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# Title: [Bernhardi Nieuwentiit Analysis Infinitorum, Seu Curvilineorum Proprietates Ex Polygonorum Natura Deductae] Bernhardi Nieuwentiit Analysis Infinitorum, Seu Curvilineorum Proprietates Ex Polygonorum Natura Deductæ (shelfmark Leibn. Marg. 149)
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5
Analysis Infinitorum.
CAD. I.
Coroll. TV. Sit Z 2d circulum, e Z 2
=2Y X =X x, item fad hyperbolam requilate
eam dC f = 2rXLXX, CTIEV ~ E AVYXX - X; CujuS
ersotansens ex circuli ex lisperbola rangentibus
coonita est; neque novichujus methodi extensio
limitem.
Coroll. V. FIOC FAIEH INEEE EXFCTA HOtCtIE.
cum omnes tansentium methodi in determinara
alicuius curvae natura substiterine, ejusque
parametros dererminatas depolcant, hanc
solam parametrorum limirationem non relpice.
rc. Verb. GITaF. SICZ  X, erit f∞ = yy:qua
requatio, i fForer determminara = r, cNet ad para-
bolam; ipta aurem f manente indererminara.
erit ad cueram ex infinitis parabolis formatam,
quarumque parametri lunt cuera pro arbitrio
sumendae se mutuo sequentes applicate; cuius
Juc aequatio ad tansentem, cum hoc in cacu fut
nx, permodo inventa, criet X FFk = 2 kX.
quae aequatio, si ad parabolam ordinariam li-
mitari debeat, AetZ =r, unde t eAt infinier;
quire, per Schol: Crener: Lemm. H. ZII. rejecta
=3, CrIt Fk = 2 k X, eC F  2 X, Uti OpOE-
TCL.
5. 38. Antequam ad alia transcam, HOC
2dd0. Sit iidem manentibus Z fX + Z X X = fyγ.
quae aeguatio, praeter infinicas alius generis cue-
vas, etiam es ad infinitas hyperbolas. Icu cur-
VaE