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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 15, page id 824573315:0227
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PrOD. 19.
drithmetica infinitorum.
MT, _C. CIME NC 2, 2, 3, 4, _C.
(Per constructionem spiralIs:)
_E PEOPEETEA CUEVE MT, NI,
_C. (illis rectis contermina)
sine in rectarum rarione dupli-
CACA (PEF PrOD. IX.) HCMDC UE
19439, 16, _c. erune ipla Ceo.
MEnIA CONFINUA, MT, TY, _C.
NC 13 4 = 1, 9 ro 49 16 n99
Ouoderat demonstrandum.
5
SCHOLIOM.
Poca haec de longicudine linex Exiralis doctrina, continuis
quacuordecim proposicionibus jam cradita, est apud Archime.
dem in libro de lincis Spiralibus penitus omillas Nelcio an ab
alio quopiam ex recencioribus eradita tueris.
PROP. XIZ. Temmao
I proxonatur Peries Ouantitatum in duplicata ra-
tione Arichnetice-proporcionalium, (sive juxta
Teriem numerorum quadraticorum,) continué
crelcentium, a puncto vel oinchoatarum, (Puta uE
0, 2, 4,9, 16, Ec. 3 propolicum sc inguirere, quam
habeacilla racionem ad seriem toridem maxima x
qualiumd
Fiat investigatio per modum inductionis, (ut in PrOP. L.)
ericu
1t1 - 2 = 6 = 3 60
ot 2t, +9-
d
X
2+ , +  = e
4 F 4 + 4 =- 12
= = + 22
c + 1 + a + 9 + cb = 3C
3t9t9+9 = 36 18 =3 18 20+ 16+ 16+16+1680
e4=
+ 2
Or xF 4 +9+ 16+ 25 -55
25F25F25+25+ 25+25 =150
1o