298 A SHORT HISTORY OF SCIENCE 



it may be done ; or two curved lines being given, to find the relation 

 of their areas when it may be. 



8. To find such curved lines whose lengths may be found, and also 

 to find their lengths. 



9. Any curve line being given, to find other lines whose lengths 

 may be compared to its length, or to its area, and to compare them. 



10. To find curve lines whose areas shall be equal or have any 

 given relations to the length of any given curve line drawn into a given 

 right line. 



11. To find the length of any curve line when it may be. 



12. To find the nature of a curve line whose length is expressed by 

 any given equation when it may be done. 



Such were the improvements in the higher geometry which Newton 

 had made before the end of 1666. 



Such is a brief account of the mathematical writings of Sir Isaac 

 Newton, not one of which was voluntarily communicated to the world 

 by himself. The publication of his Universal Arithmetic is said to 

 have been made by Whiston against his will ; and, however this may 

 be, it was an unfinished work, never designed for the public. The 

 publication of his Quadrature of Curves, and of his Enumeration of 

 Curve Lines, was in Newton's opinion rendered necessary, in con- 

 sequence of plagiarisms from the manuscripts of them which he 

 had lent to his friends, and the rest of his analytical writings did 

 not appear till after his death. 



An account of Newton's very important work in analytic geome- 

 try and the theory of algebraic equations lies outside the range of 

 the present work. 



Much of Newton's reluctance to publish his more revolutionary 

 theories may be attributed to his distaste for controversy, and he 

 was unfortunately involved not only in such issues as to priority 

 as his own reticence invited, but also in defending himself against 

 attacks on philosophic grounds. The character of some of these 

 may be illustrated by the following passages from an eminent 

 critic, Bishop Berkeley : 



He who can digest a second or third fluxion, a second or third 

 difference, need not, methinks, be squeamish about any point in Di- 

 vinity. 



