458 ANTIENT METAPHYSICS, Book V. 



ftotle gives vs an example from geometry, in a very curious demoa- 

 ftratlon*, which he gives us of the fifth propofition of the firft book of 

 Euclid, concerning the equality of the angles at the bafe of an ifoicelea 

 triangle. And the fame may be faid of every demonftration in Eu- 

 clid ; for It is only upon the fuppofition of the general propofitioa 

 being true, that any ftep of the demonftration proves any thing. 

 Thus, for example, if, in any demonftration concerning a triangle, it 

 be aflfumed. That the three angles of that triangle are equal to two 

 right ones, this proves nothing, unlefs the general propofition be ad- 

 mitted, That the angles of all triangles are equal to two right ones. 

 This being admitted, I' fylloglfe thus : All triangles have their 

 angles equal to two right ones. This figure is a triangle. I'here- 

 fore this figure has its angles equal to two right ones. Thofe gentle- 

 men, therefore, who deny that the particular propofition is deduced 

 from the general or, in other words, that the general is the caufe of 

 the particular, muft deny, at the fame time, the truth of every demon- 

 ftration of Euclid. 



further, I fay that, in demonftration, we not only argue from' 

 caufe to effe^i but the demonftration evidently Iliows us how the 

 cau/e produces its effeci ; for when from the definitioa of a triangle 

 any of its properties is deduced, we clearly perceive how the definition 

 is the cau/e of that property. And how any axiom, or propofition, 

 formerly demonftrated, produces the inference that we draw from it 

 in demonftrating any propofition, is felf-evident. 



The reader that has learned his logic, and, particularly, if he has 

 ♦•ead the two books of Ariftotle's La/l Analytics, will be fiirprifed that I 

 have been at fo much pains to prove a propofition that muft appear to 

 him perfectly evident ; for Ariftotle, in thefe books, has ihown, th.^t de- 

 monftration muft not only be from the cauje^ butfrom \.h.c primary diwA 



mojl 



* Ariftot. ibid. 



