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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 164, page id 1032977698:0186
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164
Analysis Infinitorum. C AP. TI.
infinitesima e, X a; habebiturque, Cum sIF
hC = y a, Xye = ta amotis infinitesimis
B= + = V =  R = 93.
TI. Sint omnia Be = ry = rectangulo ex 
determinata in DO, erit ra terminus infr
nitesimalis ex ry oriundus, _ Facto he= ran
crit ry omnia he= omnia ra, Cx5. 13. 2-
deoque cum (IE y e = t a, Het h -.
+
TII. Sint omnia he =. x y = rectangulo ex
AO in OD, erit juxta Schol. 5. 13. X a + pc
terminorum insinicesialIU Cx X y na(CeN
tium Cumma; haec Aat= he, Crit x p:= oma.
he= OMN. X a + ye ex S. 13. ex clisis infinitesi-
mis per aequationem: ye = +a, ACt B -
X y + +y
IV. Sine omnia he = 1y = rectangulo ex
T in OD. Crunt, iuxta 5. 24. ipsIUS L rC-
spectirae intinitelimae = e ri; adeoque termini
intinitelimales per Schol: 5. 23. hinc prodeun-
1C5y e, + yi + + a, Quibus tactis = he, Crit t y=
OM. Be = OMM. y e F y i F + a Cx 6. 13; unde Cx
hac aequatione he=. y e +y1 + F a hoc modo cji
ciantur intinitelimae, primo, eA ta = y e, quare
he= 2y C + yi; secundo, ue tollatur i, cum
haec pertincat ad subtangentem 2O Ten + RyF
AC P curvilineum Cuotansentiale, in quo sem-
DeI