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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 280, page id 1815201908:0337
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d
R
R ILLL
5
OeoIO LXXI
Considerat axium ac diametrorum coniusatarum ramaqua-
lium quam inaqualium proprietates.
ellipsi diamettorum mana c Mnima Tunc axeS.
Demonstratio.
InE A B C cllipicosaxes AB, CD, _ AB
quidem maior, CD vero minor. dico AB,
diamerrorum estemaximam, C D vero mini.
mah, cenero ellipss F: inceruallO F A circu-
lusdelerrdacur AF C: transilicis per B, _rC.
liquo tui eocus exera a cllipsim cadcc: ducatur
det per L. diamerer quacurique F C Occur
rens cllipA in EI _ I. circulo aurem in F ex C
Duoniam circulus A FC corus cadic extra cl.
liplm, exic FC linea maior rect a FTT: igieur
ec AB maior est quam EII. idem octenditur de
quavis alia diamecro; igicur A B axis maximus
est diameerorum ellipsis AB C. Ouod cracpri.
itium.
Rursum centro F inceruallo RD circulus
de(CribatuT DRL OCCUTEEMS PC linea in R
EL: cransilic is per C, ex reliqua las pacelotus inerab sectionem cadec. igiene. FT Lli-
nea maior est quam X P hoc ell C. B: Juare cum idem de ommalia linon qux Per
C e D non cransie ostendarur, ec CB diamerer omnium minima qua in ellipa
Corollarium primuit.
1. 112t3
lamecer quae maiori axi est propior, illa maior csri
ee qua remorior, minor. sic AB C cllipleos axis
AB, Cencrum C: Ponaturque C C diamecee propior
axi quam CF. dico C C maiorem ese ipsa CF. Cen-
eroenim C inceruallo C C circulus delcribatur, Oc.
currer is cellipli in quaruor cancum punctis CKHD.
quare C F ad peripheriam non percingic. vndemi.
noc est quam CC. Duod erac demonstrandum.
Corollarium secundum.
Eccrollia
ADB ducipostunE. Cubu erac demonstrandum.
erro diameter axi vicimtot eu. Que cum axCmi-
Patclaleum CPehoneoienao. Lpieos axis ma-
ior EC A C. Faciacque diamerer B Feumaxe sectorem
BE A
norem vel angulum facic vel sectorem. primum
o ut uori putis ti pta ss uptre t epue asustepietite  itsete otes  s st atu  t sue pe  ut e u e u ste  u e tu t  e et a e et a e te  e et  ti e  ue u a  pi  tu