404 ANTIENT METAPHYSICS. Book V. 



which we have thus afcended, we demonftrate the propofition to be 

 true. 



In this way, every propofition of Euclid may be analyfed ; and as, 

 in this way, every fyftem of fcience has been difcovered, fo I have 

 little doubt but that the greater part of the particular proportions of 

 Euclid have been inveftigated and difcovered in the fame way ; for 

 men would naturally fufpe£t the propofition to be true, before they 

 could demonftrate it ; and this would lead them to confider what the 

 confequences would be, upon the fuppofition that it was true. And, 

 accordingly, we know very well that the antients pradifed this me- 

 thod very much in geometry, and, I believe> likewife, in other fci- 

 ences. 



It very much refembles the demonftration ex ahfurdo. And it is 

 truly of the fame kind in this refpedt, that they are both from confe- 

 quences ; for the one fhows that, if the contrary of the propofition be 

 fuppofed true, the confequences would be abfurd and impoffible ; 

 while the other fhows, that, if the propofition be fuppofed to be true, 

 it is neceffarily connected with fome known truth. They both, there- 

 fore, argue from the efFed to the caufe, and therefore are faid to be 

 a pofteriori ; whereas, dired: demonftration argues from the caufe to 

 the cfFed, and therefore is faid to be a priori ; and, where it can be 

 had, is, for thefc reafons, more fatisfying to the mind, and more phi- 

 lofophical. 



It is in this way that Porphyry the philofopher, as quoted by Pro- 

 clus *, has explained the different methods of fcientifical reaioning.^ 

 All fuch reafonings, fays he, is tiihtvfrom the principles, or to the prin- 

 ciples ; 



♦ Proclus's Commentary upon the firft book of Euclid's Elements, lib. 3. p. 69. 



