A Theory of Fluxions. 



33:5 



1. Draw the circles ABCD, EFGH, IKLM, NOPQ, and 

 from the points, where the radius RS intersects the circles, 

 draw the ordinates Ra, Tn, Vm, Wr, and ARa, ETw, IVm, 

 N Wr, will be a series of fluents. Suppose the fluents that 

 are taken to be IVm, and NWr. Put the diameter WX=«, 



VZ=w, the abscissa Nr=x ; then Wr=(ax — x 2 ) 2 , hn= 

 — ,rw=x',ms = — , Vm=-(ax — x 2 ) 2 . Hence the fluxion 



Wwr=WrXr=(M-x 2 )V=a 2 i 2 r- - — -— , &c, and 



2a 2 



the fluxion Vxsm=Vm X _=_(«»- x 2 ) 2 x> — 



a a 2 



n^x^x" 



fl j 



n-x'x' 



<Za/> 



, &c. 



