patronage was, therefore, the keynote of the prosperity and efficiency of Nalanda. As Hiuen-Tsang [602–664] says, ‘A long succession of kings continued the work of building, using all the skill of the sculptor, till the whole is truly marvellous to behold.’14
Kumaragupta I/Shakraditya (r. c. 415–455 CE)
Skandagupta (r. c. 455-467 CE)
Purugupta (r. c. 467–473 CE)
Kumaragupta II (r. c. 473-476 CE)
Budhagupta ( r. c. 476- 495 CE)
Narasimhagupta (r. c. 495-530 CE)
Kumaragupta III (r. c. 530-540 CE)
Vishnugupta (r. c. 540–550 CE) (Last king of the Gupta Empire)

-- by Wikipedia

Gupta rulers patronised the Hindu religious tradition and orthodox Hinduism reasserted itself in this era.

-- Gupta Empire: Origins, Religion, Harsha and Decline, by factsanddetails.com/india

***

[T]he Gupta rulers practiced Hindu rituals and traditions ...

-- The Gupta Period of India, by ushistory.org

Hiuen-Tsang also recounts a few of the monasteries and temples that he saw here, giving their directions in most cases. Thus, the monastery built by Buddhagupta was to the south of the one built by his father Sakraditya; to the east of Buddhagupta’s monastery was the one of Tathagatagupta; the one built by Baladitya was to the north-east of the last; while Vajra’s monastery was to the west. After this an unnamed king of mid-India is said to have built a great monastery to the north and erected a high wall with one gate round these edifices. Hiuen-Tsang also gives a long list of the other monasteries and stupas that he found. Modern attempts to identify them with the existing ruins have met with scanty success, as the six centuries that separated Hiuen-Tsang and the final desertion of the site must have produced many new buildings and modified the existing ones.

Hiuen-Tsang was very warmly received at Nalanda and resided here for a long time. The courses of study were based on secular ideals including the scriptures of the Mahayana and Hinayana schools, hetu-vidya (logic), sabda-vidya (grammar) and chikitsa-vidya (medicine), as well as purely Brahmanical texts such as the Vedas including the Atharvaveda. From the accounts of the pilgrim it is clear that Nalanda was bustling with literary activities.

Hiuen-Tsang received here the Indian name Mokshadeva and was remembered by the inmates of the Nalanda monastery long after he had left the place.[???] Several years after his return to China, Prajnadeva, a monk of Nalanda, sent him a pair of clothes, saying that the worshippers every day went on offering to Hiuen-Tsang their salutations.[???]


Nalanda had by then acquired a celebrity status spread all over the east as a centre of Buddhist theology and secular educational activities. This was evident from the fact that within a short period of thirty years following Hiuen-Tsang’s departure, no less than eleven Chinese and Korean travellers were known to have visited Nalanda.15 [Samuel Beal, Life of Hiuen-Tsang (London, 1911), pp. 177.]
KAU-FA-KAO-SANG-CHUEN.
(Nanj. Cat. 1491.)


III. The author in the preface having alluded to the journeys of Fa-hian and Hiuen-Tsiang, who proceeded to the western countries to procure books and pay reverence to the sacred relics, passes on to notice the hardships and dangers of the route, and the difficulty of finding shelter or entertainment in the different countries visited by their successors, pilgrims to the same spots, and that in consequence of there being no temples (monasteries) set apart for Chinese priests. He then goes on to enumerate the names of the pilgrims referred to in his memoirs....

-- The Life of Hiuen-Tsiang, by the Shaman Hwui Li, With an Introduction Containing An Account of the Works of I-Tsing, by Samuel Beal, B.A., D.C.L., Professor of Chinese, University College, London, With a Preface by L. Cranmer-Byyng, 1911
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Part 2 of 2

Next in importance to Hiuen-Tsang stands I-tsing, who reached India in 673 AD and studied at Nalanda for a considerable time. His work records very minute details about the life led by the Nalanda monks that he regarded as the ideal to be followed by the Buddhists all over the world. He said that the number of monks of the Nalanda monastery exceeded three thousand in number, maintained by more than two hundred villages bestowed by previous kings.16 He also gave details of the curriculum which, besides the Buddhist scriptures, included logic, metaphysics and a very extensive study of Sanskrit Grammar.17 He further testified to the strict rules of discipline that the monks observed, their daily life being regulated by a water-clock.18

