as= (149)" 



F M-' -f- F N=' = 4-M G' -I- 2 E F' — 2 G M^ . £^;. 



lam fi punda F ct G iuiignnriir linea recfui FG, liquct efTc 

 f \1» _l_ F JV' =: 2G M' H- 2F G', hincquc coUiiiitur 

 F G' = E F'-f- G M' i<-"*--c"'', vndc ftatim dcducitur 



4(FG* — FE"j = (M F-N F/, 

 quac proprictas omnino attcntionc di^na vidctur. 



§. 9. Quoniam dcmonflratio Theorematis a Cel. Lom- 

 bert propofiti in lupcrioribus adornata ad cum cafum^ rc(lric>a f|„ g 

 ert, quo pro altcro fcctorc Elliptico «Q/wF, corda n tn pcr 

 ipfum axcm maiorcm D Q bilccatur ipfique crt ordinatim ap- 

 plicata, nunc quidem opcrac prctium vidctur \x hoc Thco- 

 rcma aliquanto gcncralius tratflcmus. Sint igitur binac Ellip- 

 lci ANQB, ani/b, quarum axcs maiorcs AB, ab intcrTah. IV. 

 fc acqualcs, tum iu his Eilipfibus ducantur binae cordae .f'8- ^ 

 N M ct n ;// cum in modum vt non folum intcr fc fint ac- 

 qualcs, fcd etiam vt fummac lincarum rcdarum cx focis F, / 

 dudarum ad punda exrrcma harum cordarum iutcr fc acqucn- 

 tur, hoc efl vt fit F M -h F N —ftn-{-fn; erit fcdor El- 

 lipticus NQMF ad fec"torcm Elhpticum nqmf vt fcmiaxis 

 miaor prioris F.llipfis ad illum poitcrioris , fcu vt C\\:cb, 

 Ponamus igitur cordas N M, n m in G ct ^ &^t bifcdas et 

 ductis Diamctris C Q, t(/, quac his cordis in G, ^ occur- 

 runt, iungantur F Q, f^, quae cordis illis N M, w w in E 

 ct e occiirrant, diair.etris autem coniugatis ipfarum. C Q, C(]^ 

 ji c\\ ipfis CO, f in puniftis D, d; tum vcro pcr punda Q, ^, 

 G,g ducantur pcrpendicularcs ad axcs maiorcb QR, 9'', K '% 

 k p ct iungantur FK, f k. Quia i^itur pcr ] emma IV^. cft 

 2 F K = F M -f- F N et zfk ~fm -hfn, ob F M -i- F N 

 — fm-i-fn, fit quoquc FK =//(:, atqui per Corol. l.em- 

 matis 111. cll C A . F K i^ C A' — C P . C F ct ca.fk=z 



T .1 ca' 



