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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 893, page id 1815201908:0950
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MIHIIIII
CE OMCL AICK.
PROPOSITIO LLtII.
Incacaractees AB, CD, guacunque.
atoem AB ad C. D racionem, calcen actre proporrio
nem quam DC ratio ad B A racionem.
Demonstratio.
AereD ad C, aB ad F
eric 2vC A ad L, icaracio
AB ad CD cacionem
Deimdlerario B L. al B A,
est ve A ad F: b sedratio
B ad L. eadem est cum
quareCD Lactoe  Veao DC ad Facionem B A. Quod erac
demouulanduD.
b Per 3. bn
ratione D ad C ex constructione, ergo rario DC ad B A, etiam eA DE A ad F.
tost1i aXXIZ.
Dicorationem B ad C D, candem habere propotctnem Guam
racio AC ad BD Tatloncm.
Donancur denuo rationes AB, CD.
dmonstratio.
Eilaere D ad C, ita B adF.
LCriE VE A Cad R, it2 AB aC
CD racionem: Similicer Po-
Eris racionibus AC _ BD.
Aac ve D ad B, ita C ad F,
exieve A ad F, ica racio AC
ad BD racionem: quia vero
ex construcione est ve D ad
C, ita B ad F, cric permurando ve D ad B, ita C ad L. ten V A B, ad Lacta
est C ad F, ergo vi C ad F ica C au L nestor a Guates Guauales L. a 1.
adeoque est Aad F, ve A ad F; scd re A ad F, ica cracracio A B ad C D racionem
_ VE A ad F, iEA rATIO CFAE A C ad BD. ergo verasio AB ad C. D racionem, ica
est ratio AC ad rationem B D. Ouod crac demonstrandum.
ROPOSITIO ZI
DOcirisicerum duabus rarionibus AB, CD.
uocueaaci lactomeu reanoo ddC A racionem.
sratio.
Acio AB est ad C D rario-  A i1 = 
nem, vedratio D C ad B A Fa-
cionem: Ccdper praecedentemre, 
FacIO DC ad B Aracionem, ita
Lacio DB u L A racionem, erso AB racio adracionem C D, eA verario DB ad
lationem C A. od tt demmontetatauto
XLZ X X X
M     1 t.      .  .     ut.   .      q      t    t  pt. . u       p  et    i