198 On the Analytical and Synthetical Modes of Reasoning 



dements of geometry ; he proceeds from simple to compo- 

 site. The undersiaiuling, or more especially the rapidity 

 with which the faculty of comparing ideas, and presenting 

 their result, exercises itself, conducted him to assertions, 

 the truth of which he afterwards demonstrated by develop- 

 ing all the intermediate propositions, which his judgment 

 had led him to consider nearly in the same manner as 

 gamesters estimate, almost at a glance, what they have to 

 hope or fear from the different ciiances which arc able to 

 present themselves. This is nmch the same as what is called 

 synthesis in geometry. This synthesis may be said to have 

 been preceded by an analysis; for the author decomposed 

 the system of sensations in order to discuss what regarded 

 smell alone. The same takes place in geometry ; and some- 

 thing equivalent to this analysis may be found in the diverse 

 abstractions made by geometers to simplify their subject : 

 thus they deprive a body of two of its dimensions, to form 

 lines. Jt is not possible to find in the n)elhods of Con- 

 diliac, that proceeding of mathematical analysis which con- 

 sists in supposing the question resolved, which it is probably 

 impossible to apply to the things which he has treated 

 upon. 



By examining his logic under the same point of view, I 

 think we may convince ourselves that it proceeds according 

 to the synthetic method. In fact, this proceeding may be 

 unknown as such by those who have been struck with the 

 difficulty of understanding tlie propositions which Newton, 

 for example, has demonstrated synthetically. But this is 

 jnerely an illusion which niaveasiiv be destroyed. The pro- 

 ceedings of Newton might be understood witli the same 

 ease as those of Condillac, if all the truths .which he has 

 manifested were to follow each other as closely as those 

 which we meet with in the works of the latter. Hut the in- 

 terval that separates them, both from each other and those 

 which arc admitted as elementary, is so great ; the number of 

 intermediates to compare, and frequently to apply, is such, 

 that the most continued application and profound talents 

 ar^ necessary to be employed, in order to avoid being lost 

 in the series of consequences, 



There is no doubt but, by establishing all the intermediate 

 Jinks, we might make the Prjneipia of Newton as easy to 

 be comprehended as the Elements of Euclid. In a word, 

 that might take place here which probably does in the na- 

 tural classifications of animals and plants; if all the species 

 were known, we might pass from one jiroposition to an<r 

 Other by almost insensible transitions. It is easy to perceive 

 1 that 



