The Pythagorean Sourcebook and Library

[admin]

INDEX OF SELECT TOPICS

Alcmaeon, 151
analogia, 29, 37
Anaximenes, Letter to, of Pythagoras, 155
Apeiron, see Unlimited
Apollo, 30; as the One, 41; see also Pythios
Apolionius of Tyana, The Life of, 40
Apothems of Aristoxenus, 243
Archytas, The Fragments of, 177-201
Arithmetic, Introduction to, 41
arithmetic mean; see mean, arithmetic
Arithmetic, On, 43
arithmology, 321; in Plutarch, 40
Athletics, On, 62

catharsis, 31, 36, 84-85
Chronicles (of Duris), 123
church fathers, 297-98
Clinias, A Fragment of, 265
Common Mathematical Science, On the, 42
Commentaries (of Favorinus), 144
Constitution of the Delians, 145
counter-earth, 129, 170, 301
Croton, 143

decad, 133, 137, 171, 175
Description of the Earth, 124
Divergence of the Academics from Plato, On
the, 41
dodecahedron, 116
dogmata agrapha, 38
doxographers, 307; fragments from, 307-314
Dream of Scipio, Commentary on the, 42
dualism, 33-34, 51-52
duality, 22
dyad, 21, 133, 137; indefinite, 24, 38, 42,
148, 308

elements, four, 174, 206-208, 291-292
Ethical Fragments of Hierocles, 275-86
Exhortation to Philosophy, 42

Fables, 123
Felicity of Families, On the, 235-37
friendship, 112-114

gematria, 41, 53
geometric mean; see mean, geometric
Geometry, Introduction to, 41
gnomon, 24, 300
Gods, Concerning the, 80, 93
Golden Verses of Pythagoras, The, 163-65
Good, On the, 41
Greek dialects, the antiquity of, 115

harmonic mean; see mean, harmonic
harmonic proportion (6:8::912), 24-28, 169,
as "metaphysical octave, " 50; see also
harmonics, musical proportions
harmonics, 24-28, 86-88
Harmonics, Manual of, 41
harmony, 22; etymology of, 51; and health,
28; and justice, 36; of Limit and
Unlimited, 168; as mediation, 25; as a
blending of opposites, 28; in the soul, 33;
and symmetry, 28
Harmony of a Woman, On the, 239-41
"Hearers;" see Pythagorean school,
akousmatikoi
Helothales, the Father of Epicharmus of Cos,
143
Hermes, 69, 149
Histories (of Lycus), 124
History of Alexander, 144
History of Philosophy in Ten Books, 42
History of Sicily, 49, 155
Hoopoe, 41
Human Life, Concerning, 245-46
Hymn to Number, 51
Hyperboreans, 13; see also Abaris

Illustrious Virtuous Men, On, 124, 141
Incredible Things Beyond Thule, On the, 125
Indestructibility of the Soul, On the, 41

justice, 253; as proportion, 33; see also, harmony,
philosophy, political, logos
Justice, On, 253

Kingdom, Concerning a, 222-224
Kingdom, On a, (of Ecphantus), 257-59
Kingdom, On a, (of Sthenidas), 255
knowledge, as harmonic element, 34
kosmos, 22, 139, 299

Laws, On, 215
Limit, 22-24, 29, 46, 168, 171-72, 182-83,
251, 301. 304
Lives of Satyrus, Epitome of the, 152
logos, 25

Marriage of Philology and Mercury, 42
Mathematics Useful for Understanding Plato,
41
mathematikoi; see Pythagorean school,
mathematikoi
maxims, Pythagorean; see Pythagorean
school, symbols and maxims
mean, arithmetic, 25; geometric, 28; harmonic,
25
microcosm, man as, 31, 139
Middle Platonism, 40-42
Miscellaneous History, 144-45, 154
monad, 40, 42, 133, 137, 148, 171, 179; as
origin of all things, 138
monochord, 24-28
Moralia, 40
Muses, the, 30
music, its effect on the soul, 34; of the spheres, 129
music theory; see harmonics
music therapy, 35, 84-85
Music, On, 43
musical proportion; see harmonic proportion
musical ratios, 168-69, 185, 191, 327; leimma
Or semitone (243:246), 27-28, 50; octave
(1:2), 25, 27; perfect fifth (2:3), 25, 27; perfect fourth (3:4), 25,
27; whole tone, 27, 28

Natural, Ethical and Divine Conceptions
which are Perceived in the Science of Numbers, On the, 42
Natural Philosophers, Account of, 147
Nature, On, (of Philolaus), 167
Nature, On, (of Pythagoras), 80
Nature of the Universe, On the. 203-11
Neoplatonism, 41-42
Neopythagoreanism, 39-42
Nicomachus' Introduction to Arithmetic. Commentary
on, 42
Number, as first principle, 301; as immanent,
34-35; as paradigm, 21, 28-30, 169, 171;
and the soul, 33; as source of divine
natures, 93; the study of, 34; as transcendent,
34-35
numbers, as emanations of the One, 11, 50
Numbers, On, 41

