i<r G. H. COSTJORDBNS 



Secior DEF = ^ An^. AGF, porro 

 A DF-F = I A DFG = i DF X FG = ^2 §;„_ q q^^^ q^ 



Posito ergo pro c valore <» 4- 2^ , erit 



S = C^ + ^^Ua + Z.) ^3^^^_ DEF- ADEF>.... (C) 



!!• S = i/*^ "^ • ^^Sm- DF = spatro Epicycloidali BAF. 



Quum circulus generator semicircumvolutionem perfecerit, erit: 



b = spatio ABrP(^A =: ^ . area semicirculi "«neratorj» 



ab 



_ (£ + a*)_l£±*_) ,., 



- ab • -* ""' 



Est vero Sector ABQA = ^abv', ergo- his sabstractis, 

 III. Spatium BFPQK = {^~^) . i^V 



^—J^ j . area semicircun generatoris .... ( D) 



porro Sector BAD = | . Sector DEF 



et A DAF = 7 . A DEF. 



b 



£x aequatione ( C ) , «juam supra invenirous , vidimus » esse 



Spatium BAF = ('» + '^) ('^ + ^) (-sect. DEP - aDEF). 

 ab 



ergo addendo aDAF et subtrahendo Sectorem BAD, erit Sector, qui contina- 



lur inier arcum cirtalarem BD, arcura EpicycloJJis BF et cliordam FD, sive 



IV. BDF = ( •'""^''^ ) (Sector DEF — aDEF) 



— (jf. — L^ . segmentum DF; et hinc ex (D) 



V. Spatium DQpFD = \^-——) (area semicirculi gencratoris — Segra. I)F) 



^^-i-^ . Segm. DFG ( i ). 



5-7. 



f O Vid. KHgtl vttt £fii)lcU7Ji, No. lo— M, ttjti. Btr*euilll In Ltct. ciit.f Lect aa «t 93 Opp, Tom. Ub 

 #»!• 451— 457. 



