ti6 BE EFlCTCLOlDIpVS 



cloidis hoc motu genitnm , habemus ideo BL : L/:: 

 Bp: ^(3; vel L/. Bp— BL. ^»(3. 



lam dicendo radium circuli immobilis BE , 

 qui eft BC"r^, radium circuli generatoris BG:=/», ar- 



2 2 



culumB^— B?r=B(3=:^<f:erunt^fc'^^' » ^P— ^ & cofi. 

 nus anguli ^eb-zzJj ; furrogatis ergo in lemm. i- ^ > ^ 



pro /> & ^ , inv.enietur /;p-,liV"L^|^^±^[l , & ^quatio 



L/.Bp— BL. ^(3 mutabitur in ab. L/=</j-.BL in 

 V{aa-2bab-^bbl hoc eft =BL. LmV(aa—2hab-\-bb)j er- 

 go ab/LIhoc e{\: ab EL—V {aa-2hab--\-bb)m fBL.Lm 

 (id eft per lcmm. i2. )= =:AB. BPl/(^^-2/'^^-H/'^):=^ 

 b. sBFV^^^cz— 2^«/'-f-/'/')&dividcndo per /'^habetur <2 ELzr: 

 GBP/^/T^-a^^^+^/^^.Quare EL : 2BP: :V{aa-'Qhab-+-bb) 

 : ^. Q. E D. Coro/A i. 



Ergo tota epicyclois eft ad dupJam diametrum AB 

 circuli generatoris ut V{aa—2hab-\-bb) ad^. 



Coroll. 2. 

 Sl /fci feu finui toti , quod conttngit,cum ambo 

 p1ana circuli generatoris & immobiiis coincidunt , tunc 

 erit Epicyclois ad duplum diametri generatoris,ut^— ^ ad a, 

 id eft ut differeatia radiorum circuU immobiiis& genera- 

 toris,ad radium immobilis. 



Froblema. 



Invenlre in plano Sphxrae ichnographico quotcun- 



que pundla ichnographica Epicloidis. Vid. Fig. 6. 



Eig. 6. Sit ALB circulus generator feorfim defcriptus, ad 



terminum A diametri AB eredla normaliter indefinita 



AQ, capiantuj: in eadem partes AO ; AQ, qu3c fint ad 



dia- 