I Ching or Yi Jing (635-713) was a Tang Dynasty Buddhist monk, originally named Zhang Wen Ming, who traveled by sea to India and studied at Nalanda for eleven years before returning with a collection of as many as 500,000 Sanskrit stanzas. He translated more than 60 sutras into Chinese, including Saravanabhava Vinaya, Avadana, stories of great deeds, and Suvarnaprabhascottamaraja-sutra, (Sutra of the Most Honored King). He also is responsible for the translation of eleven Buddhist tantras and eighteen works on monastic discipline, as well as exegetic works....

I Ching was born Zhang Wen Ming in 635 in Qizhou (modern Shandong province). He left his family at the age of 7 to live in a Buddhist monastery, where he studied under two monks, Shanyu (d. 646) and Huizhi....

I Ching was an admirer of two traveling monks: Fa Xian, who traveled to Nepal, India and Sri Lanka between 399 and 412 to acquire Buddhist scriptures and take them back to China, and visited Lumbini, the birthplace of Lord Buddha[???];
In Watters’ book ‘On Yuan Chwang’s Travels in India’ (prepared from an unpublished manuscript after his death) the following statement is found with reference to the Lumbini site:
‘Yuan-chuang, as we have seen, mentions a stone pillar, but he does not say anything about an inscription on it. The Fang-chih, however, tells us that the pillar recorded the circumstances of Buddha's birth’.

The Fang-chih -– a shortened version of Yuan-chuang’s account -- does nothing of the sort, since though it also refers to a stone pillar at Lumbini, no inscription ‘recording the circumstances of Buddha’s birth’ is mentioned in this text either. Watters, a great Sinologist, was referred to by V. A. [Vincent Arthur] Smith as ‘one of the most brilliant ornaments’ of Chinese Buddhist scholarship, and it is inconceivable that he would have made this critical mistake. Indeed, when Smith asserted that the Lumbini pillar inscription ‘set at rest all doubts as to the exact site of the traditional birthplace of Gautama Buddha’, Watters acidly retorted that ‘it would be more correct to say that the inscription, if genuine, tells us what was the spot indicated to Asoka as the birthplace of the Buddha’. Note that ‘if genuine’: this shows that Watters not only had his doubts about this inscription, but that he was also prepared to voice those doubts in public. Moreover, according to Smith, ‘Mr Watters writes in a very sceptical spirit, and apparently feels doubts as to the reality of the Sakya principality in the Tarai'. From all this, it will clearly be seen that this Fang-chih ‘mistake’ was totally at variance with Watters’ ‘very sceptical spirit’ regarding these supposed Nepalese discoveries (Lumbini included); and I shall therefore charge that it was a posthumous interpolation into Watters’ original text by its editors, Rhys Davids, Bushell, and Smith. If this charge is correct –- and I am quite sure that it is -- then the reasons behind this appalling deception can only be guessed at, I need hardly add.

-- Lumbini On Trial: The Untold Story. Lumbini Is An Astonishing Fraud Begun in 1896, by T. A. Phelps

and Xuanzang (Hsüan-tsang, pronounced Shwan-dzang, d. 664), who made a seventeen-year trip overland to India and back in the early Tang period....

I Ching was inspired to make his own mission to India. Provided with funding by an otherwise unknown benefactor named Fong, he decided to visit the famous Buddhist university of Nalanda, in Bihar, India, to further study Buddhism.... I Ching began his journey in 671. Unlike pilgrims before him, he could not take the land route to India across central Asia and the Himalayas because of political turmoil in Tibet and Afghanistan and the surrounding areas. Instead, he made his way to India by sea, taking a more southerly route....

Traveling by a Persian boat out of Guangzhou, he arrived in Srivijaya (today's Palembang of Sumatra) after 22 days, where he spent the next 6 months learning Sanskrit grammar and Malay language.

