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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 909, page id 1815201908:0966
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ex 1
GF OM EFRIC A.
90
Fiac enim ve C ad D, sic A ad F, Dicorationem AB ductam II FXCBHCM
CD Dioduccrerationem AL. Demonttraciopacee ex Deacedenei.
ROPOSIFIO LXXVI
Aca sic quaeuisrario A ad B.
Dico raltortem AB ductam in racione B A viod racio
11
nem aequalitatis.
Demonstrath.
Vancicari A a qualis aTumatur quanticas C. PatiO A ad CCPonitur exracione
AB, X racione BC, 2 hoc estracio A ad C, produoitur ex mulciplicacione ra- 2 Princip. 2.
cionum AB, _BC. sed racio BC cst rario B A, eA enim C aequalis A. PrgOracio
Aad C eriam peodulicur ex mulciplicacione racionum AB, et B A. Ccd racIO AC
ectracio aequalirarisi liquer ergo propolicum.
1. Litit dis tc
PROPOSITIO LXXVII.
lincer A e B celuis ponantur cermini C, D
Dico AC racionem ductam in C B candem producete quam ra-
Demonstratio.
in
eio AD ducta in DB rationem.:
Acio A ad B, componitur ex racio-
citur ex ractorum AC _ C B molci-
plicatione. Padem quoque rario A ad
B, componicur ex racionibus AD; ec
DB; hoc est producieur ex ductu rationum =D, D.
nem C B, eandem producierationem quam ratio L D auctain raci
etac demonstrandum.
pibus AC _ C B, hoc eAb produ-
PC
B 1bid
S
Dicorationem A C ductam in rarione
AEX sinE quatuor quanricaces A, B,
BD candea prouueele rarionem quan
tacio AB, ducta in rallonem BC.
Demonstratio.
LtarvE B ad D, Sic C ad F. Fr3op er 75. huius L
ad B, producitur ex mulciplicacione rationum
AC, d BD. Deinde quia est ve B adD, sic C
2d F, erir permutando B adC, ve D ad P. Cr9O
foratio AC ducta inracio.
DB. 46a
rioc A dvecaao Poenratione a . cl80ce rae ca cibia
in racionem B C produci racionem AF, sed hanc eriam producierario AC, dueta
inracionem BD, reostendi supra. Racio igitur AC ducta in rationem BD, idem
producis quodracio AD ducta in racionem BC. Ouod crar demonstrandum.
L. 22
corol.
ratio AD ducta in racionem D P. idem producs
quodracio AD ducta in racionem BC. sed r2-
pui   sa uu  i e s  ute    a t t  ete et te  e        te a  ut  u u. e t