[ 522 ] 



or its continuation. Becaufe tf= mzz 



73775 n p = the perpendi- 



n+I. 



cnlar from C on the tangent to the curve, mz z • 



in+i 1 Z Jll+4 2 2fl-)-22 



\ fzz pi . \ Therefore r p - m z — m z /> or /> = 



n+2 



m z 



-1 7n + 2~ a — 7T+7~ 5 the equation of the fpiral of which E « C 



is a portion. ' 



3. Let a = m z z 



— ^rr-T^rr ;i beinff any whole pofitive num- 



ber, and m a numerical coefficient, 



2r a V/r* — zi\ = 2 m r^ 



the fluent of ■( y when z = r. 



) 2 • ^ ., _ 4 ?«r3 



—a "" r* —z^ ]i 7 %=--T=~ 

 3 ' 3«+i-« + 3 



n . 



Becaufe in this hypothefis a = mzz ^ ^^^^ ^ ;^ ^^ 



odd number the relation of a and z will be algebraical ; when 



n is 



