I 



70 INFENTIO CFRFJRFM MAXIMI MINIM. 



—rdx erit is m— 7~^- Hinc area AMO crit 



-^-f'—^J = --/ ^oporteter- 



r 



go vt fit j'^^=^=ir^— minimnm; quare habebimus Q_— 

 (i±f^ et (/Q_=t^;±£^'~^^;/^-. ErititaqueL-o, 

 ul-o,^-o,V-^^^^ttW--^^P\ Quocirca 

 cumfit dd^=:dVdx\cnid^:=iVdx-\-hdx.Ent antem W 

 — f^^ ^j^ et V— j^^ - j^,- . Hanc ob rem 



erit —-dd^ 1- -ddp — ddy -t-^ax leu ^j^^j — 



±^^^^Adx fiue {i-\-pp''-dxddp — ^p(i~^pp) 

 ^x ^p^-^Adp\ Ponatur a^.v = t^ vt fi t ddp - ^ , 



(^^P)idr^^u^P)zPdP:^Adp, cuius integrale eft B- 

 Ap-'^ feu "f,^^-^=^-v. SiponaturB = o, fiet 

 .v==:7ipff=^^dF" '^tJ{UQ xdx^-\-xdf-~adx'' , vnde 

 erit dy — dxV-^^^ quae efl; aequatio pro cycloide in A 

 maximum radium ofculi habente. At fi Azro erit 

 ^■^.z=:.dx feu ^^^,-dy erit ergo jrr;-:^ feu 

 y — d§- vnde fit x — / ^J^j , quae efl: pro cyclode in 

 A cuspidem habente. Generatim vero erit d s :zz 

 Bdp-Apdp , ap-\-b 



~adj-\-bdx., quae integrata dat s^~2aj~\-ib x , et 



'Vi^.ay 



