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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 921, page id 1815201908:0978
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PROPORTIONALITALES AEDMLLRNA.
AC ad BF, cam racionem habere quam AD rectangulum ad rectangulum BF.
Ouodtuir demonstrandum.
PROPOSETIO
922
TIE AB racio, ad rationem C D, VICITACIOL F ad C FLTaCIOneM.
Dicorectangulum AD ad BC rectangulum, candem habere pro-
portionem quam P. HI rectangulum ad rectangulum F C.
Demonstratio.
C, HCF 2d1 CneL all 
sic rectangulu F Had rectangu-
lum OF. Acqui ve A ad I, 6C
bF, 2dK. ergo ve rectangulun
AD ad reccangulum C B, l
rectangulum F Had rectangu-
lum GF. Ouod crac demonstrandum.
Acislationibus B, CD. Oporcat exhibere quomodo se trabeat
PEOPOETIO rationum AB, C. D ad raltnem rectangulorum AB,
ilac ve D ad C, sic B ad Y.
cric ergo ve A ad b, SIC a rC-
ctangulum AD ad rectangu
lum C B. Rurtum hac vE HI ac
PROTOSIITO CII
Constructio ex demonstratio.
Dico propontonemracionum
AB, CD esse ad rationem re-
CtaDSUIOTUM AB _CD, VEF,
eAt ad F.
ilacveD ad C, ita B ad F. DC-
inde veBad D, ica Aac C ad F.
Demonsirdono
Amproporciorationum AB, C D per r. huius CReadem cum PatIONC AP. R a.
tet es
e
b 42 huius.
exracione Iltam habet B ad D, hoc cA quam habec ex constructien  al , leut
cum racio A adF, eriam componatur ex rarionibus AC e CL, racio rectangulo-
rum AB, CD, eadem est cum racione A F. sed racio AL elt ad rarionem AL, Ve
F est ad F. per 7. huius. ergo proxorciorationum AB, CD est ad rationem lCClau-
sulorum AB, C. D, reti eA ad F. Factumisicur elt quodperebatuF.
PROPOSITIO CIII.
LAcio veroguae est incer rectangula AB, CD componicur ex racione A ad C, e
VIracio ABadCD, crL ad t, latio quoque liHlad lR, ve L. ad MI.
Dicolaclonem rectangulorum AD, C. B ad rarionem rectangu-
lorum C,H, Cl Cande habere proporcionem quam rario P. F ad L. M..1
AL 3 eiit DeMon-
int
TaTIOReM.
1e s t   .     t. u   t e  1  s.      u .     1t   s     e   ot e t
1III