202 LIMITS AND FLUXIONS 



X and y are to each other in a given ratio, then in 

 xy = z it is argued that 2y = ìucr. of ^-^incr. of 

 x = è-^x; hence é=2yx. Whenj' = x, this becomes 



è=2x±; one has also, fluxion x-\-y =2x-\-vxx-\-y 

 = 2 X xx-\-yx-\-xy -\-yy. 



From this is derived the fluxion of any rectangle 



2 



xy, thus : The fluxion of xy, or x'^-\-2ry-\-^y is also 

 equal to 2;ri-H- 2/j> + fluxion of 2xy. Hence fluxion 

 of 2xy = 2xy + 2;ir;/. 



** In the same manner as the quantities ;r, j/, 2, are 

 conceived to flow, and to have their fluxions, so 

 may the quantities i-, j>, i-, be supposed to be variable, 

 and therefore have their fluxions, which are thus 

 represented x,y, z, and are called the second fluxions 

 of x,y, z" (p. II). **The fluent of any quantity as 

 x"'x is represented thus \x'"x\.'^ 



William West, 1762 



176. William West's Mathematics'^ is a posthum- 

 ous work ; the author died in 1760. Fluxions are 

 treated from the earlier Newtonian standpoint, 

 infinitely little quantities being used. Some novelty 

 is claimed for this text in the treatment of maxima 

 and minima. 



Janics Wilson^ 1761 



177. In 1761 Wilson coUected some of Benjamin 

 Robins's mathematical tracts in a two-volume hook, 



1 Mathematics. By the late Rev. Mr. Wm. West of Exeter. Revised 

 by John Rowe, London, 1762. There appeared a second, corrected, 

 edition in 1763. 



