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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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PROPOSI FIO CZZIV.
DROPORTIONALLTAFES
Unisrario in duas iplam componences diuisa denuo conlescir per
Parcium ex diuisione orcarum in se mucuo mulciplicationem.
Demonstratio.
TNEeE racionem A ad B, InECrPONAEE
quaenis quancicas C: eric itaque ratio A
2d B, dinila in duas iplam componentes,
scilicee A ad C, e C ad B; ostendendum
isicur est per mulciplicacionem racionis
AC in C B racionem, coalelcere denuo
rationem A ad B. Nam eatio A ad B,
composira est exrarionibus A C, et C B: hoc est, veanee propol.75. docuimus, rario
arcesrationis Aad B, plam componences, parec rarionem A ad B,
dimlam in parces, ex palcutu mupllcatione restaurari. Ouod eras demoltrandum.
Porreat daram rarionem pet aliam parriri sive ostendere quories
A ad B producitur ex mulciplicarione rarionum A C, C B. Ouare cum rationes
AC CB, C
eROPOSALTO CXXI.
Ornaalceram contheat.
num AB, C
Constructio es demonsitalie.
D, VEpatet ex V3 huiuS.
PIE AB ratio diuidenda per
CD racionem: AaEVE D L
et a
lam C
B ad F. Dico rationem
i
C D. HAMI EOTIeS A B; ContincE
C D rationem, quacies A con
cel L. cumt L d Llincde.
nominatores carundem ratio.
Corollarium.
Ine manifeltum est dinisionem rnius rarionis per alceram rationem coincidere
cum altishacto rusrationis quam concinene incer le datx rationes, inuicem
PR O P OSIL LO CXXVI.
dividenda.
leproporciorationis ad C. actonema Guaticalis.
Eate excectum quo maiorminorem exlupera.
Con