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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 31, page id 824573315:0243
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u
PrOD. 30, 39.
rithmetica infinitorum.
Ec inCcriptarum aggresacum: Quod tamen vera Epirali per.
pecuo minus erit.
Si aurem harum inseripearum prima omiecatur, ec illius vice
Post alcimam subjunsatur quxe proximé erat inlccutura, (quod
cantundem cAacq: pro tisura ex lectoribus inscripea, circum
Peripeam (ubRicuere,) acgi tandem addatur a; habebieur exe
omnibus agresata recta quae vera spirali major erit; led quae
ad justam eo proxius accedet quo plures supponantur Sectores
adCcribi.
Ec imili Forma procedendum eric (mutacis murandis) in
aliis spiralium gencribus in Scholio ProP. 45. memoratis.
PROP. ZXXIR. Lemma
I proxonatur series quancitarum in Triplicata
ratione Arichmetice proportionalium, Esive
juxta Ceriem numerorum Cubieorum,) continué
crelcentium, a puncto vel oinehoatarum, (puta Vc0,
5,8, 27, 64, eC.) propolicum sit inquirere quam ha-
beat illa rationem ad seriem coridem maxime aequa-
Dium.
Fiac invellixacio per modum inductionis (ur in proP. 1. &
I
29.) Exicg; 7 + 1 = 3= +
x2.
2
0+ 1 + 8 + 27 = 3C
27 + 27 + 27 Y27 = 10E
0t r + 8 + 27 +64 =- 100
6+ +64+6+ F 64 + 64 = 320
0 + 1 + 8 - 9
6+ 8t. 8 -24
0 + 1 + 8 + 27 F 6, Y 125 = 225
125 +, 25Y 125 F125 + 1-5 = 125 = 1750
0+ 1 + 8 + 27 + 6+ t 125 + 21b = 4a1
2167210+ 216t 2161216+ 216+216 = 1512
t IC deinccps.
2a 2t 2
Racio proveniens ekubiq: major quam subguodrux la, (eu 3.
Excel
a + 2