4S6 ANTIENT METAPHYSIS. Book V, 



Ariftotle, the author of ihe Syllogiftn, mofl explicitly declared *. But, 

 as the authority of Ariftotle is now become obfolete, and, as we live 

 in an age when the cleareft principles are called in queftion, I will 

 endeavour to prove it in form. 



And, in \\\tjirjl place, I will give a definition of caufe^ which (hall 

 be {horter than that of Mr Hume*s, and, I think, fully as clear. 

 Caufe^ I fay, is, * That without which another thing, called the effe^^ 



* could not exift.' This is a definition which, I think, cannot be 

 controverted; and, if fo, 1 alk any geometer, Whether the idea of a 

 triangle, as contained in its definition, is not the caufe of all its pro- 

 perties, as being that, without which, thofe properties could not ex- 

 ift. If it be alked. How thofe properties do thus depend for their ex- 

 iftence upon the definition of a triangle ? the anfwer is, that the idea 

 of a triangle is more general than that of any of its properties, as it 

 virtually comprehends them all ; fo that they all flow from it, and are 

 produced, as it were, out of it ; for that is the nature of this caufa- 

 tion. For the fame reafon, any of Euclid's axioms is the caufe of the 

 propofition which he proves by them. As, for example, the axiom, 



* That, if any two things are equal to a third, they are equal to one 



* another,' is the caufe, that any two particular lines being equal to a 

 third, they are equal to one another ; for the lines or figures could not 

 be equal if the axiom were not true : And the axiom being the 

 more general propofition, virtually contains in it the particular propo- 

 fition concerning thefe lines which flows from it, and is educed out 

 of it. And the effe^^ in this cafe, has that dependent exiftence which 



every 



* Analyiica, Poft. lib. i. cap. 22. Where, fpeaking oi iTi^nrrt^Hi or fcience, he fays, 

 that we only underftand a thing, or know it fcientifically, when we know the caufe 

 ■of it. oT«» T)iv mruM atu^iix ynuc-x-ir/y \i r'l to •^c^a.y^x ta-riy. — And again, in the fame 

 chapter, he fays, that fcience or demonftration is, when the premifles are the caufe of 

 the conclufion. AvxyKn tji» «a-oS^HxT<x.))y iTTie-Tn/LcnVy i| uXr,6»iy t enytn, kxi Tr^urvr, KKt xfti^ 

 »■*», KKt '/tv^ifcaiTi^tify xcci TT^uTi^tiff XXI AITIGN rev c-vf67rt^x(r[^xTC{, 



