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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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262 Analysis Insinitorum.
C AP. II.
exiF (CUM CIE S = Z, d yy = pr - ff)
f=
Y55 + ZZ aequatio curve A N R relationem ad
axem D P manifestans, huic autem curvilinco
AD P N Per Praecedenscorollarium, aequale
fuit inventum trilineum hyperbolicum; quae
ut hinc calui approprientur, crat H
rrs 2
VrrLgy It
CorolI. pexmisso, hic vero f = Y 55+ZZ. RaL CrZO
terminorum comparatio, et collatis denomina-
toribus exit s=r ec Z = y, ex numeratoribus
autem emergit:
quare loco aqua-
tionis hyperbolica rr L yy = 9 X X, AI lOCO X
sumatur k, orietur hoc in calutraec, quae sequi-
tT, ((+ZZ = er kk, hyperbolam spectans.
cujus latus transversum = 2r. rectum-
ad cujus constructionem, quadrilineo AD P N
circa DP seroluto in SDPT, latere recto
X transverlo A5 seu 2r, describatur hy-
perbola modo inventa sF, secans productam
NP in F, erit ducta recta D F, mixtilineum
AD N