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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 278, page id 1815201908:0335
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agumm cuntu
E LL FPSI5.
(tIO LXVI
VManEuESECtOres duIO B AC, D A F, sic verriangula ABC, ADF
Dsinc xqualia: Si Sectores M limul lumpri, maiores fuerinc vel mino-
Dicoillosincer (c equales esse.
Demonstratio.
enim non sinc aquales, lE B A C minot lectore
DAF: cum igicur criangula ABC, D A F. sune
aequala, erune B A C, D A F sectores limul cumpei
aequales semiellipsi: Quod est concra lirpoclietim.
igicur sectores BAC, D A F. non sunc inaqualeS
ledaequales. Quod erut demonstrandum.
PROPOSITIO LXVII.
InE AB, BC diamerri coniugatae, ducta-
que ex C recta quanis CD, duCATUT ex
Demonstratio.
Luna C D Orcariam in F, ducarut diamerer B C, d
quoniam BF. aquidistac ordinarim posex CD ad
diameerum B C ipla eriam est polica ordinacim d qui-
dempercenctum, lunc ixitur coniugacx diamceri BO.
BF. lunc aurem ex hypochesi CB, B A criam coniura.
E. Eroo bseAorCB ABar es sectori G B P, dempeoque
communi GB A, sectores C B C, AB P aquales exuie.
Acqui sector CBD duplus cH lectoris C B G. erpolc-
Ator CDD duplus quoque est sectoris ABF. 110d
crac demonstrandum.
ex OPOSTTIO LXVI
I(CCTOTES ABD, ADF, AE C Sinc x qualos, du
cancurquerecte DF. _ BC, ICcanS rECtaS AD,
DIcbBF, VL, CC ellcaqualc.
Demonstratios
ins.
Corollgs. ACqui sECtOreS BFD, BDOE, =constiruune semielliplm, er sodt sectoresBC. A.
BD CF, Cemiclliptm constreuunt. Ouo derac demonstran dum:
res lemiellipe:
B linca B F parallela rectxe C D. iungacurque DB.
tn
e
i
eb0 huino
E s1 Bain
Dico DBC. lectorem duplum esse sectoris ABF.
AF. in F _
neut recta
BD, FC, DC, DC. Ouin se
ses ADF, AF C sunc xquales, eriam eriangula
DE A 3xqualia sunc. ereo aequales sune recta
DH. HC. Dein de qu llores A DB, AC L aequales
sunc, eriam (exeC B D, F. C sunc a qualia. Froa C B.
 lunce paraluela. Anguli igitur GC H, EDH, a
QuanCUF. LunErecO impuli qUOqS G HC, B HLE xqua
les
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