276 A SHORT HISTORY OF SCIENCE 



Three appendices dealt with optics, meteors, and geometry, 

 the last containing the beginnings of analytic geometry. The 

 relation of his philosophy to mathematics may be indicated in 

 the following passages. 



Considering that, among all those who up to this time made dis- 

 coveries in the sciences, it was the mathematicians alone who had 

 been able to arrive at demonstrations that is to say, at proofs cer- 

 tain and evident I did not doubt that I should begin with the same 

 truths that they have investigated, although I had looked for no other 

 advantage from them than to accustom my mind to nourish itself upon 

 truths and not to be satisfied with false reasons. 



When ... I asked myself why was it then that the earliest phi- 

 losophers would admit to the study of wisdom only those who had 

 studied mathematics, as if this science was the easiest of all and the 

 one most necessary for preparing and disciplining the mind to com- 

 prehend the more advanced, I suspected that they had knowledge 

 of a mathematical science different from that of our time. . . . 



I believe I find some traces of these true mathematics in Pappus 

 and Diophantus, who, although they were not of extreme antiquity, 

 lived nevertheless in times long preceding ours. But I willingly be- 

 lieve that these writers themselves, by a culpable ruse, suppressed the 

 knowledge of them ; like some artisans who conceal their secret, they 

 feared, perhaps, that the ease and simplicity of their method, if 

 become popular, would diminish its importance, and they preferred 

 to make themselves admired by leaving to us, as the product of 

 their art, certain barren truths deduced with subtlety, rather than 

 to teach us that art itself, the knowledge of which would end our 

 admiration. 



Those long chains of reasoning, quite simple and easy, which geom- 

 eters are wont to employ in the accomplishment of their most difficult 

 demonstrations, led me to think that everything which might fall 

 under the cognizance of the human mind might be connected together 

 in a similar manner, and that, provided only that one should take 

 care not to receive anything as true which was not so, and if one 

 were always careful to preserve the order necessary for deducing 

 one truth from another, there would be none so remote at which 

 he might not at last arrive, nor so concealed which he might not 

 discover. 



