[ 202 ] 



arranged in what feemed the moft natural order; but as the 

 confideration of the third clafs will point out the circumftance 

 which renders certainty unattainable in the fecond, it will be 

 convenient to examine thofe two clafles in a contrary order. 



When wc compare two ideas without confidering them as 

 being conneded by the relation of caufe and effed, but merely 

 regarding them as two independent objeds of thought, it is 

 obvious that in many cafes we may be capable of difcovering 

 with certainty their agreement or difagreement. Thus the 

 mathematician may with certainty difcover that a triangle 

 correfponds in extent to a redangle of the fame altitude, 

 and whofe bafe is half of that of the triangle, or that they 

 are equal. Each idea is a certain modification of extenfion, 

 and he may difcover that they correfpond as to the quantity 

 of that extenfion. 



Probability is not however excluded from propofitions 

 compofed of ideas in this manner compared. The propofition, 

 whofe truth might be eftabliflied by demonftration, may be 

 received on teftimony ; and a mathematician, when invefti- 

 gating the conftrudion of a geometric problem, is guided by 

 the probability of the exiftence of various relations arifing from 

 the refemblance which the cafe bears to others in which fuch 

 relations have been known to exift. 



Tills 



i 



