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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 214, page id 1032977698:0236
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214
Analysis Infinitorum.
sine quadeata rationalia, Oportet
CAP. III.
quoque uE
iplorum ralores kk rbz ec ff rby ratio.
nali radice saudeant; quare allumta quadrari
Kk - rb Z radice k = + d crit k-
b Z + + + d d
2c suppolito quadratum ff- rby prerenire a
radice f.. S6, CMerBCK f.
r b y + 55Cc
25e
5 quo
verorum e tum fa fractionibus liberentur, Fac.
tiS r = 4, item 5 = F = 2, ac b = c = d, cy2
dec k = 2 + b, ec f = y + b; undeemersit h =
2. b, aut b - Z, HCCNON u = y
b auc b -.. 9.
Ducta igitur AHI ipA F M Parallela vocetur
B, completoque AOK A rectangulo, crit
temper ducta quavis ipsi F X aequidistanti recta
DI = b + y _ I5 = b y, unde Cemper arinil.
la Cx D S circa AIK, seu quadratorum in DI
e SY differentia aequalitur 4by, ec Polidum
ex spatio A F MI Circa FIK EOtatO = omnia
4by: eodem modo invenietur solidum ex AOF
circa eandem H K = omnia 4bZ. Adeoque
Patet hic ab aliis, alio tamen modo demonstra-
TUS CaHOR.
Si circaarem A0 duo quaecunque constitu-
antur spacia AF M _ AOL, tacque ducta
AEL ipA MO parallcla quodliber rectangu-
lum AOKH; crit, uc prima Figura ad sCcun
dam, seuut omnia y ad omnia 2, ita solidum
eX