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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 181, page id 824573315:0393
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 35 lines, status machine
# Lines: 35 recognised, mean confidence 0.89
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PrOD. TGI.
Arithmerica insinitorum.
dliamerri Ouadratum: E, uE Numerator ille ad Denominaton
rem. sic Ouadracum illud ad Circulum.
Si quis aurem curiolius inquirar, quonsq; continuanda erit
illa milciplicacio. concinua, uc tandem ad differenciam dacum,
Ere ipla minorem perreniaur: Nempe uc numerus justo ma-
jor, numerum jucto minorem, ipsius parce quan libce exisua
Cret ne illa quidem) superec: Id hoc modo inveltisabi-
EUT.
Ouancitas major dicacurm, minoen, (cq; carum differen-
cia, ictius pars quancum vis exisua; PAT2 B m = m - n 3 de
quaeratur quoulq; continuanda eric operatio, hoc cAt, quis Fu.
curus est numerus 2 mulciplicacorum maximus, ut illa differen
tia (vel lalcem ipta minor) prodeac.
Ouoniam isicuem - n = b m, exIE N = I = B m; Et M.
n:: m. M = B M: : p M. B M:: b. b na a : : Z. V: 2 =
1. (per modo demonAtrata.) Ideoq: B V: Z 2 = L: = b 2
in a 2. FC (vtrinq; ouadrando) b 2 Z 2 = B = =B = 2 2 +
42 22 = D ab~ 2. ACq; (dclendo verinq; b = Z =, _ reliqua
cransponendo,) 2 ab 2 = a2Z 2 = b 2. FF deniq; (uerin q3
dividendo) 27 = 2 ab a E. Hujus igitur numeri radix quactra-
Cica, (si Fverie nAmeruS PAE,) vel Calcem, (siveli Fractus vel Curdus
sic vel numerus impar) par numerus illa proxime major, Fucurus
ckmulciplicarorum maximus, uc altignara differencia, vel ipla
dalcem minor, prorenine. Quod erac imrettis andum.
Idem Aliter.
Posthanc aucem nostram, ipsius grancicoris a desonatio-
nem; libet eciam aliam lubiunsere, quaem a Nobilissimo Viros
acq; acuciltimo simul Geometra, Dom. CWliel. Vicccon, ee Ba-
rone Brouncher, acceDi.
Com illi propcessionum sliquoe mearum propoluerim, e
qua lege procederen indicaver im, id interim rogans, et qua Fur-
ma quancicacem illam commode detionanidam pucaveric, indi
CareB