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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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C AD. II.
Analysis Infinitorum.
18L
reductaque requatione ad indeterminataS fe Z
oritur Ls d 2l = s re f leu parabolitormis;
unde spatium D M N Ccu omnia fa, IuXta
S. IT. Cor. I, aquatuE k +5, eC OMMIa r =
2
fr+ sr  Omnia e seu longitudo aXis A F in
FIG. XLIX. UbI FC = DS = Z, _ FF = C
rocetur autem haec AF: h, scu omnia c. Orci
TuTG. CUIrVE AD E aquatiO F, +. 5Y h, qua
redacta per superiora ad indeterminatas h e 2,
leu AF _C CF, dabit aequationem rurlus Pa-
5 + k
5 R + s
FabOliFormem: L + 5 ∞ B = k d 2
curram ACF respicientem; adeoque cHM
maxima 2 SIE GH seur, X maxima h seu
a
L a Y
AG AC X F s, erit rectansulum A9GFI = k + 53
_c juxta 5. II. CoroIl. I. curvilineum AD HC
e dr
= k + 25: est autem hoc spatium spiralis spatii
evolutum juxta praecedentem, ergo juxta 5. 50,
hujus duplum, unde spatium spirale aquatuE
kdr
L. + 25, Uti in 5. 49. Coroll. I. malui autem iis-
dem exemplis insictere, ut principiorum con-
sentus dilucidins ob oculos ponatur.
5. 52. Idem ex alio modo problema solvi-
cur; siquidem, F1Z. LP. 2Y: 73: : rn : 7 2. (C1
5. I.d