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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 295, page id 1815201908:0352
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F L. L. IPSYS.
Demonstratio.
Veatur CFT alcera diamerrorum coniugararum x
qualium. Ouoniam AC, BD quadeaca a limul sum-
Oea e qualia (unc quadraris EF, GTTCmul Cumpeis, crune
ec quadraca AR, BK Cub dimidiis axibus, a qualia qua-
draris B K, CK lub dimidiis diamerris x qualibus; lune
aurem F. K, CK quadraca inter se aequalia, ixieur qua
draca AR, BK simul Cumpea duxla fUME quadrati E R
Ouod crac demonstrandum.
PR OPOSITIO XCIX
Apollonius l. 3. Conic. prop. X6. huiusmodi habet cheorema: 
ellipsim tansant AP, CF, convenientes in F, ex sumpro in
sectione puncto C ducatur O FI F rancentium uni parallela
OHIF. eris rectaneulum C F. A ad quadratum B C, vt qua
drarum AF. ad quadratum C F.
Verum non similitudo tanium rationum sed sariorum etiam equalitas reperretur si ran-
rentes a diametrorum coniueatarum aequalium ductae fuerint.
Elipleos diametri coniug aEX aqualeS sInE AB, C D, in quatUM FCF-
minis A, C, elliplim cangane dux recte conveniences in F, lialcetu
eri ducaneur quoruis parallele C HI orune rectangula C F H quadraris
FC aequalia.
Demonstratio.
Voniam C D eA diameter coningaca diametri AB.
Leric ad iplam ordinarim polica: ergotangenti AF.
Parallela eAt. Eodem modo AR cangenti F C parallela
Cst. AigurA IBITUE K A P C est parallelogrammum. O u2-
re cum AK, RC ex hypocheli sinc aequales, etiam AF,
CP aquales lunciae quancur isitur quadrata AE, P. C.
Aequi est requadracum AF 2d quadracum L.C, ica
rectangulum GFEC ad quadratum FC, erzorectan-
lum CFFP quadrAIO FC aquale eAt. Quod erac de-
monctrandum.
Erquoniam Theoremaillud Apollonii iam habemus
in manibus, etiam hoc addo quod similiter Apollonius
non videtur ob scruasse: nimirum E ductis cansencibus
AE. C F, iungancur puncta concactuum A, C, rectan-
pula OFH, quadraris R F aequalia esse.
Onomam F K, A F. CunEPar: HLCla,
criangula AR C, RFC Smilia PONC. CE-
SOVE AF ad F. C, AC RF ad FC. Cr.
s0 vequadratum AE ad quadracum
R C, Ec quadrarum RF ad guadracum
FiC. Sederiam requadracum AC ad
quadracum L C sic rectangula G FHI
ad guadeacum RF. Erpo quadeacum
KF X rectangulum O F II ad qua-
dearum PC, eandem habene ratio-
nem; aequancurisicur. Ouod crat de-
monstrandum.
hrins