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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 323, page id 1815201908:0380
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ELLIPSFS.
Demonstratio
recrangulum BDC, hOO DAE RECEANSMIUM A F. C ad rectangulum AF C: sed
ve BD F Kocrangulum est ad Fectangulum BD F, sic F F quadracum est ad qua-
dracum P P, igicur vereccansulum AR C est ad recrangulum AL. C, lic H F qua- 2 Per1 49
drarum est ad quadracum RH. orgo a AFC, punccalun ad elliplim.
ROP OSITIO CL.
Ic AB, CD parallelogrammi diameter AC, ducanturq; AB lareri
huius.
quorcumque parallela FC, sccances AC lineam in P: dein hanc in-
TOF PE, EO medix E FI.
Dicopuncta A, C, ec omnia puncta HL, ese ad candem elliplim, nisu
Cineadcirculum.
aete
mno Demonstratio
les
Ario BBC reccanguli ad recrangulur
FF. C est compotica ex ratione F R 2d
FF, id ost AF ad AF, _ CX F C ad F.C,
id est F C ad F C: (cd ex ij (dem compoti.
tur raciorectanguli AF C ad A F C, rectan-
sulum, igicurve F F C rectangulum ad re-
Crangulum FF C hoc est quadrarum F FI
Sd quadraTUM E FI, SIC A F C recrangulum
CA adreccangulum AP C. guarAH AHL, HIC
puncca sune ad elliplm. Duod erar demon.
Arandum.
lie E
I AB rectaBEnOrmalis ad A C, et illi FuE
Dric aequalis, crute A FIH puncra ad cundé
cireulumserit enim XD C rectanoulum x
qualo recrangulo r P C MOC CA quacaco P. H. qdeoque punera H HX ad eiroulum.
T BDE roctangulum ad recranGulum B DE, sic B DC, reccanpulum est ad
Corollarium.
u
1
1os. 341
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