442 ANTIENT. METAPHYSICS. Book V. 



And here we may obferve, in pafling, the truth of Ariftot1e*s obfer- 

 vation, that equal or unequal can only be applied to quantity^ not to 

 quality i for it is impoflible that the definition of the equality of 

 magnitudes can be applied to any thing but magnitude. And, as to 

 numbers, the equality of them is made by their conlifting of the fame 

 number of monads, which Ukewife cannot be applied to qualities *. 



That 



* Quantity, therefore, is not only a (landard Ly which it meafures itfelf, but it is 

 the flandard by which every thing elfe is meafured. Thus, without magnitude, there 

 is not only no motion, but no menfuration of motion ; for, we fay motion is great or 

 fmall, quick or flow, according to the fpace which the magnitude goes through in a 

 certain time; and, as time cannot be without motion, fo it is meafured by motion; 

 for it is meafured by the fpace which the body that is moved runs through. Thus, 

 what makes the year, is the fpace of the ecliptic, compafTed by the fun. The meafure, 

 therefore, both oi motion and time^ is ultimately derived from magnitude- (See Ariftot. 

 Metaph. lib. 5. cap, 3.) The moment, or the weight of bodies, is, in the fame manner, 

 meafured by magnitude ; for that body has the greateft weight, that can raife up or 

 impel forward the greateft magnitude. Even qualities, as far as they are capable of 

 meafure, are mealured by magnitude and motion. Thus, the thermometer meafures 

 the degrees of heat and cold by the expanfion of bodies ; and it is in that way only 

 we can fay one degree of heat is equal to another; for, when we fay fo, we do not ap« 

 ply the ^crm equal to the degrees of heat, but to the expanfion of the magnitude ; 

 meaning, that, by the one degree of heat, the magnitude was as much expanded as 

 by the other. But, as I have elfewhere obferved (p. 39i-)> even that cannot be faid with 

 cxaclnefs. 



As to quantity difcrete^ or number^ It is a meafure that applies to every thing that 

 can be divided into parts correfponding to monads ; and the ufe of it is ftill more ne- 

 ceffary than the menfuration by magnitude ; for, without it, men couM not live at all In 

 fociety, or carry on any of the common arts of iiie. I he moft; wonderful application of it, 

 I think, is to mu(;cal founds, by wliich they are divided into notes ; and the ratio of the 

 notestoone another, according totheir different degrees ofacutenefs or gravity, is afcer- 

 tained by numbers But even this was, at firlf, done by magnitudes, or weights ftretching 

 thtfe firings j but, as the confequence of that was only to make the vii. rations of the 

 firing more or fewer in the fame time, it is ultimately by numbers thai the ratio of 

 7iotes is fixed. 



