used in Mathematics and other Sciences. 201 



composite to simple, we shall see that these two methods 

 almost always meet together : there are no complete truths 

 but what result from their concourse ; but they vary a littlef 

 in their form, according to the nature of the subjects to 

 which we apply them. 



To unite synthesis with analysis at all times that we are able 

 to make use of both; to exert the most scrupulous attention 

 in the enumeration of the different appearances which the 

 various cases of the proposition we examine present, in or- 

 der to assure ourselves that all are comprised in the consi- 

 derations upon which we found it; that is to say, if the 

 connection of ideas is observed; it is to this small number 

 of principles, in my opinion, that all the art of reasoning 

 should be reduced*. But this art, like all others, cannot be 

 acquired but bv continual and well-directed exercise; and 

 all times when the theory is forced beyond a certain limit, 

 it appears to lead the human mind from one error to an- 

 other, and to present a vicious circle which produces all the 

 subtilties of the antient schools. In fact, if nothing ap- 

 pears that ought to limit the progress that may be made, by 

 applying this reasoning to those sciences which rest inmie- 

 diately upon ideas acquired by the senses; it is not the case 

 when we wish to analyse by themselves the operations of the 

 understanding. It is possible, in this case, for the same cir- 

 cumstance to take place as sometimes happens in mathema- 

 tical researches, when by some error wc combine one equa- 

 tion with another, which only differs from it in appearance ; 

 but being in fact the same, it does not aid the solution of 

 the proposed questions, but gives a result purely identic. In 

 the mathematics this result, which falls inniiediately under 

 the senses, and is also expressed by signs which are well de- 

 termined, cannot be mistaken; but when forced to turn our 

 thoughts to subjects not susceptible of the same precision, 

 we deceive ourselves so far as to regard as essential modifi- 

 eations, those triHing appearances which the intensity of 

 understanding, which is exercised when the mind dwells 

 too long upon one thought, produces in the manner of 

 judging and ])erceiving — nearly as the sight becomes con- 

 fused with being fixed too long upon one object. Wc think 



* The fifiliarticle of the Elcnifm dc Fhilosolihie, given by D' Alembei t 

 in tome 4. of liis Milangci tie Li/diimnrr', and the Supplement to ths 

 article (tome 5. pag. 4').) contain, in n few words, all that in necessary 

 to know up(in tlic natural mechanism of reasoning. With respect to the 

 different forms which can be given to svlingisins, they are to be fmind ex- 

 pti C'.l in a manner as short as luminous, in tune 2. (ks Lttira J'Eul/r a 

 .. frinceac d' Allemngnc, 



tQ 



