172 ADVANCEMENT OF LEARNING 



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; 3 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 disadvantage of the sciences, it is natural 

 for men s minds to delight more in the open fields of gen 

 erals, than in the inclosures 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 

 V 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 towering notions of mathemajicians, who would have 

 their science preside over physics. It is a strange fatality, 

 ^ that mathematics and logic, which ought to be but hand- 

 \jnaids to physics, should boast their certainty before it, and 

 even exercise dominion against it. But the place and dig 

 nity of this science is a secondary consideration with regard 

 to the thing itself. 



Mathematics is either pure or mixed. To the pure belong 

 the sciences employed about quantity, wholly abstracted 

 from matter and physical axioms. This has two parts 

 geometry and arithmetic; the one regarding continued, and 

 the other discrete quantity. These two sciences have been 

 cultivated with very great subtilty and application; but in 

 plain geometry there has nothing considerable been added 



2 Laertius, Life of Democritus. 3 Lamblicus, Life of Pythagoras. 