He then passed through the Strait of Malacca to the northwest tip of Sumatra, where he boarded a ship going to the Nicobar Islands....In 673 after ten days’ travel across the Bay of Bengal he reached the "naked kingdom" (south west of Shu).

I Ching studied Sanskrit for a year in the Buddhist temple of Vahara at the port of Tāmraliptī, in the delta of the Ganges River, then traveled to Nālandā with another Chinese monk, Dachengdeng (d. 675). They followed a group of merchants and traveled to 30 principalities. They visited sacred sites in Gṛdhrakūṭa at Rājagṛha and Mahābodhi at Bodh Gayā, traveled to Vaiśālī, Amaraba, and Kāśī (Banaras), visited Jetavana Monastery at Śrāvastī and the "heavenly stairs" (said to have been built by the god Śakra for the Buddha to use in descending from Heaven) at Sāmkāśya, and journeyed to Sārnāth and Kukkuṭapāda. They encountered mountains, woods, and swamps on the way to Nalanda. Halfway to Nalanda, Yi Jing fell ill and was unable to walk; gradually he was left behind by the group. He was looted by bandits and stripped naked. He heard the natives would catch white skins to offer as a sacrifice to the gods, so he jumped into mud and used leaves to cover his lower body. Walking slowly, he reached Nalanda where he stayed for 11 years.

At Nalanda, I Ching studied Buddhist logic, the Abhidharmakośa, monastic discipline (Vinaya), and the Mādhyamika and Yogācāra philosophies.... I Ching studied and copied original Sanskrit texts of Buddhist religious writings, and collected some 500,000 Sanskrit stanzas that he believed would fill 1,000 volumes when translated into Chinese.

With the manuscripts he had collected at Nālandā, Yijing left central India for Tāmraliptī in 685. Making his way home the same way he had come, he made short stops at Kacha and Malayu. When I-Ching again arrived at Śrīvijaya in 687, he decided to stay and begin the translation of his collection, hoping to complete it in about ten years. In 689, he found he needed more supplies for copying the Sanskrit manuscripts. He went to the port to send a letter to China requesting paper and ink, which were not available in Śrīvijaya at that time. While he was drafting his message, the ship unexpectedly set sail with him on board. On August 10, 689, he reached Guangfu, where he recruited four assistants. He returned with them to Śrīvijaya on December 18, 689, and they remained there until 695, working on the translations. In Śrīvijaya, I Ching studied under the distinguished teacher Śākyakīrti, and wrote an account of Buddhist practices and a report regarding a group of Chinese monks who had traveled to India in search of Buddhism. Yijing sent these reports, together with his translations of Buddhist texts, to China with one of his assistants in 692. I-Ching also produced a detailed geographic account of his travels through India, through the East Indies islands and along the Malay Peninsula....

Accompanied by two assistants, I Ching returned to Guangfu in 694. In 695, he traveled to Luoyang, where he received a grand welcome from Empress Wu.
In 689 Chang Yueh became qualified for the public service, and soon afterwards he obtained an appointment at the court of the Empress Wu Hou. But he did not prove acceptable to that ambitious, cruel and vindictive sovereign, and in 703 he was sent away to the Ling-nan Tao (the modern Kuangtung).

-- On Yuan Chwang's Travels in India, 629-645 A.D., by Thomas Watters M.R.A.S.

He lived at Foshouji Monastery and worked as an assistant translator in the bureau of translations headed by Siksananda. From 700 until his death, I Ching was in charge of his own bureau of translation of Buddhist canons at Luoyang and Chang'an. He translated fifty-six works in 230 fascicles, among them scriptures, commentaries, and Vinaya texts under the patronage of the empress and her successors, who provided forewords to I Ching's translations. Honors and rewards were bestowed upon him, and he was awarded the title "Master of the Tripiṭaka."

I Ching died on February 16, 713. He was buried with grand honors....

I Ching’s entire journey lasted 25 years. He brought back approximately 400 Buddhist translated texts. He translated more than 60 sutras into Chinese...

