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# Title: Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio (shelfmark Leibn. Marg. 84:2)
# Folio 132, page id 824573315:0344
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plicabilis quam
Arithmetica Insinitorum.
PrOD. 163
aot s+ + v2+ V3 + Vat vE + 16
O+ 1 +. V2 + V3+ 2+ VC + 16
726
3+ V2 + 13+ 15 + 16
vel Caltem (propter Ot r +2 - 3)
716. nihi torlan placear eam anrecedentem
quam consequencem racionis ducere in V6, uc prodeat ratio
3V6F112FV 18FV30+136, 2d7; vel pocius 316+2V 3+3V2
+V30+6, ad 7. Ec similicer in aliis ejulmodi Ccriebus.
Verum h eadem Ceries supponacur in infinicum concinuanda,
prodibic candem rario Z, vel 2 ad3, auc 1 ad r Z. ut dictum
cl proP: 53,54. ipla quidem infinicare (quod micum videa-
cur irracionalitacem destruente
Ec limilicer in Cubcercianis, Tubquartanis, _c. Continzet, ut
Pacec ex luperius cradicis proD. 54,59.
Cum icaq;, illa disticulcare non obstante, quacratura Pa-
rabolae e ab aliis ancehac e a nobis eciam nostra mechodo, led
e Paraboloideos cujulris quadratura (eadem manence diffi-
culcare) a nobis in luperioribus lacis Feliciter cradica AC; non
plane omnis aberae lpes rationem tandem inveniendi quam
Radicum univercalium (Periei vel auctae vel muletate) series
hiabeac ad Ceriem aequalium, e quidem s non universaliter, in
quibusdam Calcem, quadancenus explicandi; Forcastis etiam in
illis ipsis quae Circuli vel FIlipleos, & quae Hyperbole quadra-
curam accinsune nonnihil protcere.
Uc autem quid deinceps sic inguirendum rectius perspiciacurs
meminisse licee nos sincer alia) circuli (vel etiam Ellip(cOS
cujuris) quadracuram huc vlg: perduxisse.
Nempe, Per PrOD, 278, _ TZT, A racionum Ceries illa 133,
+8 38
25, 105 395, _c. incerpolari pocerit; rario illa quae primae de
Eccundae Pmenda ek incermedia, est ea quam habet Circuli
Guadrans ad Ouadcacum Radii, vel Circulus iple ad quadra-
eum Diamecri.
ICem, Per PrOD 133, _ 235, s incerpolari pocerie rationum
Ceries ilta 2, 5. 30, 1203050, _c. racio illa quae primae et Ce-
cundae ponenda est incermedia, est ea quam habet Cemicirculus
ad Ouadracum diamecri.
Sed e inluper, hincerpolari poterint numeri diag oniales ca-
bella