RECIPROCIS. loi 



coR,%j^J-^. Dcnotabunt femper P parcs et Q im- 



pares fundiones ipfius /. Erit ergo ^azz NV/^, etdjzndt 

 ^jvR^e.^n. ^^^^^^ forniula eodem modo tradata dat, 

 dx—Wf^et djzz^^dt (5^)\ Huiusmodi formulae ge- 

 nerales infinitae poffuntinueniri, alias aequationes loco 

 />=:(P4-Qf afliimendo : cuiusmodi eft haec formula 

 dx =: Ndt, et dy =: N^/ ( P -H 0^^ 



(S4-T/SS-j-(PP-QQ)"^; denotante S fundione im- 

 pare , fed duabus formulis inuentis tanquam fimplicifll- 

 mis et foecundiffimis in productionetraiectoriarum alge- 

 braicarum contcntus ero , quarum altera irrationalitate 

 cft afFecta, altera verb rationalis. 



XXV. Accipioformulam priorem, cafusquibusr/K 

 integrabileredditur,euoluturus. Sitprimo N=z lerit^a— ^^ 

 unde djm^x (iQ-\~Vi'{-QQ)''. Pono porro Qjzzx 

 erit dyzzdx {x-^-Vi-^-xxf cuius integrale obferuo 

 generaliterhaberipofle-jponatur .r-|-i/(i-4-xrt?/, erit 

 .r="-^;l,confequenter^j':="4!f4-!iX^" ,,,,{,, ^r-iL^' 



7l-}_l 



go h.c aequatio algebraica generdis infinitas curuas fnn 

 peditans numeros rationales loco n (hbftituendo 



XXVI, Antequam autem ad deriuationcm p.e 

 quat.oaum determlnatarum exgeueraUpergam inuaeda n 

 ex aequutione diffcrentiuli d.^ucenda funt, quae cx H e 



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