X 
FROM PLATO TO EUCLID 
Whateyee original work Plato himself did in mathematics 
(and it may not have been much), there is no doubt that his 
enthusiasm for the subject in all branches and the pre-eminent 
place which he gave it in his system had enormous influence 
upon its development in his lifetime and the period following. 
In astronomy we are told that Plato set it as a problem to 
all earnest students to find ‘ what are the uniform and ordered 
movements by the assumption of which the apparent move 
ments of the planets can be accounted for ’ ; our authority for 
this is Sosigenes, who had it from Eudemus. 1 One answer 
to this, representing an advance second to none in the history 
of astronomy, was given by Heraclides of Pontus, one of 
Plato’s pupils {circa 388-310 b. c.) ; the other, which was 
by Eudoxus and on purely mathematical lines, constitutes 
one of the most remarkable achievements in pure geometry 
* that the whole of the history of ' mathematics can show. 
Both were philosophers of extraordinary range. Heraclides 
wrote works of the highest class both in matter and style : 
the catalogue of them covers subjects ethical, grammatical, 
musical and poetical, rhetorical, historical; and there were 
geometrical and dialectical treatises as well. Similarly 
Eudoxus, celebrated as philosopher, geometer, astronomer, 
geographer, physician and legislator, commanded and enriched 
almost the whole field of learning. 
Heraclides of Pontus : astronomical discoveries. 
Heraclides held that the apparent daily revolution of the 
heavenly bodies round the earth was accounted for, not by 
1 Simpl. on De caelo, ii. 12 (292 b 10), p. 488. 20-34, Heib.