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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 355, page id 1815201908:0412
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ELL IPSTS.
Constructio e demonstratio.
invenire diamectum comgatam ipti A, quam
cum daris axibus oportet in cadem collocare ellipa.
AXCS ED, BC ad ansulum ponaneur rectum F CB,
iunetaque BP, super ca lemicirculus delcribatur
E CB, in quo daca, A aequalis apFeTUE P F, ducacuTGs
FB: quoniam isituE F C, C. B axium quadrata aequa-
lia sune quadearis cuiuluis coniusationis in ellip(, c2-
demque axium quadeaca aegueneur quadratis R. F, F B,
_ F F aequalis A una sic ex diamerris, recta FB di2-
mecer est coniugata FP: exhibuimus isitur didmetro
A, comuertum, quod primo taciendum fuic.
CTE A diamerer data, _ aXCS daci BC, D E, OPOTFeE
Tunganeus deinde arium exerema DB P. C qua parallelosrammum extribeane
DBE C: cui aquale hat parallelogrammum = IHI R C, quod IK, OHI diamerrOS a Perele-
habear rectis D F, F B aequales. daca isicur diamCerorum LR FI C coniusatione, menca.
extribeantur positione aXeS B L M, NY O adeoque e cllipsiS L. MIN. cric illa ae qua- b ge huins
lis ellipsi BF. C cujus axes daci sune BC, F. D; cum enim per extrema coniuracio-
nis posirone darx, vnica raneum cellipliS Fran (CRE, _ LK, C FI coniugatio policio- c 1bid.
ne sic in ellips L. MIN, cademq; pertineat ad cllipsin B R C, cllipleS L MNI, BF C
ad eoque _ aXes aquales simE: ellipsS igitur L MN, illa est in qua coniugacaS R P,
FB, id est IK, C H polirione cum dacis axibus BC, DB, id est L M, NO collo-
care oporrebat.
PROPOSTTIO CCVI
cala ellipsi _ circulo IIIdM
incerlecante puncta inter-
Cectionis reomerrice exhribere.
oporcet aurem circulum de ellip.
lim idem habere cenerum.
Constructio es demonstratio.
ILlipum AB C cuIuS CenErANI D3
incerlecet circulus AB, CF, 0-
porcer incersectionis puncta exhibere.
quoniam igitur circulus _ cllipss
COIMUnO HABCRE CCHErUM D, ( CX
illo ad incerlectionis aliquod punctum
323
iatsii