DISCOURSE ON METHOD. 21 



thus be the better able to apply them to every other 

 class of objects to which they are legitimately 

 applicable. Perceiving- further, that in order to 

 understand these relations I should sometimes have 

 to consider them one by one, and sometimes only to 

 bear them in mind, or embrace them in the aggre 

 gate, I thought that, in order the better to consider 

 them individually, I should view them as subsisting 

 between straight lines, than which I could find no 

 objects more simple, or capable of being more dis 

 tinctly represented to my imagination and senses; 

 and on the other hand, that in order to retain them 

 in the memory, or embrace an aggregate of many, 

 I should express them by certain characters the 

 briefest possible. In this way I believed that I 

 could borrow all that was best both in Geometrical 

 Analysis and in Algebra, and correct all the defects 

 of the one by help of the other. 



And, in point of fact, the accurate observance of 

 these few precepts gave me, I take the liberty of 

 saying, such ease in unravelling all the questions 

 embraced in these two sciences, that in the two or 

 three months I devoted to their examination, not 

 only did I reach solutions of questions I had for 

 merly deemed exceedingly difficult, but even as 

 regards questions of the solution of which I con 

 tinued ignorant, I was enabled, as it appeared to 

 me, to determine the means whereby, and the extent 

 to which, a solution was possible; results attribu 

 table to the circumstance that I commenced with the 

 simplest and most general truths, and that thus 

 each truth discovered was a rule available in the dis- 



