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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 900, page id 1815201908:0957
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900
PROPORTIONHLITATES
Demonstratio.
Voniam eadem est ratio AB ad
LCB, cum racionc D F ad F C, &
cum racio AB ad C B, AC ve A 2c
Beric paricerratio DF. ad FC, DEA
est ad C. sedbrario DF ad HC, el
E ica est D ad F, proxoreionales itaque lunE AC d L,LL
Bains.
ve
Duod tuic demonstrandum.
Aad
Dremrario A de  Cace CuILAHIOnCF. adF.
Dicoctiam ralloe a D, candem esse cumratione C ad HI.
Demonstratio.
Nueneis denominaroribus rarionum AB,
CD scilicet A ex I, icem racionum F F, C+ II
denominatoribus F. d R. quoniam raciones
suneproporeionales, eric ve A ad P, ica P ad R.
icaque cum A ad B; cciam sc ad B, VE F 2d
E, eric deliam BadI, ve F ad R. Sed re D ac
C, ica estBadT, ergo ve D adC. Aaen L
adK. Sed HadC estere Lad R. ergo vet
adC, ira D est ad C. Quod crac demon
R O e OSIFIO LVII.
VIcrario AB ad C D rarionem, vrratio P. P ad rarionem OHI: SIE Au.
ROPC
llandum.
5
L. VII
talio AB ad FF rarionem ve C L TaO Ad C AlatIOnem.
Dico rarionem AE adracionem BF, eandem habere proporrion
nem quam rario es ADILacoM.
bl.
F39. hn
et
rionem BF, vetracio AB ad rationem P. F: a laC
ad rarionem DTI, ve ratio CD ad rarionem CTI. sed racio AB cM CX
hypochehadrarionem B F, veratio CD ad rationem C FI. ergo rario AF. est ad
Cacom BF, vEtalio E C ad rationeta D H. QuOd ctac dem ontrandum.
PRO.