He also translated 11 Buddhist tantras and 18 works on monastic discipline, as well as exegetic works that are important not only for Chinese Buddhism but for the religion as a whole. His translation of the Sarvāstivāda Vinaya texts systematically preserved one of the most influential monastic traditions in India, and his translations of the Yogācāra texts and of Buddhist logic are quite significant.... His glossary, the Fanyu qianziwen (A Thousand Sanskrit Words), is the earliest extant Sanskrit-Chinese dictionary. Although the translations of his predecessor, Xuanzang [602 – 664], overshadow those of I Ching, a sample examination of both renderings of the Viṃśatikā (Liebenthal, 1934) concluded that Yijing was a better translator than Xuanzang.

I Ching praised the high level of Buddhist scholarship in Srivijaya and advised Chinese monks to study there prior to making the journey to Nalanda, India.
"In the fortified city of Bhoga, Buddhist priests number more than 1,000, whose minds are bent on learning and good practice. They investigate and study all the subjects that exist just as in India; the rules and ceremonies are not at all different. If a Chinese priest wishes to go to the West in order to hear and read the original scriptures, he had better stay here one or two years and practice the proper rules…."

I Ching's visits to Srivijaya gave him the opportunity to meet with others who had come from other neighboring islands.

Srivijaya was a Malay Buddhist thalassocratic [maritime] empire based on the island of Sumatra (in modern-day Indonesia), which influenced much of Southeast Asia. Srivijaya was an important centre for the expansion of Buddhism from the 7th to the 12th century AD. Srivijaya was the first unified kingdom to dominate much of the Malay Archipelago. The rise of the Srivijayan Empire was parallel to the end of the Malay sea-faring period. Due to its location, the Srivijaya developed complex technology utilizing maritime resources. In addition, its economy became progressively reliant on the booming trade in the region, thus transforming it into a prestige goods-based economy.

The earliest reference to it dates from the 7th century. A Tang dynasty Chinese monk, Yijing, wrote that he visited Srivijaya in year 671 for six months.[???!!!] The earliest known inscription in which the name Srivijaya appears also dates from the 7th century in the Kedukan Bukit inscription found near Palembang, Sumatra, dated 16 June 682. Between the late 7th and early 11th century, Srivijaya rose to become a hegemon in Southeast Asia. It was involved in close interactions, often rivalries, with the neighbouring Mataram, Khmer and Champa. Srivijaya's main foreign interest was nurturing lucrative trade agreements with China which lasted from the Tang to the Song dynasty. Srivijaya had religious, cultural and trade links with the Buddhist Pala of Bengal, as well as with the Islamic Caliphate in the Middle East.

Before the 12th century, Srivijaya was primarily a land-based polity rather than a maritime power, fleets are available but acted as logistical support to facilitate the projection of land power. In response to the change in the maritime Asian economy, and threatened by the loss of its dependencies, Srivijaya developed a naval strategy to delay its decline. The naval strategy of Srivijaya was mainly punitive; this was done to coerce trading ships to be called to their port. Later, the naval strategy degenerated to raiding fleet.

The kingdom ceased to exist in the 13th century due to various factors, including the expansion of the competitor Javanese Singhasari and Majapahit empires. After Srivijaya fell, it was largely forgotten. It was not until 1918 that French historian George Cœdès, of l'École française d'Extrême-Orient, formally postulated its existence.[!!!]

-- Srivijaya, by Wikipedia

George Cœdès (10 August 1886 – 2 October 1969) was a 20th-century French scholar of southeast Asian archaeology and history.

Cœdès was born in Paris to a family of supposed Hungarian-Jewish émigrés. In fact, the family was known as having settled in the region of Strasbourg before 1740. His ancestors worked for the royal Treasury. His grandfather, Louis Eugène Cœdès was a painter, pupil of Léon Coignet. His father Hyppolite worked as a banker.

Cœdès became director of the National Library of Thailand in 1918, and in 1929 became director of L'École française d'Extrême-Orient [EFEO: French School of the Far East. Since 1907, the EFEO has been in charge of conservation work at the archeological site of Angkor.], where he remained until 1946.
Thereafter he lived in Paris until he died in 1969.

