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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 292, page id 1815201908:0349
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aCoroll 46.
oti
CgI. huiu
I. huius
Seron. l. 2
rop. 45.
1
E L. L. IP5 L5
Demonstratio.
lE ABC ellipiis cenerum D ec in ea dequales dia.
MCErI COnIUGAEX F D, F D: dico alias diamiectOS COn-
ingacas e aquales in ea exhiberi non polte: sinc enim, (1
Pocestheri, Praeter E D, FD diamerros; alixe aquales et
Coniugaca GD; TID: cricigicura V D I sectori aequalis
sector EDFT. Ouod herition porest; nam CD; HD
diamerri cum linc ae quales necese est inaiores vel mino-
resillas esse diamerris F D; F D, adeogi ambas simul ca-
dere supra vel inFra diameErOS F. D, FD. IGIEIIE PPRTCE
F. D, FD diamerros coingaras aequales, nullas alias xequa-
les in ellipsi est exhibere. Juod erac demonstrandum.
PROPOSITIO XCILI.
ellipsi requales dIAIEHL CMMaSaEa Simul CumpEx; maximx lune
omnium diamerrocum Ciugacarum simul Cumpearum.
Demonstratio.
Inc AB, CD diamerri coniugacae aGuates, HC alcetm
ec alia queuis diametrorum coniuisatio F. F, ( Ll: dico
diameeros AB, C D Cmul sumpeas mdiores ese diame.
eris PF, C FL Gmul sumpeis: cum enim sCCtOFCS ARC
GR F b. Snc incer se xequales, necesse est unam coniura-
carum inaqualium (AER F) axi viciniorem esse verauis
aequalium AB; C D: alceram vero IIC; remotiorem
vride c ex quaruor diamectis P I’maximas. et OF
minima cAt. lunEauTeM R F, OFI d quadraca simul sum-
Peaaqualia quadracis AB, C D amul Cumpeiss ixitur AB,
CDlinex Simul sumpex maiores c quoq: Tunc lincis R P,
C. HI simul sumpris: Ouoderac demotistrandum.
eR O POSITTOXCIV
Inex gux extrenia damerrorum coniugatarum aequalium coriun.
c ab axibus Mlariam secattur.
Et A: E l
12SSLEL. NI , EL II. 1
s. u. emonstratio.t
Inc AB. CI diamecriconingace aequales, innoaneu
queillarum exttema AV. AC, C B, DB. Dicoillas
ab axibus bifariam secari, divisa enim A D bitariam in
F, AGaEUE(PEF F CenErUM P F C NCCUEreNS C B rectae
in et. Duautequidem orso AB, C. D ponancur ae quales,
harum dimidia AE, DdB, eriam (UME aqualeS. XqUanEVE
aurem ex const. similiter A F, D F. leaque in criangulis
A F F, D F F cum F P sic commune, omnia lacera sibi in-
nicem aequantur. ergo anguli ad L equales, adcoguere
Etii ∞ angusi quoque F F A, F F D, aequales. OuarO an.
suli criam GF C, GF B prioribus ad verricem oppo.
BEi RqUaNEUE. CunE vero lacerarurIum CF, F B xqualia
ex F. C communeverique triansulo (EC, G F. B. I8i
CUIX
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