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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 183, page id 824573315:0395
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P. I9I.
Arithmetica Infinutorum.
(DATa LX3 =3 = 4 = 1 = O2 = 1. 3. =5 --15 = 16-
2 =O+ = 1. _C.) FC Similicer duos pareo proxime poheos
rectangulum Facere quod unicace minus sic quam quadrarum
incermedii numeri imparis, ( DUTa OX 2 ==O= 1 L I =
I m 1. 2 + 4 = 8 = 9 un Y = 3 ma T. 4 X B = 24 =
25 n 1 = 2 5 = L. _C.) Ouarebat igitur qua ratione au-
gendierant Factores, ue prodirent rectanpula, non quadratis il-
lis unicate minucis, sedipsis quadraris aequalia. Invenit aurem
id heri polle, E ucriqu Factores Fractione auxeantur, quae denomi-
nacorem haberer continue Fractum in infinicum, ad cam For-
mam quam luxerius exhibuimus: Nempeur parcicularium tra-
ctionum Numeratores line quadraca numerorum imparium, Di
nominator vero ubiq; inceori duplus tractione auctus in inti-
nicum. Ad hanckormans, quoulq; libet concinuandan.
2 22E.
04
9 = (D3
 2 25
4+
25 =-c
q
2325, 36825 5 10 1825
+
6
+
10
49 = 27 81 -99
22
8 1b 1825
1∞
7 it 1425
2020 208
915, 325
8∞
222+22=
via carvica
4 = 2 16 = 4 36 =6 64 = 8 100 - 010
Factores aurem illi Ec consticuri, quantum libee concinuaci,
(modone in intinicum,) rectangulum Faciene debiro quadra
covel minus, E numerus Fractionum inceoro adjunctarum RE
Par; vel majus si impar; ica camen ue quo lonsius procedatur
eo propius ad quadracum debicum accedtar. Ouod hac demon-
AracIONE CONALMIAEUES
Fiko, ex debicis Factoribus quibulris, peioris numerus inteser
P, adeoq: posterioris F F2; numerus ipicur inceriectus (quod
lacus eA quadraci) F F c. Eorum rectangulum P9 + 2 F mi-
nus est quam hein gnadiacum F9 =+ 2F + L.
sam adjungacur veriqi factori fractio una; Factores isicur
2F, B F 2+ 2 F +q, conttimene rectangulum
4F 44 + 16F cF 0F g+BF + 9
+F9+, 8F
Gua
Quvit majus erut Gutals