(180 



Simili aiitcm rationc qua /__liz__ nunc ad fc(florcm El* 

 lipticum circa focum dcfcriptuiii ct quantitatem algcbraicam fucrit 



rcdudum, ctiam / ^^-^ -, quoties U\a forma in fadores 



reales cft refolubiiis, ad fedorem hypcrbolicum circa focum dc- 

 fcriptum et quantitatem algcbraicam rcduci potcrt, cui rci cx- 

 plicandae, cum ex iupcrioribus abunde fatis clarcat, non ert vt 

 vlterius immorcmur. Quamuis autem ifta cxprcirio /_ 



r d r 



( L -H M r — r' ( 



non Itutui qucat proportionalis fc<fto i Elliptico circa focuni 



defcripto, tamen facile reducitur ad fe<florcm Ellipticum circa 



aliud quodpiam puncflum in axe minori dcfcriptum. Nam ob 



a e ;/(w* a' — (n a — uY) = H — 'T(n-.> 



i?bi S— fccfl. AFP, et T r= triang. F P C, fi nunc capiatur Tr>b. V. 

 FI:FCz=:;; — i : i, fiet trianguhim 1 P F — 2 T (« — i), F'S- 9. 

 ideoque fcdor AIPzzAFP — AlPF — S — T(/;— i), 

 vndc fi ilk" fcdor AIP exprimatur per U, fiet 



a & — i/(m' a' — (n a — uY) ~ iiL___. 



Hincque fi iungatur I P^, et exprimatur fcdlor A I P^ per U^, 



fi" ^'^^"■"^/ v,L^M:-r^) ~ n;::,7-:. ,^ ^j ^^^ ^^^ ^ecfto. 



ris Elliptici P 1 P^, diuifo per quantitatem n a y (ji* — m*). 



§. 2 8. Nunc deniquc ifte cafu? rcmanet expendcndus, 

 quo formula L -f- M r -f- r" in fadores reales prorl\is non elt 

 refolubilis. Pro hoc igitur cafu fupponamus centro C, femi- pj- la 

 axe tran^ucrfo C A ct coniugato C H dcfcriptas efle hyper- 

 bolas coniugatas AMQ, H J. I/, et fi ex pundo quocunquc 

 L hypcrb<jlac coniugauic in axem transucrfum demirtatur nor- 

 malis J P, eric L P* - C H' : C P' = C H^ C W Hmc l\ di- 

 catur CArz/7, CH— ^, dilbntia foci a ccntro CY — c 

 =z\/ ^a*-h^') , abfciifa C? zizu et applicata L P :^j, erit 

 y — h' :u' — if* : a', vnde colligitur 



2 3 r = 



