22 
INTRODUCTORY 
ft 
It would appear therefore that, notwithstanding the in 
fluence of Plato, the attitude of cultivated people in general 
towards mathematics was not different in Plato’s time from 
what it is to-day. 
We are told that it was one of the early Pythagoreans, 
unnamed, who first taught geometry for money : ‘ One of the 
Pythagoreans lost his property, and when this misfortune 
befell him he was allowed to make money by teaching 
geometry.’ 1 We may fairly conclude that Hippocrates of 
Chios, the first writer of Elements, who also made himself 
famous by his quadrature of lunes, his reduction of the 
duplication of the cube to the problem of finding two mean 
proportionals, and his proof that the areas of circles are in 
the ratio of the squares on their diameters, also taught for 
money and for a like reason. One version of the story is that 
he was a merchant, but lost all his property through being 
captured by a pirate vessel. He then came to Athens to 
prosecute the offenders and, during a long stay, attended 
lectures, finally attaining such proficiency in geometry that 
he tried to square the circle. 2 Aristotle has the different 
version that he allowed himself to be defrauded of a large 
sum by custom-house officers at Byzantium, thereby proving, 
in Aristotle’s opinion, that, though a good geometer, he was 
stupid and incompetent in the business of ordinary life. 3 
We find in the Platonic dialogues one or two glimpses of 
mathematics being taught or discussed in school- or class 
rooms. In the Erastae 4 Socrates is represented as going into 
the school of Dionysius (Plato’s own schoolmaster 5 ) and find 
ing two lads earnestly arguing some point of astronomy; 
whether it was Anaxagoras or Oenopides whose theories they 
were discussing he could not catch, but they were drawing 
circles and imitating some inclination or other with their 
hands. In Plato’s Theaetetus 6 we have the story of Theodorus 
lecturing on surds and proving separately, for the square root 
of every non-square number from 3 to 17, that it is incom 
mensurable with 1, a procedure which set Theaetetus and the 
1 Iamblichus, Vit. Pyth. 89. 
2 Philoponus on Arist. Phys., p. 327 b 44-8, Brandis. 
3 Eudemian Ethics, H. 14, 1247 a 17. 
4 Erastae, 32 a, b. 5 Diog. L. iii. 5. 
6 Theaetetus, 147 n-148 B. 
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