Of GRE'ATEST ATTRACTION, 221 



bafe, and AB for its altitude; therefore m*=:-X*b z X2a 



9 3 



= 3 * a £ 2 : fo that b = — — = 2 , and - = 2 — s . 



But becaufe AF : AC : : 1 : cof <p, or b:a:: 1 : cof <p, h 1 — 



— —j., and — = — jr-p 

 cof<p # coi<p 



Now fince £ 2 = — ^r-,, and alfo ^ = £—, we have — ^-, = 

 cof <p 4.^ a coi <p 



3J^I, and «' = -^ . cof <p 2 , or if l£i = «*, a J = »* . cof>\ 



4 *■# 4 a - 4?r 



and # = /zcofp s . 



Hence, as — zz — ? — , — zz ■— 



a cofp* a cof<p 



£* a__ b % __ nco{<p 3 _ 



0\ 



cof<p 3 

 By fubftituting this value of — in the value of F, we have F 



a 



___ 4sr» tanp — <p r fin <z> 3 ,, 



= — — - • — r 1 ! and becaufe tan <z> 3 — — -i-, F ~ 



cof>* t " n * co£ > J 



2 «■ » . (tan <p — <p) . cof <p * mm 2 <x n (tan <p — <p) cof p 7 __ 



2 a- n (tan f — ?) . cof 9 3 . fin £ . 



Now when the product of any number of factors is a maxi- 

 mum, if the fluxion of each factor be divided by the factor it- 



Ee 2 felf, 