In 1935 he married Neang Yao.

He was also an editor of the Journal of the Siam Society during the 1920s.

He wrote two texts in the field, The Indianized States of Southeast Asia (1968, 1975) (first published in 1948 as Les états hindouisés d'Indochine et d'Indonésie) and The Making of South East Asia (1966), as well as innumerable articles, in which he developed the concept of the Indianized kingdom. Perhaps his greatest lasting scholarly accomplishment was his work on Sanskrit and Old Khmer inscriptions from Cambodia. In addition to scores of articles (especially in the Bulletin of the École française d'Extrême-Orient), his 8-volume work Inscriptions du Cambodge (1937-1966) contains editions and translations of over a thousand inscriptions from pre-Angkorian and Angkor-era monuments, and stands as Cœdès' magnum opus. One stele, the recently rediscovered K-127, contains an inscription of what has been dubbed the "Khmer Zero", the first known use of zero in the modern number system. The transliteration system that he devised for Thai (and Khmer) is used by specialists of Thai and other writing systems derived from that of Khmer.

George Cœdès is credited with rediscovering the former kingdom of Srivijaya, centred on the modern-day Indonesian city of Palembang, but with influence extending from Sumatra through to the Malay Peninsula and Java.

-- George Cœdès, by Wikipedia

According to him, the Javanese kingdom of Ho-ling was due east of the city of Bhoga at a distance that could be covered in a sea journey of four or five days. He also wrote that Buddhism was flourishing throughout the islands of Southeast Asia. "Many of the kings and chieftains in the islands of the Southern Sea admire and believe in Buddhism, and their hearts are set on accumulating good actions."

-- I Ching (monk), by New World Encyclopedia

The Pala emperors held east India from the eighth to the twelfth century AD and were noted for their patronage of Mahayana Buddhism. At the same time they established monasteries at Vikramasila and Odantapuri in Bihar.19 It was even stated by Taranatha that the head of the Vikramasila monastery had control over Nalanda. Still, there are ample epigraphic and literary evidences to show that the Palas continued to be liberal in their munificence to Nalanda.

Mention may here be made of some famous scholars who, by their deep learning and excellence in conduct, created and maintained the dignity which Nalanda enjoyed. It has been already stated above that the early Mahayana philosophers, Nagarjuna, Aryadeva, Asanga and Vasubandhu, were all, according to Taranatha, the high priests (pandita) of Nalanda. Next in point of chronology comes Dinnaga, the founder of the medieval school of logic; he was a southerner who was invited to Nalanda to defeat in disputation a Brahmanist scholar and received the title tarkapungava. The next famous pandita was Dharma Pala, who had retired just before Hiuen-Tsang arrived. At the time of the pilgrim the head of the monastery was Silabhadra, under whom the pilgrim studied and whose scholarship and personal qualities he described eloquently. Silabhadra was probably succeeded by Dharmakirti, who is credited by Taranatha to have defeated a Brahmanical philosopher, Kumarila.

The next important figure was Santarakshita, who was invited by King Khri-sron-deu-tsan to Tibet, where he lived for many years till his death in 762. About the same time Tibet was also visited by Padmasambhava, who acquired great fame as the founder of the institution of Lamaism in Tibet. It was no mean honour for Nalanda that one of its scholars gave to the Tibetan religion a form that is continuing to the present day.

Thus, Nalanda succeeded in attracting the best Buddhist scholars whose fame spread to distant countries and persisted through the ages. Rightly has it been said that ‘a detailed history of Nalanda would be a history of Mahayanist Buddhism’.20

It is evident from the account of Hiuen-Tsang that Buddhism was slowly decaying when he visited India. Important centres of early Buddhism were deserted, though some new centres, such as Nalanda in the east, Valabhi in the west and Kanchi in the south, had sprung up.[???] After some time Buddhism lost its hold in other provinces and flourished only in Bihar and Bengal, where royal patronage succeeded in keeping alive a dying cause. But it is clear that Buddhism was no longer popular and centred round a few monasteries. The Buddhism that was practised at these places was no longer of the simple Hinayana type, nor even had much in common with the Mahayana of the earlier days, but was strongly inbued with the ideas of Tantricism, inculcating belief in the efficacy of charms and spells and involving secret practices and rituals.

