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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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129. h1.
Ibid.
LLIPSIS
quadratum B F ad quadrarum BF, SIC F K, quadratum ad quadrarum FR: sed ve
BF quadrarum ac adracum B F, sic FIFC Eectangulum est ad rectangulum
sulum ad rectangulum MHL HC quaaTaCM LR ad quadracum BH. quare = B, B
puncta lune ad ellipum. Duod erar demonstrandum.
ROPOSITIO CL
26
HIFO, id CA MR L rectansulum ad rectangulum MIR P, isiEUE VE MRI. rectan-
que normales BD: de sectis BD fianc aequales B P. parallela
Dicopuncta Fe ad pCuu Maiherer cA AC.
Demonstratio.
Vcancurrectae DR. quo-
niam anguli BDC recti
sunE, et B H Parallela, anguli
quoquo DBF crunc rectis
QuacFATA ISIEUF DR, Rquancur
quadratis; BD, BB, hoc est
quia BD, B F. Punc aequales,
dupla sune quadracorum BD.
Crro ve quadeacum BD ad
facile apparebit si pertecto Cco elsiplis eadem constructione ad parcem alte-
ram producatur, cunc enim parallelae omnes DP a recta AC bitariam dividenturs
linex BI aGdaICStCCCS FG SCcanteS F G lineas in FIFI.
Dico puncta B, HI, F. esse ad eandem clliplim.
Sco AB C Temicirculi dianieter AD, quam in D SCCENE quOEcCUn
diaMCErO AC.
quadearum BD, hoc est ve rectangulum AD C ad rectangulum AD C, ita quadra.
anvuli D BF recti sinc, et lacera BD, BP aequalia, erunE BD F Comirecti. cum
cum D F. ad quadratum D R. Suntvero d DP rectae incer se parallelae: cum enim
erso etiam BD C rectus sic, reliqui F DC sunc lemirecti; a deo que xequalos; vnde
DE Parallelx. Punctaisicur P, EBlunc ad ellipum. Quod aurem AC (c diameter.
PROPOSITIO, CLVI.
tIrculum ABC sccent ad anoulos rectos diamerti AC, BD ductir
aque rectis FG que AC, diamerro xquidiltent, demittanEUF ex B
Demonstratio.
Poniam F C+ guadtato a
ale eB rectagulu BOL
Hoc eAt BC F, 2 rectarirulur
bis sumpeum sua cum quadra.
to BG; crit a Quaatatm
AB aequale rectangaIO BbL
B
SlUMDEO HHA CAMI Guaatac
: sed F B quadracum elt
equale quadraris 1L, B6
ablaco isicur communi qua
dracum aequale rectangulo
BC F bis sumplo. Smiliterre
drato BG Manet HIO, qua
liqua quadraca H C duplalune
ecta
qo ueusiei eiue aese u es ue e 1       u. t   s  e  s e n ete 1e  e es te  e e e e  e  et a  et t ut   (    e t . 1ete  t  s  1