Chap. in. ANTIENTMETAPHYSICS. 391 



and therefore we fay of them, as Ariftotle has obferved, not that 

 they are equal or unequal, but more or ids, like or unlike *. 



The firft geometrical axiom I fliall mention Is this, ' That the 

 * whole is greater than the part.* The meaning of which is, when it 

 is analyfed according to Ariftotle's method, thut greater than the part 

 is an accident or quality of the idea of ivhole. Now, this is a felf- 

 evident propofition; becaufe the connection betwixt the praedicate aod 

 fubje<fl is immediately feen, if we underftand the meaning af the 

 terms ; for a whole being that which confifts of parts, two or more, 

 all which together are only equal to the whole, we immediately per- 

 ceive that it would be a downright contradiction to fuppofe that one 

 of thefe parts was equal to the whole. 



Another of thefe axioms, and which Is placed firft in Euclid's or- 

 der, is, * That things which are equal to the fame thing are equal to 



' one 



• See Ariftotle's Categories, cap. 6. injlne. This Ariftotle fays of quantity in ge- 

 neral ; and it is as true of quantity difcrete^ or number^ as it is of quantity continu- 

 QUSy fuch as body \ and, for the fame reafon, namely, that number furnillies for itfelf 

 a fixed ftandard oi meafure, by which its quantity is precifeJy afcertained •, fo that 

 one number maybe faid to be exadlly equal to another, or in a certain ratio to it. A- 

 mong other difcoveries of Nature we have made in modern times, by means of expe- 

 riments, we have found out a way of meafuring the degrees of heat and cold, by the 

 afcent of fluids in a glafs tube. But, in the firfh place, as we do not know the begin- 

 ning of heat or cold, we cannot tell what ratio any degree of it has to the whole. But, 

 idly^ we are by no means fure that the degrees marked upon even a mercurial ther- 

 mometer, are exa£tly equal to one another. We are very fure that the afcent of fpi- 

 rit of wine, in a thermometer, is very different, according to the diilerent degrees of 

 heat; and, though the difference is not near fo great in a mercurial cheimometer, 

 there is good reafon to think, or, rather, there is a certainty, that there is fome differ- 

 ence. We cannot, therefore, prccifely know even the excefs of one dcgret of heat or 

 cold above another. — See what I have further faid concerning the difference of qua- 

 lity and quantity, in a note upon page 297. 



