THEUDIUS OF MAGNESIA

(fl. fourth century b.c.)

mathematics.

Theudius, an early member of the Academy, is known only from a passage in Proclus’ commentary on Euclid’s Elements (In primum Euclidis Elementorum librum commentarii, G. Friedlein, ed. [Leipzig, 1883; repr. 1967], I, pp. 67–68). After mentioning Leo (who made an improved collection of the elements of geometry and invented diorismi, means of determining when a problem is soluble and when not) and Eudoxus, Proclus says:

Amyclas [or, better, Amyntas] of Heraclea, one of Plato’ friends, Menaechmus, a pupil of Eudoxus who had also studied with Plato, and Dinostratus his brother, made the whole of geometry still more perfect. Theudius the Magnesian had a reputation for excellence in mathematics and in the rest of philosophy; for he ordered . . . the elements carefully and made many of the limiting [or partial] theorems more general.

Proclus then states that another geometer, Athenaeus of Cyzicus, lived at about the same time. “These men associated . . . in the Academy and undertook investigations jointly.” Next are mentioned Hermotimus of Colophon, who added to the Elements, and Philippus of Medma (or Opus), who is said to have revised and published Plato’s Laws. All these statements by Proclus may well have originated with an excellent authority, the historian of mathematics Eudemus of Rhodes. Theudius may be placed between Eudoxus and Philippus; that is, he was a contemporary of Aristotle. Indeed, T. L. Heath made the resonable suggestion that the propositions in elementary geometry that are quoted by Aristotle were taken from Theudius’ Elements. We have, however, no means of knowing which propositions and theorems were his discoveries; nor are we told which Magnesia was his home.

BIBLIOGRAPHY

See K. von Fritz, in Pauly-Wissowa, Real-Encyclopädie der classischen Altertumswissenschaft, XI, pt. 2 (1936), 244–246; T. L. Heath, A History of Greek Mathematics, 1 (Oxford, 1921), 319–321; and The Thirteen Books of Euclid’ Elements (repr. New York, 1956), 116–117; Glenn R. Morrow, Proclus: A Commentary on the First Book of Euclid’s Elements (Princeton, 1970), 56, n, 45; and F. Wehrli, Die Schule des Aristoteles, VII Eudemos von Rhodos (Basel, 1955).

G. L. Huxley