440 A N TIEN T MET A PHYSICS. Book V. 



it is menfuicJ as the orhcr is 7iumhered\ for, thougli the parts, into 

 whicii q.ia icity continuous ib divided, may be numbered ; yet that 

 divifi )ii iuto parts can;iot be without menfuration, that is, the ap- 

 plication of ibme quantity of the fime kind to it j fo that the capaci- 

 ty of being meafured is the primary atfedtion of this kind of quantity. 

 It is a quantity of this kind that Euclid calls magnitude^ and which is 

 nothing elfe than body, or matter extended, but of which the exten- 

 fion only is confidered by geometers, not the thing itfelf that is ex- 

 tended. Now, this extenfioii is in three feveral ways, the diftindion 

 of which, as is natural enough, we have taken from the pofition of 

 our own bodies ; for, what is before and behind us, we call length ; 

 what is to the right and left of us, we call breadth ; and what is up 

 and down, with refped; to us, we call depth. Thefe are the three di- 

 menfions of body ; and whatever has all the three, is called a foUd, 

 which Euclid has defined to be that which has length, breadth, and 

 depth, or thicknefs. But he has not told us what any of thefe three are, 

 leaving that alfo to common fenfe and apprehenfion. As to the real 

 exiftence of body, and by confequence of its dimenfions, the geo- 

 meter proves nothing ; but he goes upon the fuppofition that they 

 do exift ; and, as there is nothing impoffible in the fuppofition, there 

 is no reafon why it Ihould not be granted. 



Further, geometry fuppofes that all magnitudes are not infinite or 

 indefitiite, but that fome are terminated or bounded ; and, therefore, 

 that there is fuch a thing di^fgurCy which is nothing elfe but ??iagni" 

 tude tenninated \ this, alfo, is an hypothefis that muft be granted. 



This being admitted, the p:eometer proceeds, and fays, that a fo- 

 lid is bounded b) fuperficiefes ; and a (uperficies, as Euclid has defi- 

 ned it, is that wl\ich has length and breadth, but not thicknefs. That it 

 muft have length and breadth, is evident ; but he has not told us why 

 it has no thicknefs, leaving this likewife to xhtfiji philofophy to ex- 

 plain 



