(175)= 



hincquc acp. fln.Cp^^if, ct' fiircp rz ^ >/(^^ r=- (p - ;-';, 



idcociue ^0= ^ , ctr'd(5) — Ll^.! ^, 



quae formula ob p — a {i — c") in hanc transformatur: 

 r' d(b — LLi-!_ -; 



^ M> — e-^JTi — a'(i — *»i-(-3ar — r») 



quia igitur eft ^— ^ tcmpori proportionale, quo fciflor Fnip- 

 ticus ^ r' 3 (p percurritur, crit clcmciitum temporis quoque 

 proportionale formuhic differcniiali ; ^_rdr Cac- 



i I i( — a' ^i — f-')-l-2ar — r*> 



terum haec exprclho pro dificrcntiali r d (^ pcr fola ratioci- 

 nia Gcometrica fic cruiturj quia cll dr: rr)(^^z:rdr: r^^d^P^, 

 =. 1 : tang. T Q F, fitquc fin. T Q F : i =: C H : C O , fiet fL , 

 cof. TQF — >>rn»--cH>, j^^^^^- cft ]/(C0' — CH^ — 



/(F C — F D'), quum igitur fit YC^ea ct FD=rCA — 

 Q F ~ fl — r, erit omnino 



/(F C* — F DO =: /(^= a^ — (a — rO) 



et ob C H — ^ , fict 



> (I — f'1 ' 



tang. T Q F r^ Li! z=i t _ , 



vnde patct propofitum. Quod i] iaiii iatcgralc formulae 

 ^^ r, ita accipiatur vt euancfcat pofito r — d, 



V ( — a* ( I — f * ) -t- a a r — r* ) f J ' 



ex iis quac fupra dcmonftrauimus omnino liquct, hanc for- 

 mulam diffcrcntialcm rcduci poffe ad dilfcrentiam binarum ali- 

 arum tiusdcm formae, fcilicct 



p <>? p^ ^e' 



y^f^ a» — ,0— «)'( >',e-^a^ — la — f)>) ' 



modo fumatur e-f-^^ — r-}-5, tumqiic fit corda quae fub- 

 tcndit arciim Kllipticum radiis vecfloribus r et d intcrccptum, 

 aequ::li-> illi quac rcfpondet fcclori Hljiptico radiis vccloribus ^ 

 et ^^ iuterccpto. Simili quoquc rationc liquct, pro Hypcrbola 

 formulam ditfcrentiam ^" '^ ^" rcduci polfc ad diffcrcn- 



y ((o H- rc' — «■' a' ) '■ 



tiam 