One, the, 11-12, 21, 133, 137, 179, 302-303,
308; above being, 41; and the Good, 38,
41; above monad and dyad, 40
oracle at Delphi, 77
Orphism, 31, 36

Parents, On, 261
Peras; see Limit
Philolaus. The Fragments of, 167-75
philosophy, aesthetic, 52; as the care of the
soul, 32-33; educational, 33-36; ethical,
37, 185-190, 225-228, 249; political,
36-37, 99-103, 190-193, 217-220,
222-224, 255, 257-259; as purification,
see catharsis; term invented by
Pythagoras, 30; as a way of life, 30-33;
of whole systems, 43-48
Physics, 156
Piety, On, 143
Place, On, 41
Platonic solids; see regular solids
poiitikoi; see Pythagorean school, politikoi
praxis, 35-36
Preface to the Laws of Charondas the Catanean.
231-33
Preface to the Laws Of Zaleucus the Locrian,
229-30
Prudence and Prosperity, On. 251-52
pseudepigrapha, 39
Pythagoras, addressed boys of Croton, 68; addressed
men of Croton, 66-68; addressed
by a river, 90, 128, 144; addressed
women of Croton, 69-70; addressed young
men of Croton, 65-66; Anaximenes, Letter
10, 155; as the offspring of Apollo, 58,
123; Athletics, On, 62; his birth, 58-59;
biographical sources of information, 49;
brought down eagle, 71, 127-28; Croton,
143; cured by music, 72; descent to underworld,
147, 152; his diet, 130; dietary suggestions,
84; Education. On, 143; his
family, 152-53; Gods. On the, 80, 93;
received golden dart from Abaris the
Hyperborean, 92; possessed a golden t
high, 90, 128, 144; Golden Verses.
163-65; Helothales. the Father of
Epicharmus of Cos, 143; initiations in
Crete, 126; journey to Egypt, 60-61;
meaning of his name, 147; antiquity of
"miracle stories, " 49; use of music,
84-86, 129-30; heard the music of the
spheres, 72; Na1J4re, On, 80, 143-142; his
use of number, 133; his past lives, 71,
132, 142.312; personal habits, 146; Soul,
On the, 143; spoke against Phalaris,
109-110; called himself a philosopher,
143; Politics, On, 143; predicted number
of fish in net, 65, 128; religious observations,
94-96; Sacred Discourse, 93, 95,
119; Sacred Poem, 143; seen in two places
at once, 90, 128; spoke to an ox, 71, 127;
studies in Egypt and Babylonia, 61; tamed
wild bear, 70, 127; transmigration,
126; Universe, On the, 143; various
Pythagorases, 154; writings of, 142-43;
wrote poems under the name of Orpheus,
19, 143
Pythagoras, The Life of, (by Apollonius), 40
Pythagoras, The Life of, (by Aristoxenus),
113, 135
Pythagoras, The Life of, (by Diogenes),
141-56
Pythagoras. The Life of, (by Iamblichus),
57-122
Pythagoras, The Life of, (preserved by
Photius), 137-40
Pythagoras, The Life of, (by Porphyry),
123-35
Pythagoras. On, (by Hermippus), 144
Pythagorean, The, 151
Pythagorean Numbers. On, 38
Pythagorean school, akousmatikoi, 30-31, 63,
76, 130; cenobites, 63; daily program,
81-82; mathematikoi, 31, 76, 130, 137;
list of members, 121-22; politikoi, 31;
revolt against 37-38, 116-20, 134, 151-52;
the succession, 120; symbols or maxims,
78, 83, 131-32, 146, 159-61; teachings,
see philosophy
Pythagorean Symbols, On, 93
Pythagorean Woman, The, 151
Pythagoreans, On the, (by Aristotle), 49, 38,
63, 149
Pythios (Apollo), 147

Quadrivium, the, 34

regular solids, 34, 174, 291, 309, 315, 315
reincarnation; see transmigration
Reincarnation, On, 41
Republic, On a, 217-20
resonance, 34
Rules of Education, 145

Sacred Discourse, 93. 95, 119
Sanctity, On, 221
Secret Doctrines of Plato, On the, 41
Select Sentences of Sextus the Pythagorean.
267-70
Silli, 150
Sotion, Abridgement of. 143
soul, associated with body through number,
174; divided in three parts, 32-33
Soul, On the, 143
stereometry, 34
"Students;" see Pythagorean school.
mathematikoi
Successions of the Philosophers, (by Alexander),
148
Successions of the Philosophers. (by
Sosicrates), 143
symbols, Pythagorean; see Pythagorean school, symbols or maxims

Table of Opposites, 23, 34, 130, 301 -02
Tarentines, The, 151
temperance, 103-108; see also philosophy,
ethical, and virtues
Tetraktys, 28-30, 307-308, 312, 77; as the
"Harmony of the Sirens, " 77; symbolism
of, 29
Theology of Arithmetic (by Iamblichus), 42
Theology of Arithmetic (by Nicomachus), 41
theoria, 35-36
therapeia, 35
Tranquility, On. 247-48
transmigration, 36; see also Pythagoras, his
past lives
triad, 133, 300
Tripod, The, 49