The crusade of the Brahmanical philosophers and preachers such as Kumarila and Sankara-charya in the eighth century must have been another potent factor in rendering Buddhism unpopular. They are reported to have travelled all over India, defeating the Buddhists in arguments and retionale.

On the other hand it has been propagated that Muslim invaders drove away the monks and damaged the monasteries, but it does not stand correct in the light of scrutiny of the facts. The whole story of Muslim invasion has been woven on the basis of “Tabaqat-i-Nasiri” of Minhaj-i-Siraj, without going through the text honestly. The text reads as follows: “Bakhtiyar Khalji organised an attack upon the fortified city of Bihar and he advanced to the gateway of the fortress with two hundred horsemen in defensive armour and suddenly attacked the place. Muhammad-i-Bakhtiyar Khalji, by the force of his intrepidity, threw himself into the postern of the gateway of the palace, and they captured the fortress and acquired great booty (Tabaqat-i-Nasiri, tr. H.G. Raverty, Calcutta, 1881, pp. 552) The greater number of inhabitants of that place were Brahmans, and the whole of those Brahmans had their heads shaven; and they were all slain. There were a great number of books there; and, when all these books came under the observation of the Musalmans, they summoned a number of Hindus that they might give them information regarding the import of those books; but the whole of the Hindus were killed. On becoming acquainted with the contents of the books, it was found that the whole of that fortress and the city was a college called Vihara.

The above account mentions the fortress or Vihara as the target of Bakhtiyar’s attack. The fortified monastery which Bakhtiyar captured was known as “Audand Vihara” or “Odanda-pura—Vihara” (Odantapuri in Biharshariff, then known simply as Vihara). He did not go to Nalanda from Biharshariff, rather he moved Nadia in Bengal through the hills and jungles of the Jharkhand region, which is attested to by an inscription of 1295 AD. So, destruction and burning of the university of Nalanda by Bakhtiyar Khalji is based on concoction and imagination. It is clear from the above mentioned facts that Bhaktiyar Khalji invaded and conquered parts of Bihar and destroyed the Mahavihara in the region,22 but he did not move towards Nalanda from Biharshariff; so, the question of destruction and burning of Nalanda Mahavihara does not arise. (The above facts in detail are from Professor D.N. Jha’s account in sacw.net of July 9, 2014.)

Two Tibetan traditions tell a tale of destruction of Nalanda Mahavihara by Tirthika’s fire. History of Buddhism in India by Lama Tara Nath [Taranatha] (17th century AD) and Pag-Sam-Jon-Zang by Sumpa Khan (18th century AD) narrate the event of destruction almost in the same manner.[!!!] Both the narratives agree that “during the consecration of the temple built by Kakutsiddha at Nalanda, the young naughty Sarmanas threw slops at the two tirthika beggars and kept them pressed inside door panels and set ferocious dogs on them.” Angered by this, one of them went on arranging for their livelihood and the other sat in a deep pit and “engaged himself in Suryasadhana (solar worship), first for nine years and then for three more years and having thus ‘acquired mantrasiddhi’ he performed a sacrifice and scattered the charmed ashes all around”, which immediately resulted in a fire, that consumed all the eighty-four temples and the scriptures some of which, however, were saved by water flowing from an upper floor of the nine-storey Ratnodadhi temple.23 (Professor D.N. Jha’s account, op. cit.) The above facts indicate that there was longstanding antagonism between Brahmins and Buddhists which resulted in destruction of Nalanda by fire.

Destruction by fire is confirmed by excavations also. While excavating the sites the excavators are frequently seen commenting that the particular monastery was probably destroyed by fire; but they do not state the probable causes of such fires. We have nowhere any evidence to suggest that the fires were caused by outside agencies or in the course of any political catastrophe except for a solitary instance as quoted in a Tibetan source alleging that the Brahmins deliberately set fire to the famous library.

