i6o SCIENCE IN GRECO-ROMAN ANTIQUITY 



proposition of which includes as consequences sixty of 

 those of the four first books of Apollonius, has gained 

 for him the esteem of savants. 1 



In conclusion, what characterized the spirit and 

 methods of Greek geometry was an ideal of logical 

 rationality which may be defined in the following 

 terms : 



1. To postulate primary propositions (definitions, 

 hypotheses) as logical and as few in number as possible. 



2. To construct by means of reasoned deduction 

 the whole edifice of mathematics on the basis of these 

 propositions. 



Logical rigour is thus safeguarded, but at the price 

 of complications which, as we have just seen, do not 

 allow the methods of invention and demonstration to 

 be given all the generality of which they are capable. 



1 Chasles, Apergu historique des me'thodes, Gauthier-Villars, 

 Paris, 1875, p. 78. 