Unlimited, 22-24, 46, 168, 171-72, 182, 251,
299-301, 304

Virtue, Concerning, 249
virtues, the 225-28. 249
Virtues, On the, 225-28

Wheel of Generation, 36
Wisdom, On, 181
Woman's Temperance. On. 263-64
World and the Soul, On the, 287-96

Y, Pythagorean The, 158

[admin]

FIGURES

FRONTISPIECE. PYTHAGORAS (From Stanley's History of Philosophy, 1687)



FIGURE 1. UNlTY, DUALITY AND HARMONY



FIGURE 2. THE PYTHAGOREAN TABLE OF OPPOSITES



FIGURE 3. SQUARE NUMBER



FIGURE 4. OBLONG NUMBER



FIGURE 5. THE MONOCHORD. String, sounding box and moveable bridge.



FIGURE 6. THE HARMONIC NODAL POINTS AND OVERTONE SERIES ON THE MONOCHORD. The above figure illustrates the reciprocal relation which exists between string length and vibrational frequency. By stopping the string at the geometrical nodal points the harmonic overtones may be individually emphasized.



FIGURE 7. THE HARMONIC PROPORTION



FIGURE 8. THE TETRAKTYS.



FIGURE 9. THE THREE LIVES



FIGURE 10.  IAMBLICHUS



FIGURE 11. COIN FROM CROTON



FIGURE 12. THE PYTHAGOREAN Y



FIGURE 13. THE MUSIC OF THE SPHERES



FIGURE 14. THE MUSIC OF THE SPHERES. Shown in this engraving from Renaissance Italy are Apollo, the Muses, the planetary spheres and musical ratios.



FIGURE 15. A TABLE OF TONE NUMBERS. There is evidence that this table of tone numbers is a later addition to the text. The abbreviations I. and ap. represent the two types of semitones, the leimma and the apotome respectively.



FIGURE 16. THE REGULAR SOLIDS. The regular solids, also known as the Platonic solids, were first described by Plato in his Timaeus. Plato identified the dodecahedron with the cosmic sphere (later identified with aither), and the four other solids with the four elements. Each one of the elemental "molecules" is constructed out of the triangular "atoms" shown below. The five regular solids are the only polyhedra that can be constructed out of the same regular polygons. The archetypal ratios and geometries with which they are associated underlie the structure and divisions of three-dimensional space.



DODECAHEDRON: Aither / 12 Sides
TETRAHEDRON: Fire / 4 Sides
CUBE: Earth / 6 Sides
OCTAHEDRON: Air / 8 Sides
ICOSAHEDRON : Water / 20 Sides

FIGURE 17. THE PLATONIC LAMBDA



FIGURE 18. THE DIVINE MONOCHORD. This particular monochord is tuned in the key of G, while the examples on the right and in the introduction use the key of C. The three top notes on this monochord are incorrectly placed.



FIGURE 19. THE RATIOS OF THE PYTHAGOREAN SCALE



FIGURE 20. MAP OF THE ANCIENT WORLD

[admin]

BACK COVER

PYTHAGORAS (fl. 500 B.C.E.), the first man to call himself a philosopher, was both a brilliant mathematician and spiritual teacher. This anthology is the largest collection of Pythagorean writings ever to appear in the English language. It contains the four ancient biographies of Pythagoras and over twenty-five Pythagorean and Neopythagorean writings from the classical and Hellenistic periods. The Pythagorean ethical and political tractates are especially interesting, for they are based on the premise that the universal principles of Harmony, Proportion, and Justice govern the physical cosmos, and these writings show how individuals and societies alike attain their peak of excellence when informed by these same principles. Indexed, illustrated, with appendices and an extensive bibliography, this work also contains an introductory essay by David Fideler.

"The material in, this book is indispensable for anyone who wishes to understand the real spiritual roots of Western civilization." -- Jacob Needleman, Professor of Philosophy, San Francisco State University; author of The Heart of Philosophy

"The Lives of Iamblichus, Porphyry, and Diogenes Laertius together would be a boon, but to have the whole Pythagorean corpus is a bonanza. The clearly written and instructive introduction of Fideler is a rousing paean to Pythagoras and his abiding influence .... Appropriate for all levels." -- Choice

"This book deserves to establish itself as the standard sourcework on Pythagoreanism. Definitely recommended." -- The Hermetic Journal

"Fideler's introduction provides invaluable background material for the student by highlighting and analyzing clearly the principle themes in the writings and judiciously alerting readers to the difficulty of separating fact and fancy in the master's biography. The Pythagorean Sourcebook thus succeeds in introducing students to the range of Pythagorean thought without misrepresenting it -- a feat that is not unimpressive ..." -- Sixteenth Century Journal

"The Pythagorean Sourcebook and Library is an indispensable compilation of original material in very readable translations to satisfy all needs for increasing our knowledge and understanding of Pythagoras and Pythagoreanism." -- Platon