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Wilbur R. Knorr

Bryson (early 4th cent. bce), of Heraclea (3) Pontica, a sophist associated with the following of *Euclides (1) of Megara, he is criticized by Aristotle for an allegedly fallacious quadrature of the circle (An. post. 75b4; Soph. el. 171b16, 172a3). The argument, whatever its original intent, employs a form of two-sided convergence of polygonal sequences to the circle, a procedure later exploited by *Archimedes in his measurement of the sphere.



G. J. Toomer

Woman learned in mathematics, astronomy, and philosophy (d. 415 ce). Daughter of the mathematician *Theon(4) of *Alexandria (1), she revised the third book of his Commentary on the Almagest. Commentaries by her on *Diophantus and *Apollonius(2) are lost. Influential in Alexandria as a teacher of Neoplatonist philosophy, she was torn to pieces by a mob of Christians at the instigation of their bishop (later Saint) Cyril (but see cyril of alexandria).


Leucippus (3), originator of the atomic theory in the second half of the 5th cent. bce. His birthplace is reported to be *Elea, *Abdera, or *Miletus (Diog. Laert. 9. 30), but all of these may be inferences from affinities between his work and that of philosophers known to come from these places; Miletus is slightly more probable than the others. He wrote later than *Parmenides, and almost certainly later than *Zeno (1) and *Melissus. *Epicurus is said to have denied his existence (Diog. Laert. 10. 13), but this is not to be taken seriously, in the face of *Aristotle's frequent mentions of him.

Of the Democritean works (see democritus) collected by Thrasyllus (Diog. Laert. 9. 45–9), two are sometimes attributed to Leucippus: The Great World System and On Mind. Both attributions appear to stem from *Theophrastus and may well be right.


Andrew Barker

Like many philosophers and Christian fathers, Porphyry was suspicious of real *music but not of musical theory. The introduction to his incomplete Commentary on Ptolemy's Harmonics explains why he chose to work on *Ptolemy rather than other theorists, but not why he thought any treatise in this science worth his attention. Having accused Ptolemy of borrowing heavily from unacknowledged sources, he names many earlier writers in the course of his work and quotes lavishly from their writings, so preserving much important material (selections translated in A. Barker, Greek Musical Writings 2 (1989)). His commentary is the platform for significant ideas of his own, especially in epistemology and on issues related to *Aristotle's theory of the categories.


Charles H. Kahn and Fritz Graf

Pythagoras, son of Mnesarchus, one of the most mysterious and influential figures in Greek intellectual history, was born in *Samos in the mid-6th cent. bce and migrated to *Croton in c.530 bce. There he founded the sect or society that bore his name, and that seems to have played an important role in the political life of *Magna Graecia for several generations. Pythagoras himself is said to have died as a refugee in Metapontum. Pythagorean political influence is attested well into the 4th cent., with *Archytas of Tarentum.

The name of Pythagoras is connected with two parallel traditions, one religious and one scientific. On the religious aspects, see below. Pythagoras seems to have become a legendary figure in his own lifetime and was identified by some with the *Hyperborean*Apollo. His supernatural status was confirmed by a golden thigh, the gift of bilocation, and the capacity to recall his previous incarnations. Classical authors imagine him studying in Egypt; in the later tradition he gains universal wisdom by travels in the east. Pythagoras becomes the pattern of the ‘divine man’: at once a sage, a seer, a teacher, and a benefactor of the human race.