n8 SCIENCE IN GRECO-ROMAN ANTIQUITY 



the circle, which Greek geometry made from its 

 beginnings and never ceased to pursue. 



The search after harmonious simplicity is not sufficient 

 by itself to explain the direction of Greek mathematics. 

 It seems to us that it is necessary to add on one hand 

 the influence of the technical arts, and on the other the 

 fear of clouding reason by bringing in mechanical means 

 other than the rule and compass. The first point 

 appears to be beyond question. As G. Sorel has 

 repeatedly pointed out, it was certainly from the art 

 of the engineer and the architect that Greek geometry 

 borrowed its primary problems and, up to a certain 

 point, its definitions. Thales was an engineer as well 

 as a geometer ; according to a tradition, which appears 

 to be true in spite of the reservations of Herodotus 

 (I, 75), he diverted by a canal the waters of the river 

 Halys and rendered it fordable by the armies of Croesus. 

 It must not be forgotten either that the father of 

 Pythagoras at Samos was an engraver of seals. These 

 possessed a magical value universally recognized, and 

 the glyptography of Samos was famous for its produc- 

 tions. 1 Perhaps the invention of regular polyhedra 

 ought to be attributed to the stone-cutters whose 

 fumblings must have preceded the reasonings of 

 geometers. G. Sorel believes likewise that a consider- 

 able part of the Elements of Euclid is derived from the 

 art of building. He considers that the definition 

 XXIII of parallels as straight lines produced to infinity 

 and never meeting, is an interpolation, because it is not 

 in keeping with the necessity for Greek geometry of 

 avoiding the direct intervention of infinity. Euclid 

 certainly ought to have defined the parallelism of two 

 lines as a function of their equidistance. He was only 

 translating into geometrical language the practice of 

 architects, who for the construction of a wall use 



1 G. Sorel, De Vutilite du pragmatisme, Riviere, Paris, 192 1, 

 p. 198. 



