The Pythagorean Sourcebook and Library

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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

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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