444 A N T I E N T METAPHYSICS. BooTc V, 



Thefe are the definitions prefixed to the firft book of his elements : 

 And I mighti in the lame way, go over the definitions prefixed to his 

 other books ; but enough, 1 think, has been faid, to fliow, that Eu- 

 did's definitions are truly nothing more than fo many hypothefes. 



As a definition is an hypothefis of what is poffible in theory, fo a 

 poftulate is an hypothefis of what is poffibie in pradice. The one is 

 what may be conceived, the other what may be done. Of this kind 

 are Euclid's three poflulates ; for certainly a ftraighi line may be drawn 

 from any one point to another, which is his Jir/i poftulate ; and, like- 

 wife, a terminated ftraight line may be produced to any indefinite 

 length ; which is his fecond. And his third is, that a circle may be 

 defcribed from any centre, at any diftance from that centre. This 

 poftulate might have been made more evident to fenfe, if it had been 

 expreflTed In this way, ' That any circle may he defcribed by the ex- 



* tremity of any ftraight line being moved round, till it return to the 



* point from which it fet out, the other extremity remaining fixed ;' 

 for, this way exprefled, we not only fee the poftibility of its being 

 done, but we diftindly conceive the manner in which it is done *. 



As 



authority for which I have great refpe£l, as he was not only a fuhlime metaphyfician, 

 but a good geometer. In this pafTage he fays, that there is but one fcience that is 

 •»yx<>*£T«j, meaning Metaphyfics. 



• A circle would have been better defined in this way by Euclid, than by its pro- 

 perty of having al! the lines drawn from the circumference to the centre equ.il ; for 

 every definition from the generation and production of the thing, is better than from 

 any of its properties, after it is produced. In this way, Euclid has defined a fphere 

 from the revolution of a femicircle about its diameter, when he might have defined it, 

 as he has done the circle, from the equality of the lines drawn from its ct^ntre to its 

 fupcrficies. But, as Barrow has very well obferved, (Mathematical Lectures, p. 223.) 

 when a thing is defined by its generation, the puiribiliry of its cxiflience is evidently 

 fhown, and mathcmitical truth requires no more than that the fubjcct of it Ibouid have 

 a poflibility of exiftence- In like manner, he has defined a tylinder from the turning 

 of a parallelogram round its fide^ and a cone from the rotation of a triangle about its 



