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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 449, page id 1815201908:0506
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# Lines: 46 recognised, mean confidence 0.84
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lales
BR
Ie2
lo
at.
im
ale
B.
eis
est
2ei
11-
0.
P A R ABO L A.
id est quadrato B C ona cum rectangulo B E D;igicur quadratum B C vna cum re-
ctangulo BC,D aequarur P HI Frecansuloriia quadrato FIC, cum id ele B Ci; dem-
Ocoisicu communi quacLATO BG, ManCC F HIF rectal   quale rectangulo
PROPOSITIO CCII
B CD, id est quadrato C I. Ouoderac demonstrandum.
IEdempolitis:
Dico FI, OII, LF lineas proportionales este.
Demonstratio.
Vonam L. F linea divisa est bitariam in C e non bitariam in P, rectanoulum
LF PF vna cum quadraco YC, id estrna cum rectanoulo. BD, aGualC c qua-
deaco. GF, id esta rectangulo CB D id est quadraco BC. V2 cum rectangulo BCD 2 Ibid.
id est cum quadraro GI; dempro isitur communi quadraco TC; anet F IF rC-
ctangulum aequale quadraco BC id eA quadraco FI C. proporrionales itaque lunE
FI, CH IF. Quod erat demonstrandum.
LNNOStTIO COML
Seo super A BC patAVOIA AXC AC X-
Aquan lateecto delcriptus lemicir-
culuS AFF, Sumpeaque AD aequali AF,
ducacur ordinarim quaenis BF lecans
aRem AF in C, occurrens circulo in F
IHNOAREUEGS AB, AF.
DicoD C ad DA rationem habere
duplicatam eius quam habec AB ad AF.
Demonstratio
Ventam AF quaatatum aquale elt quadra-
ris FC, AC id est rectangulo D AC recte
AC, AF, D A continux sune proportionales:
sed _ AC, AB, CD Tunc in b concinua ratione;
igitur cum AC prima verique scrici commu-
nis sE, D C ad D A, cerria ad certiam, in dupli-
cara est racione c AB ad AF, secundx ad sC- C)
cundam. Ouoderac demonstrandum.