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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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PROPORTIONALITATES GEOMETRLCL.
Construitio  demonstratio.
AEx SinEratiOneS A B, C D et
AaC VED ad C; ica B ad F. crune
AB, F. B, aquales racionibus AB,
L
CD: habeneautem rationes AB, LB, commune conteglens B; isicur exhrbuimus
quod pecebatur.
igitur rationes CD _ F B, Xqu2
les incer sc: ac proinde rationes
PROPOSAITO CXVII
Aca rationis duplam alsignare ale eus e  
a
proporrione.
Constructide demonstratio-
berc: hacC cpra Gancicaris A. DI-
corationem C ad B, duplam esse ra.
cionis eius quam habet A ad B: 8
racionem BC, dimidium esse cius
tacionis quam habet B act A: nam FaeO C B, ad A B, est ve C ad A, est aurem
C dupla rectae A, isicurracio C ad B, dupra est racionis A ad B. Racio aurem B
ad C; ee B ad A, eAt ve Aad C. Led Acamlia ipsius C. nraco B aCse
dimidia eiusracionis, quam haber B ad A. LsituE PruS quod reGuebatur.
eddempraxi dabitur tacio qua ad rationem dacam, Habcat dlatam proporrionems
eROeOSITIO CATI
DAca Cirrario AB, cuius duplam
auc dimidiacam oporceae exhi.
Acis quibuluis cationibus oporteat eet Cadere qua in V-
natu  alfualEM aBGrCGCHEUT.
Constructio e demonstratio.
auabuo ec cuncratiopullo e Cu 1. at B acano eM adellacoerium rario
Inerationes AB, C D in
Vonamaserchande; Aac
ve D d C, Il B 2d C
Deinde Hac HI aqualis A
_ O, simul Cumpeis. Dico
racionem H ad B, aqua
lem esse aggrerato duaru
rationum AB; CD: CA
enimracio AB, cum C B
ex conAtr. aqualis duabus
rationibus AB, CD. sed
ratio HIadB, aequalis est
rarionibus a A B _ CB.
Toicur ccantraco L a B, agas ea SSaIM AB, _ CD.
ari4 hitus.
Eodem modosihacre F ad L. ICa B L, de quamicas aa al eua a quans i
num AB, CD, FF, _ Sic pergiporeric in aceruando quonis numero rationu. Ouoc
sixariones dare commune BCa C, C  LCOeS R MT; L. MI.
colligea uae Va H. ete rac E alt, xqualis eacioni-
Aipu ue  uu sut i ue e pt e  u eu te  a u petse u i1
bus KW. L. V.