SECTION 16. DEFINITE, EXACT, AND MATHEMATICAL PROCEDURE. 127 



the body and motion, but in certain periods. Moreover, in the 

 explosion of several guns at once, which are heard sometimes 

 to the distance of thirty miles, the sound is caught by those 

 who are near the spot where the discharge is made, sooner 

 than by those who are at a greater distance. Even in sight, 

 whereof the action is most rapid, it appears that there are 

 required certain moments of time for its accomplishment; as 

 is shown by those things which by reason of the velocity of 

 their motion cannot be seen as when a ball is discharged from 

 a musket. For the ball flies past in less time than the image 

 conveyed to the sight requires to produce an impression." 



The application of the higher mathematics to science evidently 

 had its origin in the difficulties encountered in direct measure- 

 ment, difficulties which made recourse to complex calculations 

 inevitable. 1 On this subject also, we venture to quote Bacon. 

 This will serve a double purpose, demonstrating both the high 

 scientific and philosophic status of mathematics, and their 

 generous appreciation by Bacon. The gay medievalism of the 

 style renders the more remarkable the sober modernity of the 

 conceptions embodied therein. 



"There remaineth yet another part of natural philosophy, 

 which is commonly made a principal part, and holdeth rank 

 with physic special, and metaphysic, which is mathematic ; but 

 I think it more agreeable to the nature of things, and to the 

 light of order, to place it as a branch of metaphysic: for the 

 subject of it being quantity, not quantity indefinite, which is but 

 a relative, and belongeth to philosophia prima, as hath been 

 said, but quantity determined, or proportionable, it appeareth to 

 be one of the essential forms of things ; as that that is causative 

 in nature of a number of effects ; insomuch as we see, in the 

 schools both of Democritus and Pythagoras, that the one did 

 ascribe Figure to the first seeds of things, and the other did 

 suppose Numbers to be the principles and originals of things ; 

 and it is true also, that of all other forms, as we understand 

 forms, it is the most abstracted and separable from matter, 

 and therefore most proper to metaphysic ; which hath likewise 

 been the cause why it hath been better laboured and enquired, 

 than any of the other forms, which are more immersed in 

 matter. 



"For it being the nature of the mind of man (to the extreme 

 prejudice of knowledge) to delight in the spacious liberty of 

 generalities, as in a champaign region, and not in the inclosures 

 of particularity; the mathematics of all other knowledge were 

 the goodliest fields to satisfy the appetite. 



"The Mathematics are either pure or mixed. To the pure 

 mathematics are those sciences belonging which handle quantity 



1 A comprehensive survey of this problem will be found in Leon Brun- 

 schvicg's work already cited. 



