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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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106
Analysis Infinitorum.
CAP. I.
Si vero idem quoriens per exponentis dicti dC
uniaris summam mulciplicetur, Orictur
C+F 2X +r
in 2k, quod in lecundo catu requie
Ficur, ubi Z mulciplicatur.
Demonstrationem ex praemissis quilibet cruet
camque proinde cum caereris hinc deducendis
(R2 ef, 2d terminos quolrismixtos extendan-
cur, ipsique signorum exponentesq e k, quam
Pari posinE, rarietarem admittant) brevitatis er-
Copexcerco. aequatio currae mox insinuata cH.
98. RCaNUMaTuE Fis. X P. TerVaTiIquCS. 36.
Symbolis, ac 5. 37. hypochcs fZ = yy, invenitur
aequario subrangentialis nt + kF = 2 en, undo
 +=
ns
X15Z
(2
2tn  21+ 2n  21 Y 2n
Coroll. I. Unde sequitur, duabus curvis ad
eundem axem deleriptis, si correspondenrium ap.
plicatarum rectangulum fZ per utriulque currx
subransentem, nes l succestire dividatur, crit
quoriencum summae lemissis aequalis Tubnor-
malit, ad tertiam quandam curram pertinenti,
cujus ordinatx quadratum y y aequivaler f2 seu
exposico applicatarum in reliquis curvis rectan-
2
(Z
ButO; l  26 + 2n
Coroll. IL. Hlinc etiam patet problema COr:
S. Praecedent: infinitis modis lolvendi mertodus;
polita enim 2 xquali cuidam quantitati irrario-
nali.