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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 24, page id 1032977698:0046
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2
2Z-
Analysis Insinitorum.
M
+
Y
nn Y de
5 i
+yy
CAP. L.
2199,I1yy
5 m
55IM
Oux, rejectis per Lemm. 20. rejiciendis, ac
terminis se muruotollentibus, nec non dirision
ne per in instituta remancoit reducta equatione,
22 5 = 2
Ex qua aegnatione sublatas aurt, per aquatio-
nem +F + yy= 55 (qua triansulo rectansulo
EPZ orrum suum debet, quod si obliguan-
culum Foret, aliam aeguationem exhiberet.)
Tum ec loco iplius 2 lubsticuo valore ex xqua
tione currae data 22 =r x F yy eliciendo, orie
TUE EFYY + 4 F Pyy= 4FFY X Y 4 FFy y + 4 rXyy,
ec cognita eric ipla + ex Colisrectis x e p.
3. In tPANSIEU ROTO, Curvarum aequationes.
quae alioqui line curra supposita lonsicudine ex.
primi posse non videnene, tansentes nihilominus
exhibere lolis lineis rectis explicabiles; adeo-
que, si ipsius auts valor aliunde per lincassec.
tas significari porser, mechanicarum Cartesii
plurimas, si non omnes, ad totidem Gicome.
tricas hac ratione reducibiles exittere.
Hoc Caltem liquet, modo dictas aequationes,
per Tolas rectas naturâ sua designabiles. eNc.
Laequatio enim currae inibi discua ZZ,
rx F yy, qux ipsam curram Z comprchendit,
aeGUd