ARCHYTAS 
213 
told that Plato ‘ explained {ela^y-qa-aTo) to Leodamas of Thasos 
the method of inquiry by analysis ’ 1 ; Proclus’s account is 
fuller, stating that the finest method for discovering lemmas 
in geometry is that ‘ which by means of analysis carries the 
thing sought up to an acknowledged principle, a method 
which Plato, as they say, communicated to Leodamas, and 
by which the latter too is said to have discovered many 
things in geometry’. 2 Nothing more than this is known of 
Leodamas, but the passages are noteworthy as having given 
rise to the idea that Plato invented the method of mathe 
matical analysis, an idea which, as we shall see later on, seems 
nevertheless to be based on a misapprehension. 
Archytas of Taras, a Pythagorean, the friend of Plato, 
flourished in the first half of the fourth century, say 400 to 
365 B.c. Plato made his acquaintance when staying in Magna 
Graecia, and he is said, by means of a letter, to have saved 
Plato from death at the hands of Dionysius. Statesman and 
philosopher, he was famed for every sort of accomplishment. 
He was general of the forces of his city-state for seven years, 
though ordinarily the law forbade any one to hold the post 
for more than a year; and he was never beaten. He is 
said to have been the first to write a systematic treatise oil 
mechanics based on mathematical principles. 3 Vitruvius men 
tions that, like Archimedes, Ctesibius, Nymphodorus, and 
Philo of Byzantium, Archytas wrote on machines 4 ; two 
mechanical devices in particular are attributed to him, one 
a mechanical dove made of wood which would fly, 5 the 
other a rattle which, according to Aristotle, was found useful 
to £ give to children to occupy them, and so prevent them 
from breaking things about the house (for the young are 
incapable of keeping still) ’. 6 
We have already seen Archytas distinguishing the four 
mathematical sciences, geometry, arithmetic, sphaeric (or 
astronomy), and music, comparing the art of calculation with 
geometry in respect of its relative efficiency and conclusive 
ness, and defining the three means in music, the arithmetic, 
] Diog. L. iii. 24. 2 Proclus on Eucl. I, p. 211. 19-28. 
3 Diog. L. viii. 79-88. 
4 Vitruvius, De architectural, Praef. vii. 14. 
5 Gellius, x. 12, 8, after Favorinus (Vors. i 3 , p. 325. 21-9). 
0 Aristotle, Politics, E (©). 6, 1340 b 26.