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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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Definit. 2.
ius
634. hacls.
119
DROBORTIONALLFATEL
Demondiratio
TVoniam E _C F, ponuntur denomina-
Lorestacionum AB, CD: ergoracioF
adF, esta proporcio rarionum AB, C D: lca
Roporrioracionum AB, C. Db compolica
est exracionibus AB, _D C. ergo racio L.
2d F ex racionibus AB, et CD compolca
CA. led ratio F F componitur etiam exracio-
_e CF, Cadem sunt. Duod erat demonstrandum.
nibus DC
Eper hypocheuim AB) e G F. ratioisiEuF A B cum racionCDC
candem rationem componic quam rario A B cum racione C F; racionesisitur DC
II proporciorationis, AB ad racnem CD, compotica sic ex ldem
racionibus ex quibus conspenlicur proporio rarionis EL ad Ctl,
Dicorationem AB CHC act C D, ve rario F F ad G II rationem.
rusi
PROPOSITIO XXXVI.
racionem:
morstata.
FilarveD adC, ita B ad F: _ vE F ad C, ita
F ad K, cricicaque cracio AB adt CD r2-
tionem, ve A ad I; _ Facio F F ad C FFr2-
tionem, veF ad K, sed racio A B ad racionem
CD. Proporrionem haber copolicam ex hy-
porhes exijsdemracionibus ex quibus copo-
scam habecracio P P ad C FPracionemiigi-
cur cciam rario denominacoris A act I, deno-
minacorem, ex ijidem racionibus ex quibus
ratio denominatoris R ad denominacorem K
eH composita. quare A est ad L, SCVE F. est ad
K. vnde a AB al C Dracionem, est verario P. F ad C FLrationem. uod
demonstrandum fuie.
lincel o Poa e C, D.
Dicorationem AC esse ad AD rationem, verario DB est ad C B
PR OF OSITIO ZZXVII
Demomoratio.
 AC ad AD, est ee D ad C, d rario
ucem DB ad CBcracionem, rurlum est, vi
D ad C, igicur est racio AC ad AD racionem,
LHABLIECLAMAUMD.
ralbhCM.
re estracio DB du CLacionem. Ouod etat de.
PRO.
en