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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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78
Analysis Infinitorum.
C AP. I.
D. datum cA) invenietur parameter parabola
g-
1
P= x exnatura parabolx, unde X = 29
2. Quare ex cognita A  Seux _ latere recto
parabolae ca poterit deleribi.
73. ExPCTatuE jam AD F circulus, Cujus _
quatio 2Y X = X X = yy, quae rectam T F in D
contingat. ea reducta ad infinitesimas exie:
remXe
=a = p; unde circuli semidiameter r=
37  B X yy 4. X X
2X ex aequatione circuli; ex quio
bustum x, tum r in quancitatibus cognitis da-
buntur; uti nocum ost.
74. Ouod Cchyperbola dictam T F. tangens in
D delideretur, cujus aequatio, rX x + r BX
hyy, Posito latere ipsius FCCtO = r; tranSVer-
(0= h; erie hac ad infinitesimas sedaeta,
2rx c + rhe
2by
2by7
=
 ex aeguatione trianguli,
y.
unde r= ch F21X = XX F bX ex quibusr _ x in-
notescent. Cum autem ad iplam h determinan-
dam aequatio non suppetat, ca mancbithoc in
casunon omnino limitata.
Onde, licet liyperbola AD F in puncto (ui D
unicam tantum admittat tangentem rectam;
econtrario recta data Y F. in puncto sui D innu-
meras haber hyperbolas tangentes, prour haec
AVE