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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 942, page id 1815201908:0999
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PROPORFIOHALLLATFS
Demionserati.
DOnacur incer A ad B, me-
dia 1, ex similicer incer B. C
media ponaeur K. Deinde Aac
ve D ad F, 1Ca F ad C
V
I ad F, ica C ad H. Duaniam
igicur rario AB duplicaca est
camracionum AI, TB, quam
racionum DE, E C crunera
ciones AL, IB, cxdem cum ra.
cionibus DF. F C. Pari argu-
meneoraciones BR, KC cum
racionibus F. F, GH exdem
Sunc. rationesigicur AC, DH
ex iiidem racionibus (quamis
diverlimodc dilpoliis) compo-
nuncur, ac proinde a aequales
TunE. Sed racio D H est duplica.
DF, vei Facile de ducitur ex consructione. ergo de rario AC est dupli-
alarationis D F. Ouod erac demoerandum.
Corollarium.
Inc colligicur idem esse pronuneian.
dum de quavis conrinuarione ter.
minorum quod peacedenci proposicione
decribus est dictum: nam A hac rario A
ad B duplicaca CD; X B aet R duplicata
DB, _ F. C, CI duplicace FHI, HIR: in-
Ferri etiam legicime poccle, quod rario A
2d I sc duplicaca eius racionis quam la-
bec C ad K quocunque candeim numero
termini constiruancur:
Imo quod de duplicata rariotie prae.
sens proposcio enunciar, criam cM incelli-
sendum de criplicari, ousdruplicata,
quineuplicata, et sic de quavis alia mul.
ciplicaca ratione respectulimplicis rario-
nis C ad D, D ad F, _c. quod manifesté
collisetur E dilcurlus demonstrationis
cerminis illius mulciplicacionis apCCTUI.
ae u ut it ete
Ine quacuor numeto quancitares A, B, C, D, _ rario A ad D, suppo.
nacur compolica eAe ex rarione duplicara A ad B, et ex ratione B
l
Dted tarioneta e ad t catidem elte elta talionee ad L.
Demon.