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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 924, page id 1815201908:0981
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eROPORTIONALLEALES
R O P OS
Tine qualisrationes AB, C D.
CIO CIX.
Dicoquodrario AB ducta in DC, aquec acOM quam habet
rectangulum AD ad C B rectangulum.
Demonstratio.
Acio crenim AB duu
Cracionem LauCCA
cum proporcione quam b.
bec racio AB ad C D rario-
nem. Requibracio rectangu.
lis AD ad C Brectangulum
eadem quoque est cum pro-
924
leBCILI.
poriton
incproportionales ABC, Iem L, L l.
Dico rectangula AF, BE, DC. eandem quoque rarionem conci-
naFe. Lect ceboeir
in AB, C D. Igicurracio AB ducra inrarionem DC producie pro-
porcionem reccanguli AB ad C B reccatGutul. Suod demonstrare oportuie.
ut Aot o P 1105++1B. CA.
Demonstration
 Eccangulum e F ad BP. FC-
ctangulum, compoliam ha-
becracionem exracione A ad B,
Ine BC Guaicales ploporonales. deinde ve A ad B hac quaeuis
DD
DicoLeccaSua AD, BB, BC, L. C, elle in ContinUatA PFOPOrEIOnE.
e 4
plum quoque D F ad D C, hadecracionem ex iiidem compon
tamnempe exracione B, C, qux eadem elecumrarione A ad B, ex supposicione, e
ex ratione F. ad D, cullem cum racione Lad F. parec igirur rectangula AF, BFo
CD proportionales esse quancirares, quod oporruic demonstrare.
22. Sex1t.
IF.
tROeOSITIOBAI
Lbiloltobiliti
Acio rectanguli AD ad DB
cangulum est re 2 A ad B,
cum habeae commune balim D
AD. DB, BP. L C concinvanc cap dem rationem A ad B. Quod Euic demonstran.
dum.
simili pactoratio recranguli DB ad B F, cR ca quam habec D ad F, hoc est A ac
B exhyporheli. Denique racio B P. recranguli ad F. C recrangulum, eriam estra
tio B ad C, hoc est A ad B: sune enim proporrionales A. B, C. igieur recrangule
111
P R O.
10