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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 62, page id 1815201908:0119
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PR O GR FSSIONF S
imonorratio.
apsccunai D Eclangulum ADE aequarur  rectangulo A F D cum quadrato FD: rect anou-
2. Sccudi. = Ium aUEe A F D, aequacurrectangulob DF C, _ DF C B, hoc eA rurtuS rC
Elandulo DF C (cum CF, C B MM aguates) e rectangulo DV B A. Scd percorol
sulo DHC bIs, a Guadio F. C. quare rectangulum AD P. aequatur rectangulo
c4. Secun- D L.C, bis, ee quadraris P CC eA c quadracO C D. VndC AD, CD, E D lunE
d7. Sexti.
Aliter.
Voniam DA, C A, B A PonuC Concinux, exicper primam huius D A ad C A.
CUE DC ad C B, id cs C F. Guia aequales sunc ex daris BC, CF: Ieaque di-
uidendo ve D C ad C A, sic D L dd F. C: _ inverrendo vE A C ad CD, ita C F
ad F. D, et componA D ad CD, sic C. D ad F. D. Quod erac demottrandum.
Corollarium.
IX hac propolitione educitur hoc
TheOTCMA. SInE AB, CB, DB prOPOF-
tionales, crigatur aucem ad angulû quem-
cunque recta B K, aequalisipsi C B, iun-
santurque puncta AF, CF, DF. DicO
AF C, CF D angulOS CMC aequaleS: d A
AE C, C ED anguli Fuerinc aquales, e
CB linca aequerur recte BF, dico AB,
CB, DB esse proportionales: s vero
AFC, CFD anguli aquentuE; _ AB,
CB, D B sincproporcionalesi dico C B,
EBlincas eseae quales.
Demonstratio.
Voniam ponitur ve AB ad CB, hoC est BE, sic BF ad DB, ee anguluS ABF
LMEcommunis, erie D F B d criangulum, A F. B ctiangulo simile, adeoque angu-
IuS D E B angulo F A B aequalis. Rursum cum C B, F B LaFCTA XGUENEUE, CrUnE
c32. Primi. anouli CFB, F CB aequales; est aurem angulus F C B, aequalis eduobus angulis
E AC, AF C isicur angulus C R B equacur duobus angulis A F. C, F. A C: Sed D F. B
aequalis ostentus est angulo F. AC, dempris ixicur aqualibus F. AC, D F. B, manenE
AF C, CF D reliquixquales.
SinEiam anguli AF C, CFD _ CB, BF linex aquales, dico AB, CB, DB
esse concinuas. Ouoniam angulus F CB hoc CA CF B equocur angulis F A C, FAF Cd
ee C E. D ponacuraequalis ips AL. C, erie D F. B reliquus reliquo P AC aqualis:
estaurem angulus AB F. communisi ergo cerrius certio equatur, adcoque _ AF B,
DE B criangula similia: vndeve AB ad F B hoc CA CB, ita F B Euc C B ad DB.
Duod craclecundum.
ta VCrO SInE AF C, C F, D anguli equales, d AB, C B, D B ETES CONFInUE PEOPOF.
cionales: dico CB, F. B lineas aequari: (i enim non sinc equales, (c C B maior, fiarque
CC ip(F BF. aequalis. eruncigiur per secunda parrem huius propol. A C, C C, DC
Huius. concinue proporcionales. vnde Ii hac FI C aequalis ipH C D, CrUNECaMB AC, AC.
A TI; quam AB, AC, AII concinue proportionales; isitur eam A C A II rectan
sulum, quam AB AEIrectangulum, aequale quadraro AC medic communi: quarc
i A G A FI, A B A FL rectanGUIA RQUANEUF INECFSC. VndCVE A FL, ad AFT HSC AB
ad A C; led A FF sunEXe quales, CrgO A G A B rectX egnancur, ex e punctum idem est
quodpunctum B: e C B, C C, id est B F. linex aequales. eodem modo ostendicur
CB non ehe minorem ipsa BF.
PRO.
Erbid.
 50.
larium nonx huius, AB, BC, F D sunc continue, ergo rectangulum F D A B aequale
CAquadraco B C, hoc est gnadeaco P. C. rectangulum igitur A F D aequacur rectan
ciescof dod erar demonstrandum.