LATER BOOKS AND ARTICLES 245 



generating celerity uniformly contìnued during that 

 time." 



*'. . . If the motion of increase be accelerated, 

 the increment so generated, in a given finite time, 

 will exeeed the fluxion : . . . But if the time be 

 indefinitely small, so that the motion be considered 

 as uniform for that instant ; then these nascent 

 increments will always be proportional, or equal, to 

 the fluxions, and may be substituted instead of them 

 in any calculation." 



The fluxion oi xy is derived in two ways : the first 

 by the method of considering the rectangle composed 

 of two parts, as previously expounded by Rowe. 



The second method finds algebraically the incre- 

 ment xy +yx'' +xy, " of which the last term x'y is 

 nothing, or indefinitely small, in respect of the other 

 two terms, because x' and y are indefinitely small 

 in respect of x and y. . . . Hence, by substitut- 

 ing X and j> for x' and y, to which they are propor- 

 tional, there arises xy-\-yx for the true value of the 

 fluxion oi xy." 



S. Vince, 1795, 1805 



213. Vince's Principles of Fluxions appeared in 

 1795 as the second volume of the Principles of 



Mathematics and Naturai Philosophy in Four 

 VolumeSy^ which were brought out under the 



general editorship of James Wood. A second 



^ The Principles of Mathematics and Naturai Philosophy in Four 

 Volumes. Voi. II, The Principles of Fluxions : Designed for the Use 

 of Students in the University. By the Rev. S. Vince, A.ÀI., F.K.S., 

 Cambridge, 1795, 



