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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 938, page id 1815201908:0995
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13C
DR ODOR PIONALITATES
Facionem F G, hOC CCPATIONES PF, F C incer se mulciplicacx producune rarioneM
F C. Similicer racio FR cum ratione R C componic eacioite C raTIO L K
ductamrationem KC producieracionem R C. Ced racio K e ex constructione est
eade Cum ratione FR. Ergoracio F R in sciplam cta producit racionem LG
candem scilicer quam producebane rattones LF, L e  et ex constructioncra-
Collisicur ciones dat_ AB, CD. Ergo arario P. R  elt incex FaciOHCS dataS AB, CD.
9+. ha-
Fecimus ergo quod pecebaeur.
Aliter.
ett.
Aca sinc rariones bina AB.
ETI, inter quas media siC ex
hibenda. Fiac ve FIad G, bcD ac
ee incer A ac l mediam tac pC0-
porcionalem R: cum ve A CM sd
R, AICB ARC FaEIO AB acrationen
CD. Dicohanc
IacO. NaMm VE A ad R
crepostu
EcpetCon-
Aruct. racio A B est ad rarionem
CD. quare cum ex construct. ra
eio A ad I. Ec duplicaca rarionis
A ad X: eric quoquerario A ad Y duplicaca proxorcionis lacionum AB, C. V. lea
c17. huins. VE AadI, hccracio AB ad racionem C, FI. ergo proporcraos AB ad CHra-
cionem, eciam duplicaca est proporcionis quam haberracio AB de Lallonem C
Bvirrs.
FHF.
Ergoraciones AB, CD, C HL sunr proporrionales. Factum igitur est quod peceba.
eROPOSITIO
lem extribere.
CXL
Constructio amonstrario.
lacree adD, cD adF. 1
arem C ad F, I K ha
ad Z. Dicoracionent DL daci
racionibus ese cercta PCopor
cionalem. Nam rario C D ducta
construct in sciplam, producit ra
sed eciam rario AB ducta in rarionem BZ. Plocuen Tactonem candem A L. ergo
dColligiur draciones AB, C D, BZ. sunc in concinua anatoBla. LCeMmus ergo quod perebatur.
Alio eriam modo licebit demonstrare Luctonte  llah elle proporrionalem
racionibus dacis AB, CD. Duoniam enim per comituconemlationes AL, CH
tacio C D, ad racionem BZ.
xg4. ha-
ino.
in racionem DF, hoc est ex
CF, hoc est ex construct. rarionem AZ
ccrtnius. similes lune, erir cracio AB ad rationem C D, veratio D F, hoC es ex construct. VC
ROPOSITIO CXLIII
ubio ecinoate o betda Edt a  t
CoB