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
arithmo10gy, 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
DivergenceoftheAcademicsfrom 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, 2~.; in the soul, 33;
and symmetry, 28
Harmony ofa Woman, On the, 239-41
"Hearers;" see Pythagorean school,
akousmatikoi
Helothales, the Father ofEpichannus ofCos,
143
Hermes, 69, 149
Histories (of Lycus), 124
History of Ale:wnder, 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 Undastanding Plato,
41
mathematikoi; see Pythagorean school,
mathematikoi
maxims, Pythagorean; see Pythagorean
school, symbols and maxims
359
360

mean, arithmetic, 25; geometric, 28; harmonic,
25
microcosm, man as, 31, 139
Middle Platonism, 40-42
Miscellaneous Hiswry, 144-45, 154
monad, 40, 42, 133, 137, 148, 171, 179; as origin of all things, 138 monochord, 24-28 Mora/ia, 40 Muses, the, 30 music, its effect on the soul, 34; of the spheres, 129
music theory; see hannonics
music therapy, 35, 84-85
Music, On, 43
musical proportion; see hannonic proportion
musical ratios, 168-69, 185, 191,327; leimrna
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 wuJ Divine Conceptians 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
Nicomm:hus' 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, poiitikoi praxis, 35-36 Preface to the UJws of Charondas the Catanean.
231-33 Preface to the UJws Of 2aleucus 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 ofCroton, 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; Crown, 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 thigh, 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 offish 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 Iamb1ichus), 57-122 Pythagoras, The Life of, (preserved by PhOlius), 137-40 Pythagoras, The Life of, (by Porphyry),
123-35 Pythagoras. On, (by Hemtippus), 144 Pythagorean, The, 151 Pythagorean Numbers. On. 38
'
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"
INDEX OF SELECT TOPICS
361
Pythagorean school, akousmatilwi, 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
Reincamation, 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, 4\
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 philo,ophy.
ethical, and virtues
Tetraktys, 28-30, 307-308, 312, 77; as the
"Hannony of the Sirens," 77; symholism
of, 29
Theology of Arithmetic (by lamblichus), 42
Theology ofArithmetic (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

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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
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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
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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.
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