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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 169, page id 1032977698:0191
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CAP. TI.
Analysis Infinitorum.
DD = FM: y, OZ = D M: t; OP: e,
T: I; Crir area A F P = Omn: ye, huiuS quX-
FITUEmenTUEa. Z, Cum esit infinitesima ad AO
eu x referenda, hoc in ipsius locum reposito ha-
bebitur: ux, cujus termini infinitesimales y et x a;
CE ILIXTa S. X3, Omnia ye F OMM. X a = y X; unde
Patet cognitis omnib. x a, cognosci omn. y e: cA
autem x a ad dati spaTI COPLCMENEUm R F. A,
Uti nOtuM.
II. Cum infinitesima e Spectet SimuI Subtan-
SenteM, Z 9 TCW F, emergCt, + ip(I e TUITO-
sato, yF; cujus intinicesimales get vit ta.
(eu 2y C + yi; ec per S. 13, OMN. 2 y C + OMM.
yi = yF: unde inventis omnibus pi, nOt2
crunt omnia res jam yi esc ad currilineum
L V Anemo ignorat. Hlaec autem methodi gratia.
Schol. ut vero pareat, non sempercangentium inventio.
nem aut subnormalium ad mensuras currilineorum necesta-
riam esse; verum e solam aequarionis currae ad infiniresi-
mas redactionem Expenumero leri opera pandere, quae
non nis incricaciori calculo, per rangencium merhodum in-
quireremoris est, sequentia subjunso.
5. 43. SIt, In FIG. XXXIX, A Q = X,
2
D: Y, InFnIFC(IMX D HI: C, EHI: a, _C CIIEVR
aequatio ad quamlibet parabolitormemmrD = 4X9
= ye; exit haec aequatio ad inAnitelIaS rC
dacta, ac in yx ducta grD = 9 X 47 C = p y P X a,
dux per aequationem datam dirila dabit qye=
PXa; quocirea juxta lemm 43, p: g:: Om-
1Id