340 ANTIENT METAPHYSICS. Book III. 



Thefe are the rabjedls of arithmetic. As to geometry , the fubje6: 

 of it x^Jigure^' which is either plane ox foil d. Of the folid, the plane 

 or fuperfcies is the boundary ; and what is contained within the fu- 

 perficies bounding the fohd, is what we call body, T\\q fuperfcies^ a- 

 galn, Is bounded by lines^ and the lines by di point. 



Thus, it is evident, that geometry does not go deep into the nature 

 of things ; for the fubjeifl of it is neither body nor 7?iind ; of which 

 two the univerfity of things confifts ; but It Is only the furface of 

 things with which It is converfant : But, as the ideas o^fgiires^fuper^ 

 fciefeSi and luies^ are fimple and determinate, and therefore capable of 

 moft prccife definition, the fclence from thence arifing Is accurate and 

 demonftratlve, though it do not, as Plato has obferved, and as we fliall 

 afterwards ihow, demonftrate Its principles, but afTumes them. 



There is a third fubjed of mathematical fclence befides number^ and 

 the dimenfions of body ; and that Is motion : For the mathematician 

 confiders ^0^/ in motion, as well as at reft; explains the different 

 kinds of its motions ; fhows how they are compounded ; and applies 

 arithmetic to calculate the force of the movi?ig pozver^ and the quanti- 

 ty of motion produced by it. From motion, thus confidered, arife 

 three branches of mathematical fcience, viz. aftronomy, mechanics^, and 

 vnific ; which, in fo far as they derive their principles from geometry 

 and arithmetic, are demonftrative fciences. 



Thefe are the fubjedls of mathematical knowledge ; and we are now 

 to (how how much farther metaphyfics go into the nature of things — 

 The fubjed of metaphyfics is the ivhole of things. This, as I have 

 obferved, cannot be otherways known than in its principles or caufes. 

 Now, thcle muft neceffarlly be what is mofl general in nature ; for it 

 is from generals \\\zX particulars are derived, which cannot exift with- 

 out the generals \ whereas the generals may exift without th^ particu- 

 lars^ 



