84 THE HISTORY OF SCIENCE 



ent on the other powers of the mind, Descartes 

 resorted in his mathematical demonstrations to the 

 use of lines, because he could find no method, as he 

 says, more simple or more capable of appealing to 

 the imagination and senses. He considered, how- 

 ever, that in order to bear the relationships in mem- 

 ory or to embrace several at once, it was essential to 

 explain them by certain formula, the shorter the 

 better. And for this purpose it was requisite to 

 borrow all that was best in geometrical analysis and 

 algebra, and to correct the errors of one by the other. 

 Descartes was above all a mathematician, and as 

 such he may be regarded as a forerunner of Newton 

 and other scientists ; at the same time he developed an 

 exact scientific method, which he believed applicable 

 to all departments of human thought. " Those long 

 chains of reasoning," he says, " quite simple and 

 easy, which geometers are wont to employ in the 

 accomplishment of their most difficult demonstra- 

 tions, led me to think that everything which might 

 fall under the cognizance of the human mind might 

 be connected together in the same manner, and that, 

 provided only 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, 

 or so concealed which he might not discover." 



