Chap. VIII. A NTIENT METAPHYSICS. 441 



plain, which Is not difficult for him to do; for, if ithad depth orthicknefs, 

 rt would not be the boundary or extremity of the folid ; for it would 

 have itftlf an extrenuty, which would be the extremity of the folid. 

 This Ariftotle fhortly expreflfes, by faying, * That an extreme muft ne- 

 *'ceirarily be different from that to which it is the extreme*.* 



Further ftill, a fuperficles, if it be not infinite, which is contrary to 

 the hypothefis, mulf have bounds or extremities likewife. The bound 

 or extremity of a fuperficies is what is called a line^ defined by Euclid 

 to be length without breadth. But neither does he tell us why the 

 line has not breadth, leaving this alfo to the metaphyfician, who gives 

 the fame reafon for a line wanting breadth, that he does for a fuperfi- 

 cies wanting depth, namely, that it would not otherwife be an extre- 

 mity, for it would itfelf have an extremity. 



Again, according to the hypothefis, a line alfo mufl: have Its extre- 

 mities; and thofe extremities are called points, which, fays Euclid, have 

 no parts, though he does not add the reafon, which is, that otherwife 

 they would not be extremities,. 



All thefe confequences refult from the hypothefis of magnitude li- 

 mited ; And, from the fame hypothefis, there is another neceflar^^ con- 

 fequence, that it muft have a fite or pofition, which, as Ariftotle has 

 oblerved, is what diftinguifiies eflentially the fubjedl of geometry from 

 that of arithmetic ; for monad and number have no fite. Now, if 

 magnitude have a pofition, it mufi neceflarily occupy a certain por- 

 tion of fpdce, which is called \i2, place. 



And from hence we may colled the definition of equality^ namely, 

 occupying or filling the lame (pace, of which Euclid has made an axi- 

 om, viz. axiom eight, though, 1 think, he rather Ihould have put it 

 among his definitions. 



K k k And 



• Phyf. lib. 6. cap. f . 



