CHAP. VI.] AijVAiiTAGES OF MATHEMATICS. 147 



CHAPTER VI. 



Tlie Great Appendix of Natural Philosophy both Speculative and Prac- 

 tical. Mathematics. Its Proper Position not among the Substai.tial 

 Sciences, but in their Appendix. Mathematics divided into Pure 

 %nd Mixed. 



It was well observed by Aristotle, that physics and ma- 

 tliematica produce practice, or mechanics;^ therefore, as we 

 have treated both the speculative and practical part of the 

 doctrine of nature, we should also consider mathematics as 

 an auxiliary science to both, which being revived into philo- 

 sophy, comes in as a third part after physics and metaphysics. 

 But upon due recollection, if we designed it as a substantial 

 and principal science, it were more agreeable to method and 

 the nature of the thing to make it a part of metaphysics. 

 For quantity, the subject of mathematics applied to matter, 

 is as the dose of nature, and productive of numerous effects 

 in natural things, and therefore ought to be reckoned among 

 essential forms. And so much did the power of figures and 

 numbers prevail with the ancients, that Democritus chiefly 

 placed the principles of the variety of things in the figures 

 of their atoms ;^ and Pythagoras asserted that the nature of 

 things consisted of numbers.*' Thus much is true, that of 

 natural forms, such as we understand them, quantity is the 

 most abstracted and separable from matter; and for this 

 reason it has been more carefully cultivated and examined 

 into by mankind than any other forms, which are all of 

 them more immersed in matter. For, as to the great disad- 

 ••''imtage of the sciences, it is natural for men's minds to 

 delight more in the open fields of generals, than in the in- 

 closures of particulars, nothing is found more agreeable than 

 mathematics, which fully gratifies this appetite of expatiating 

 and ranging at large. But as we regard not only truth and 

 order, but also the benefits and advantages of mankind, it 

 seems best, since mathematics is of great use in physics, 

 metaphysics, mechanics, and magics, to make it an appendage 

 or auxiliary to them all. And this we are in some measure 

 obliged to do, from the fondness and toweling notions of 

 mathematicians, who would have their science preside over 



* Metaphysics, i. and xi. ^ LaertiuB, Life of Demociituat 



' lamblicus. Life of Pythagoras, 



1.8 



