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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)
# Folio 53, page id 1032977698:0075
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51
C AP, I.
Analusis Infinitorum.
aequatio generalis ad tansentem, fZ n t + fZ tk
 2γyk n, e Facto, yy = f2, aC divitione in-
AiTUTa, nF + F k = 2 K n.
Inde, ex daris duarum quarum libet curvarum
subeangentibus, Tubransens tertiae manifectatur.
Corolt. P. NOTCTUEHanC, ut e Contimiles X-
quationes ad intinitas curras determinari posle,
Carumque omnium tansentes hac ratione una
Overa detiniri. Verb: Crat: Sic, f ad triansu-
LIM SeU, f= X crick = f= X, X (ICZ ad trian-
suli complementum Peu 2 = 2Y = X, CTIE
∞ = = Z = X = 2 r, adcoque y ad circulum, leu
2y = Z YX = X X; CUjuS EKGO LUBTANSeNSF = n L P
2X- 27 (CD ZY X- X X
r- X AE FUPFa.
: N ∞- 4Y x
Coroll. LI. Sic yy ad hyperbolam, (eu 77
=rX + = x x. Porest sumi fad trianguluM, de
Aeri f = X; unde, uti MOX, K = f=. X. e
remanebit 2 = Y + x ad alind criangulum.
unde n = 22 = g + x; 2de0guo hyperbola sut
TaHSONS + = 29X + 2 X X
9 4 2 X
Coroll. TFF. Ouin es hoc generaliter obtinet:
datistribus curris, guarum applicatae sint in con-
tinua proxortione, uE SIE f: J:: V: 2. erit ut sum-
MTA (UIBEANSCNLIUM EXEFCMaEIIM, n + K, ad alteru-
trius subtansentem k, ita subrangeus reliqua, n,
ad lemissem subtangertis modix :F.
C. D.