One inscription of about 1003 AD, found at the temple site no. 12, actually refers to such destruction by fire and something saved from it and a grant made by one Baladitya of Telhada near Nalanda. It does not, however, say how the fire was caused. Unfortunately, the inscription does not refer to what was actually destroyed, whether it was the temple itself in the ruins of which it was found or a monastery nearby. The record is on a piece of a stone door-jamb. It does not mention Nalanda by name. It has been presumed that it refers to the restoration of the temple. From the list of inscriptions from Nalanda it may also be observed that this is the last datable inscription so far known to us and found at Nalanda.

It has been stated that the temple shows clear indications that it was restored during the declining day of Buddhism as inferred from its “plain exterior” and from traces of a protective compound wall seen around it. If Baladitya had really restored this temple, or had done a part of the work, as appears quite probable, the fact would be very significant for the history of Nalanda and its final end. It would give an impression that the end of Nalanda was fast approaching by the first decade of the 11th century AD.24 Unfortunately, the antiquities and finds from the excavations have not been closely studied and dated; though we can say that the above is the latest datable inscription so far known and recovered from the ruins. There is, therefore, reason to believe that Nalanda had met its final end some time in the 11th century AD, that is, more than hundred years before Bakhtiyar Khilji invaded Bihar in 1197 AD.[???]

_______________

References

1. In ancient literature both the forms Nalanda and Nalanda occur indiscriminately.

2. Hirananda Sastri in Proceedings of the Fifth Oriental Conference, I (Lahore, 1930).

3. B.C. Law, Geography of Early Buddhism (London, 1932).

4. Chattopadhyay, D.P., History of Buddhism in India, Calcutta.

5. [Saqmuel] S. Beal, Buddhist Records of the Western World (London, 1906), II, p. 167. The derivation na-alam-da has been proposed, but it does not convey the sense that it is intended to.

6. Chattopadhyay, D.P., op. cit., pp. 65 ff.

7. Ibid., p. 68ff.

8. Ibid., p. 83.

9. Some scholars are in favour of a date earlier by a century.

10. Chattopadhyay, D.P., op. cit., p. 122.

11. For Hiuen-Tsang’s description of Nalanda, see [Samuel] Beal, op. cit., pp. 167ff. His biographer, Hwui Li, adds some interesting details: [Samuel] S. Beal, Life of Hiuen-Tsang (London, 1911), pp. 109ff.

12. Legge, Travels of Fa-hien (Oxford, 1886), p. 81.

13. Beal, Records, II, p. 118.

14. Beal, Life, p. 160.

15. Beal, Life, p. 177.

16. For a list, see Beal, Life, pp. XXVIIIff.

17. J. Takakusu, A Record of the Buddhist Religion (Oxford, 1896), pp. 65 and 154.

18. Takakusu, op. cit., pp. 167ff. It appears from his account that all the existing grammatical texts of the Paninian school, including the Ashtadhyayi itself, were taught to the students. It is strange that in spite of this the Buddhist texts in Sanskrit should have been written in incorrect language.

19. Ibid., p. 145.

20. Vikramasila was founded by Dharmapala (Chattopadhyay, D.P., op. cit., p. 217) and is generally identified with Patharghata in Bhalgalpur District, Bihar. Odantapuri or Uddandapura was erected near Nalanda by either Gopala or Devapala, ibid., pp. 204 and 206, and may be identified with modern Biharshariff in Nalanda District. Jagaddala was founded by Ramapala, one of the last kings of the dynasty, somewhere in North Bengal.

21. Chattopadhyay, D.P., op. cit., p. 2018.

22. Chattopadhyay, D.P., op. cit., p. 131ff.

23. The identification with the famous Brahmana mimamsaka Kumarila is at once suggested but does not seem to be very likely as Kumarila probably lived somewhat later.

24. Encyclopaedia of Religion and Ethics, IX (Edinburgh, 1917), s.v. Nalanda.

Professor O.P. Jaiswal is a Retired University Professor, Patna University.
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