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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 47, page id 824573315:0259
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PrOP. 59.
Arithmetica insinitorum.
42d5: eorum cabi racionem habebune (ad Teriem eocidens
maximo gnalium) ucr 2d1 Z, vel q ad7. Ouia nenpe 1, 2 4
2L, 1 2, Vel 2 Z Z. Z. Cune Arichmerice proporcionalia, sicuelni-
145, Racix, Ouadracum, C ubur, _C. LunE GEOMetrICC. PEOVOF-
Exlimilicer in poreltacibus maxis adhue compoliris; puta
tionalia.
Radices quadraciex cuboru Cerici (utquintanorum. Nam Cerici
lubquincamoru conrenieracior ad X 3 vel 5 ad6; creocorum
cubis conreniet racio 1 ad 1 E vel 5 ad 8 (quia nempe 1, 1 5,
23, 13. vel 5, 5, 2, 5. lunc Arichmecice proxorrionalia;) e coru
Radicibus quadracis, ratio 1 ad 120, Vel 10 ad 13, (quia nempe
2 20 CA medium Rrirhmecicum incer 1 ad x3, Tunc enim 1, 2 303
E = 1 3 rel 28, 28, 25, = 3 Rrichmecice provorcionalia;)
2
VCeriam cum radices ouadrarica subguineanorum Anc Ccrics
Subdecimanorum; cui conrenie racio 10 ad Xr vel Xad 1 20 3
Earum radicum Cubi rarionem habebunt eam quae ett r0 2d 13
vel 22d130: GMIa 1, 1 20, 2 203 1 70 vel 203 2es 203 aes Tune
c
22 2
quacuor termini arichmerice proporcionales.
Acque eodem modo, in Ceriebus aliarum Porectacum utcun-
que compolitarum, carundem racio ad seriem aqualium inve
cigabicur. Adeoque..-
PROD. LIX.
EBeorema.
Y incelligatur series infinita quantitatum, a pun
cto seu o inchoatarum, e continue crescenti
um proratione pocectatis cujulvis ex simplici
bus (PrOP. 44. eF 54 MeMOTATIS) compolica; CrittO
cius racio ad seriem totidem maximae aequalium, Ca
ouxe sequitur in hac Tabella. Nompe
Kacced