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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 880, page id 1815201908:0937
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PRODORTIONALLTATES
eROPOSITIO VI
Dico F. B ratiOneM C LACOHCM C, D, vE L CA ad A.
II rationes AB, C D, Similes Fuerine, ex allumatur quaevis tinea F.
monioran.
m SimileS POTUnEuE Pa-
reSCD, _ AB. VEEL
rationd CDTdc
tea euela
dem racio EB ad racionem AB:
(Cd per (ec
undam huius, racio F B
2d AB racionem, eA vE P ad A
ergovcF ad A, ica quoque est ra-
PROPOSITIO VII.
Demonstratio.
cio EB ad CD rationem. Quodtuir demonstrandum.
ationes dux commune anrecedens Porrirxe, eandem obtinene rario-
nem quam secur e Guens ad primum.
Ine dux Faciones A B, N AC.
quact commune existac an
cecedenis A. Dico illas raciones.
incecle candem aabece peopoi.
cionem, qua l lecundum cole
quens, ad B primu: Hacenim ve
2. tonin
C ad Ag ita B ad D, arario AB, ad tacionem DB, eA Dc A ad D, CC d ex tryp. racie
DB, estrario AC. ergo rario A. B ad rationem A C, est ve A ad D, SCd ex hyp. VE
A est ad D, Sic C eA adt B; PaFCE isituE raciones duas AB S CB, habences com
conlequens ad primum. Cuod demonttrandum tuccal.
eROPOSTTIO VII
IIproporcio ratien D ad rationem ADI eadem liC. CuMI PFOPOE
cione rarionis AB act laionem C ad D, hoc eB(irariO A B LF ad ra-
rionem, AD, ve ratio B cM ad rationem C D TC sisr., 3 uluil
30ai deer 1o 143oet
Ei
 3q EM cA.
munc ancecedens, cam incer seratiohem obrinere quam haber C ad B, secundum
Dico A e C aequales este quancirates.
Oomonsdrio.
sit
II
e
Toniam eacio AB ad A Drationem, esL VErA.
cioae au rigluceacio ali, cadcluca
cum racione C. ad D: ell aUTCMEatio AB ad CB
orhniu. rationem veb    aflalet Elala C.
P R O.