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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 287, page id 1815201908:0344
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ma
alec
EL L IP SIS.
Demonstratio.
InEaxeS AB, C D d alia quaeuis diamerrorum coniu-
Satio DF, C II: inniganeurque excrema cam axium,
quam aliarum diameerorum. dico lineaS C A, AD, DB,
P C simul sumpeasmaiores esle lineis FG, GF, FFI FTF
Cmul sumpeis. Duoniam CK ips FTK aequalis cAt, F R
vero communis, ec F HI a recta maior quam F G7, erie
anguluS R RFI, maior angulo FR C ioicur e angulus
F. K HI maior eAtrectO A K C. (InE AUTEM B AR C, LR II
crianoula aequalia, quare _ F FI C es maior quam AC:
eadem modo octenditur AC linea maior ele recta R C+.
ergo F. C minima eA, _ F FT, maxima linCaFUM F FI,
AC, AD, F. C. igitur cum d F FP, F. C quadeara simul
Cumpea uncaequalia quadracis AC, AD Cmul Cumpeis,
CrunE CF TI, FC linex simul sumpre minores lincis AC,
CD simul lumpris. eodem modo ostenduncur linex C F, P. IY minores lincis CB,
BD. ergo, _c. Ouod crar demonstrandum.
PROPOSITIO LXZXV.
N nulla ellipsi est inuenire diametros coniuxatas qua lese ad rectos
LlCCCNE, PTXTCE AXCS.
Demonstratio.
IDE axCS, AB maior, CD minor et alia quaevis dia-
mecrorum coniugario B F, GII: Centrum aucem cl.
LipESSIEK. diconeucrum an gulOFUM F RG, CR F re-
ctum este: iungancur enim puneta F C, GF: Ouoniam
ER, R C duabusrectis FR, X C aqualeS SUINE, DE F C
eminor quam FOn cric angulus F. R C minor angulo
CiKF: Cuare cum eorum summa sic duobus rectis equa-
lisneurer illoru rectus est: idem de aliis omnibus osten-
dicur: igicurinnulla ellipsi est invenire, et c. Quod erat
demonstrandum.
PROPOSIFIO LZZXVI
InF ABC ellipsiS axes AC, BD ex alia quaeus diamerro
Dgatio EF, CHI: iunetisque punctis AB, BC, rectX duCAHEUE
FFL, FC.
Dico angulum ABC qui circa
minorem axem existie, maiorem
esse anguloCFH, ac proindemaxi-
mum esse omnium angulorum
qui concinentur a lineis exrre-
ma diamerrorum coniusatarum
coniungentibus.
a83. tinins.
3iea ex7.
dd0. huius
c
1. 2. Prop. 45.
lu coniu-
Demon-