nVOl-VIAE IPSAE SE GENERAKT. 223 



ob arcum MG=DG, angulus DOG— 4 MRGrr^-EKB; 

 Ergo PMLr=:EBK-4EKB-^OD=EBK-i-i^EKB -^, 

 EKB - ^ EKB-rfOD =EBK -+- + EKR-£^1eKB- 



r/0D=:90^ - ^^^1 EKB-r/OD . 



5. Ergo tandem elicitur/JwN-PMLmpo— ^ 



o-h& 



EKB-90-H^^ EKB+^/OD ; hoceft ,/)/«N-PML=z 

 angulo conftanti ^OD. Q: E. D. 



Corollarhim i. Quoniam DB : BEA~DOBx^: 

 iSox^; erit ob DBn: BEA, DOB:=|- i8o; et angulus 

 D0r/=90-D0B — 90-^180. Sit iam difFerentia 

 data angulorum nuJla , Yt triangula j);;/N , PML liant fi- 

 miiia , erit 903=^180, aut h^zrza Iioc eft, OBzzBAj 



qui efl: cafus fimpliciflimus, ^bi nempeEpicycJois termi- 

 natur in fine quadrantis d. 



CoroUarlum 2. Poterit vero inqualibetEpicycIoi- 

 deobtineri,Yt (iib iisdemconditionibusTheorematis, an- 

 guh intra radios okuli et perpendiculares ad reiflam ali- 

 quam pofitione datam demiffas, fmtaequales, confe- 

 quenter triangula illorum angulorum fimilia. Dncatur 

 enim Fig. 6. reda AN , fub quouis angulo NAO, nt- 

 que ad eam perpendiculares demittantur MS , ;;/Q, erit 

 perTbeorema 2^e-i-f-cz=:k, et ob triangula MSR,RAP 

 fimilia, hzzj:zid. \g\im e—czzik — h^ et ^ — r — ^zrangulo 

 conftanti k—2h. Itaque fi ponatur h—^j^k , erit e-c-d 

 :::zo^ et ez:z.c^d. 



Por- 



