20 



A .P P E N D I X. Chap. I. 



mines the dimenfions or boundaries of bodies by lines or figures. 

 Befides thefe, there is a quantity of moving force in Bodies that are 

 moved, which the mathematician computes ; and this part of the 

 fcience is what is called mechanics. 



From this account of the fubjeds of mathematics, it is, evident that 

 an inquiry into the caufe of the beginning or the continuation of 

 Motion does not belong to that fcience, but to another fcience quite 

 different, though, as 1 have obferved, it h by tlie fcience of mecha- 

 nics that the Motions of Body are meafured and computed. At the' 

 fame time, 1 will let the geometer know, what perhaps he does not 

 know concerning his own art, if he has not learned the antient 



philofophy That it is in one fenfe the dodrine of caufes. To 



underftand this, he muft know^ Ariflotle's divifion of caufes in- 

 to the material^ the efficient, \\\& formal, and ihtJinaL Now, geome- 

 try, when it defines the feveral figures, and demonftrates their pro- 

 perties, fhows the formal caufe of them ; for it fliows that which 

 makes them what they are, or, in other words, their nature and ef- 

 fence. The fame is true of the fcientific arithmetician, who defines 

 numbers, divides them into feveral claffes, and demonftrates their 

 different qualities and properties. And Sir Ifaac Newton, when he 

 has demonftrated the laws of the ccleftial Motions, may be faid to 

 have alfigned the caufe of them in this fenfe of the word. Thus 

 far, and no farther, does mathematics go in the inveftigation of cau- 

 fes ; for, as to the material caufe, or matter, of which any of its 

 figures are compofed, or with refped to the efficient caufe, by which 

 anv of the fubjedls it examines are produced, fet in motion, or con- 

 tinued in motion, or with refped: to the final caufe, that is the end 

 for which they w^ere produced, and are moved, concerning thefe it 

 inquires not, but leaves them entirely to the philofopher. 



And 



