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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.



Henriette Harich-Schwarzbauer

The philosopher Hypatia (350/370–415 ce) is one of the outstanding figures in the intellectual life of Late Antiquity. She is considered a symbol of the transformation of science and philosophy under the Christian bishops in Alexandria at the end of the 4th century ce. Her life and her works are well documented in different literary genres and by famous authors, namely by Synesius of Cyrene in his letters. The extant testimonies on her work prove that she was the guiding light of astronomy in Alexandria, where she was held in high esteem. Unsurprisingly, she became the target of aggression, and she was murdered ferociously in 415. Hypatia has been commemorated in the Byzantine and the Western traditions. She has experienced an impressive revival since the Enlightenment; even in the 21st century she is depicted as a heroine in fiction and film.Hypatia appears to have spent her entire life in her hometown of .


Leucippus (3), Greek scientist, 2nd half of 5th cent. BCE  

David John Furley

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.


Porphyry, music theory  

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.


Pythagoras (1), Pythagoreanism  

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.