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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)
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u
ErOD. 45.
drithmetica insinuoram.
non minus innocelcet (uc e tgurarum adjacencium Lalle di
circulam vel sectorem) quam
in illa Archimedea. PxCempli
BraCIa. Si ARGCATUT rectae MX in
duplicata ratione anguli PMT; erii
dinea Spiralis (a principio in-
chorta) MX, ed arcum contermi-
num PF, UI Y ad 3; (quippe erie
spiralis illa, Teries Secundano.
rum; arcus aurem, Ceries A qua-
lium:) Et Pieure adjacons erit ad
conterminum Sectorem, ut L ad 4:
(nempe ut series Tercianorum
ad leriem sequalium:) Et simi-
liter, si crescat recta MX in anguli MIP Y ratione Triplicara, Quadru-
plicata, ec. Frit Spiralis (sensu quo supra) ad conterminum Arcum,
ut 1 ad 4, 5, BC; e Figura adjacens ad sectorem comerminum, ut L ad
5,6, 8c. Oux omnia eodem modo (mutatis mucandis) de
monstrabuncur, quo prop. 5, 24, _c. Arg; hinc quidem Ipira-
lium doctrina in immentum augeri possic. Cum aurem id (u0
quilibet Maric per jam dicta lacis postie incelligere, neq; nobis
sic animus labore superracaneo hac ulcerius ampliandi: Cufici.
ac id in crausieu monvisse.
Sed e hinc ceiem Facilis essec cransicus ad Spiralesnon can-
cum in plano, sed in Colido descriptas, puca in Cuperficiebus
Coniee Sphaix, Are etiam concidum et lphaeroidum, rice con-
Eiderandasi _, ad spirales auc C irculos in Cylindro comparan
das. Ficuras icem illis adjacentes, ad fixuras adjacentes hilce.
Adhibicis camen iis, quae de Periebus auctis ee diminucis deincexo
secururx lunt, propolicionibus. Hec aurem omnia, ne nimius
m, intacta praecereunda judico: Cum ca quilibce, ex iis
qua hic tradica lune vel deinceps cradenda, Facile possit de
dacere.
PROP. XL. VI. Temma:
em (per proD. 44.) Data ratione quam habet Ceries
una, cujustibet pocestatis, (ad seriem aqualium;
TEDETIEUL