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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 352, page id 1815201908:0409
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CL115
Demonstration
Tuita KI bitariam II DaUCatUT per O diameter HT: dein appliceeur ad
F F. diameerum ordinacia PO. segmencum auterens aquale segmento
AB: divih(que AB, AD bitariam in R ee S, dueancur semidiametri CTR I, CrSV
iunsancurque puncta AC, BC CC, DG. Duoniam seomenta AB, BC, CD, DA
per constructionem Cunex qualia, crune ec lectores AEB, BC C, CCD, AG D X
246. huius. Quales, adeoque A C B C a diametri coniugatx pexcere a cum ex const. GT, GV
650. bums. BilCCenEC CenErO rectAS AB, A Db sectoreS AC F, AC V, dimidia parssunc sectO.
rum AC B, A C:D, hoc es Semielliplisslector isitur TC V quarca pars est ellipleos
C46. huius. CrSDCO F, C V sunE conIUBAEX _E AB, AD lince ordinacim ad illas polIEX: isieur
2187. hu-
15.
cum per constructione segmentum, PF. O aequalC SIC(COMENEO AT B, EIUC AFD:
exic P O quadrarum bis sumprum, aequale quadracis AB, AD simul sumpris, 2dc09;
P O quadeatum quarro sumprum aequale quadraris AB, BC, CD, D A. Rursum
cum Ccgmenrum P O sIT adsCGIENEUM RI, vrd ABC ellipES ad circulum R L. NI,
=188.hu- F, F, FII diamerri sunc e in X e O, proporcionalicer dimla, ad eoque FPO linca
15.
C178. Lou-
aequalis lincx KL. isicur ee quadratum K P. quater sumprum xequale est quadraris
AB, BC, CD, AD. Ouoderac demonstrandum.
eR OPOSITTO CCTII
Sto ABC ellipsi inscripeum quodcunque polygonum regulare
ABCD, EFGFT: duclaq; TK vna ex diamerris coniugaris rquali
buS; desCTIDACUF CITCMIAS L MI N habens diamerrum equalem diamerro
LK: dein circulo inscribatur polygonum regulare tor lacerum quor est
Polysonum elliphinleriprum.
Dico omnia quadrata lacerum poly goni ellips inscripri, simul Cumpra
aquari quadratis laterum polysoni circularis limul lumpris.
Demonstratio.
10.
Paruantes L, C, ollipuae emompa cuc barsona regularia, eadem quip.
Dc demostracio polygonis omnibus convemiet. in circulo L. M N ducatur diame.
CeF NO sCCAnS LM, lincam bitariam in S; diameerum vero IR secet ordinarim
linca PO seomencum auferens x quale legmento AB, cum ducancur semidiame.
60. ha- ErI TIX, A X, BZ, CX, item TZ, V X que lineas AFT, CB dividane bifariam.
IHS.
Duoniam sesmenta AB, BC. CD, XC. lune ex constructione xqualia, erurit s ee
secto.
( e u u     1   .  .  s  .    Au nu n   u  u H .           A   tuttu              a u u r pui i