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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 389, page id 1815201908:0446
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P A R ABOL A.
Corollarium.
Tinelequicur: rum AD dividacur in L. _ ML, H LL, DM linex aquales
LsnE _ OIMNATIm PONANEUT LN, MO, quadrara L N, MO limul lumpea
aequari quadracis B B; F. C Simul sumpeis: Pacet ex demonstraris, quia Fam L. D, L
quadraca, quam L. H, MO AmuL Cump Ea = qualia LUNCqUAdEaCO C. D.
PROPOSITIO LV
DArabOlam A VC cuius diamerer AD e ordinarim ad illam polila
CD, COnMMaCin A linea AF, quam in E (CCOE AIALLICLCTC L: 2(-
sumpeoq; in lectione puncto quouis B, ponacurper Bordinarim linca
FO, Occurrens AD lineae in F, e F. C in C: dein per B ducacur diame-
cer HTI(ccans A C D ordinacim policam in I.
Dico parallelogramma AB, A C, AI, AC in concinua csc analogia.
Demonstratio.
Droniam AB, FC linca aequidistane, paral-
Lleloocammum AB ad parallelogrammum.
A Cn eA ve F B linea ad lincam F C, Id cAtC D:
est aurem parallelogrammum AB ad parallelo-
scammum A B VE A F linca ad lincam AD, hoC
elt in duplicara b rarione FB ad D C: igieur pa-
rallelogrammum AB, ad parallelogrammum
AT, duplicacam habec racionem cius, quamhra-
ber AB parallelogrammum ad parallelogram-
mum AC: Parallelogrammaigieur AB, A C
AI in continua lunc analogia: Rurlum parallelogran
mum AC, ve DIlinca ad lincam D C, hoc est ve AB parallerorammum ad pa-
rallelogrammum AC. Parallelogrammaisitur AB, AC, AL, AC luMCMML
nun proporcione. Duod erat demonstrandum..
PROPOSITIO
DArabOlam ABC, cuius diamCFEF AD, COnFinGACMI LLHHCA AL, aU-
atisque ordinacim FB, DC, criganeur ex C _ B, diamerri LC, B6
occurrences concingenciin ( e L.
Dico AGB parallelogrammum ad parallelogramnom a L. C ecipli-
caram habere rationem eius quam habet AC linea ad lincam AF.
Demonstratio.
a2. Botit.
B2. hacind
AI est ad parallelogr2.
Acioparalleloprammi AOB ad AEC pa
rallelogrammum ccompolica cs, exratione
A C, 2d AF, d G B ad F C; sed racio GB ad
mumigitur AC d pacanctborammu AP C
E C, id est AF ad AD, duplicaca cA rarionis
AC ad AF; id est FB ad DC, parallelogram
eriplicacam habet racionem ejus quam habet
AC linea ad lincam AF. Ouod erac demon.
Arandup.
CcC 3