. Commentarii Academiae scientiarum imperialis Petropolitanae . aturam curaarum perhuiusmodi aequationes indicare, difficultas commemo-rata quidem toUeretur, at vtrum curua etfet algebraicaan tranlcendens non tam ficile appareret. Huic veroincommodo fequenti modo occurreretur. §. 45. Sit arcus AMrrj- et radius ofculi M O — rdataque fit aequatio quaecunque inter s et r. Ponan-tur APzi;jv, PMzq/ fitque dy:izpdx\ hisque pofitis, . , , , —dx{x-\-pp)lerit ds—dxVipp-^i) et r— ^-—-^—. Ex illa vero aequatione eft dx^ji-pj^zrr-» ^^ ^^^^ autera — rdp , . • ^^~ 1 Zxl—\^ Quamobrem proueniet haec aequa- ti

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. Commentarii Academiae scientiarum imperialis Petropolitanae . aturam curaarum perhuiusmodi aequationes indicare, difficultas commemo-rata quidem toUeretur, at vtrum curua etfet algebraicaan tranlcendens non tam ficile appareret. Huic veroincommodo fequenti modo occurreretur. §. 45. Sit arcus AMrrj- et radius ofculi M O — rdataque fit aequatio quaecunque inter s et r. Ponan-tur APzi;jv, PMzq/ fitque dy:izpdx\ hisque pofitis, . , , , —dx{x-\-pp)lerit ds—dxVipp-^i) et r— ^-—-^—. Ex illa vero aequatione eft dx^ji-pj^zrr-» ^^ ^^^^ autera — rdp , . • ^^~ 1 Zxl—\^ Quamobrem proueniet haec aequa- tio ds{pp-\-x) — --rdp feu ^—?;^^. Denotet /— arcum circuU cuius tangens fit q pofito radio i • eritque — — \ vnde fit p — ~^ et y(;,;,4-i)=^i^|i^. Ex his oritur ^A-^^ et dy^^j^^-^. Vnde intelligitur fi primo J% de-notet arcum circuii cuius tangens algebraice per q pof-fit exhiberi; atque deinde tam v^t^^ quam y^.t+^jia-tegrationem admittat fore curuam algebraicam. Co7r?7,,^nf.^:/ccz^. J:.%„?. ^l. V^. cT,. A T P (^o,n7,?, Jc.^Em ;. V^. cTo.

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