THE HELLENIC PERIOD 25 



that the theorem of proportions by* which he calculated 

 the height of the pyramids, and the theorem of the 

 triangle inscribed in a semi-circle are attributed to 

 him. In arithmetic, it appears to have been Thales 

 also who introduced into Greece the use of Egyptian 

 fractions, the numerator of which is always equal to 

 one. 



Belonging to a younger generation, Anaximander 

 was the disciple as well as the fellow-citizen of Thales. 

 He was born about 610 B.C. ; the date of his death is 

 uncertain, but is generally supposed to be about 546 

 B.C. Anaximander wrote a treatise which contained 

 his doctrines, and which Theophrastus certainly may 

 have read. According to the latter, this doctrine was 

 as follows (Diels, Dox, 476, 3) : " Amongst those who 

 admit one sole primary element, mobile and infinite, 

 Anaximander of Miletus, the son of Praxiades and 

 disciple and successor of Thales, says that the aJteigov 

 is the essence and element of beings ; it was, besides, he 

 who first introduced this term of primary element, 

 understanding by this, not the water or any other of the 

 elements known to us, but a certain endless unlimited 

 mass (ojzsiqov) from which were formed all the heavens 

 and all the worlds which they have contained, etc." 

 What is to be understood by the word ojzeiqov ? Does 

 it stand for a substance extending to infinity in space, 

 or a substance finite in its extent, but qualitatively 

 indeterminate ? The great majority of commentators, 

 ancient or modern, lean towards the former inter- 

 pretation ; at the origin of all things is a primitive 

 matter, which extends to infinity and which we cannot 

 perceive, since it has been transformed into derivative 

 elements such as water, fire, etc. Teichmuller and P. 

 Tannery consider that such a conception cannot be 

 attributed to Anaximander, because the idea of spatial 

 infinity only appeared later in philosophy and in 



