Chap. VIIL ANTIENT METAPHYSICS. 443 



That a magnitude fliould have a fite or pofition, is abfolutely necef- 

 fary ; but it is not necclTary that it (hould change its pofition, that is, 

 fliould be moved : Yet this is a geometrical hypothefis, which every 

 one, but a quibbling fbphilt, fuch as, they fay, Zeno the Eleatic was, 

 who contended that there was no fuch thing as motion, muft admit. 

 And the conlequence of this movement of magnitudes is, that they 

 may be conceived in any part of fpace, or in any pofition, with re- 

 fped to one another. 



Thefe may be called the general hypothefes of geometry ; and I 

 come now to fpeak of Euclid's definitions, which are only more par- 

 ticular hypothefes ; for he feems to have imagined, that thofe general 

 hypothefes did not belong to his fcience, but that it was the bufinefs 

 of the firft philofophy to examine them, and to inquire whether they 

 were to be admitted or no. Of his definitions of a point, line, and 

 fuperficies, I have already fpoken. The fourth definition is an hypo- 

 thefis concerning a line, by which it is fuppofed to lie evenly betwixt 

 its extreme points, and then it is called 2.Jiraight line. The feventh 

 definition, of a plain fuperficies, is an hypothefis of a fuperficies, in 

 which any two points being taken, the ftraight line between them lies 

 wholly in that fuperficies. The eighth definition, of a plain angle> 

 proceeds upon the general hypothefis above mentioned, of magnitudes 

 being capable of variety of pofitions, with refped: to one another, and 

 fuppofes that two lines in a plane inclineone to theother,foasto meet, 

 but not in the fame direction. The definition of a right angle is, in like 

 manner, taken from the pofition of one line, with refpedt to another. 

 And the fame is true, not only of all his definitions of angles, but of 

 all his definitions of plain figures, that is, lines inclufingZ/j^cd". And 

 what he calls parallel lines are lines fuppofed to be in luch a pofition 

 to one another, that, though produced ever lo far at either extremity, 

 they never will meet *. 



K k k 2 Thefe 



* That Euclid's defiii'ttons are all hypothefes, is the opinion of Proclus, in the 

 fecond book of his commentary upon Euclid's Firft Book of Elements, p. 22. An 



authority 



