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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 911, page id 1815201908:0968
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SAD
_  L L A IC A. 15
ac proinde acto au Prone ex acuatien AB. BC. LacePou
cic ductusrarionum AB, CD, X B C bislumipea quod producic ductus racionum
AD. BC. Sed per 78. huius ductus rarionum AD, B C idem producie, quod ductus
rationum AC, BD. ergo ductusrationum AB, C D, ex BC bis sumpea idem pro-
ducic quod ductus racionum AC, BD. Quod erac demonsrandum.
P R OPOSITIO LXXXI.
VInEaux qua_IS rationes AB, CD.
D Dicopreportionem racionum AB, CD esse candem cum ex qua 
oritur ex mulciplicationerationum AB, DC.
Demonstratio.
A ad F, etiam coponitur ex rationibus A D e D F, hoC eA ex rarionibus A D, BC,
lat veD ad C, HC B ad L.
Valec ex 75. lsiusracionem
adracionem CD, ve A ad Li, ac promde proportio Falou AB, CD oadem est
cum racione AB. ergo proporciorationum A, B, C. D eadem eltoum ca qua AC ex
mulciplicationerationum AB, DC. Ouodtuerac demonstrandum.
eROeOSITIO LXX XHI ep unie
AcaHIE quaeuiscario A ad B.
csto
alato
Dico quodrario AB ductain le, dupilcat eus Gllam haber
Demonstratio
lane preporciorales A, B, C. exit 2 et 8
racio A de C, illa quae Ac ex AB duct
in B C, hocest in sciplam. Sedracio A ad C
duplicaca est eius quam habet A ad B, igi-
cur racio A ad B, ducta in Ce iplam duplicaca
estrarionis A ad B. Ouod erac demonstrandum
PROPOSITIO EX LXALF 1D. d R il 30
D Atio A ad B similis sicrarioni C ad D.
Dicoracionem AB ductam in D C, produccte lattolem xqua
IIEaris.
HEeol Scubla 
Demonstratio.
AF. produci exmulciplicario.
neracionum AB, DC. Dcin-
de per 13. huiusracio A B est
A ad B.
CD, crir inverrendo ratio B A simi-
lisracioniDC. quod et8 ata
DVoniam racio AB similis est racioni
cacione racionis AB in racionem B A; AC
eciam ex duccu racionis AB in racionem
DC. sed ex ductu rarionis A B in raTIONE
BAB proaUaaqualicaris; ergo 
m a
1.11C1.
Dunirime io
ex ductu racionis AB in racionem D C, producicur rario x qualitaris. Ouod exac de
2
1
qsi ue uu t  a t   pue