[ 34^ ] 



Example IV. Having given the logarithmic fecant of 45° 

 to the modulus radius (r) = s, and the logarithmic, fecant of 

 any arch a — s + I to find a in a. feries afccnding by the powers 

 of /. 



Solution. Let « = the fecant of a. Then by the circle 



n r' 



alfo becaufe s + / ~ log. « to the modulus r, / ~ 



riy/n' — r' 



r n 



rl 



.• a = -^=_^=z or (A) a^ X «" — r' = r' /^ To facilitate the 



v/2» r 



3 



computations of <7, <?, ^, &c. from the equat. A, when /— 0, 

 <; = the arc of 45, and when alfo 72^ = 2r2, let a^ = iv* = B, 



Now becaufe n — — . 

 /■ 



I ft. FliTxion of K- = inn — z'^rl^ fubftitutlng for /, L 



2d. Fluxion of «* = — ^ — •— - = 2' /*. 



m + 1 

 2 /"■ 

 m"' Fluxion of «^ = ri^z:; — 



Whence 



