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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 533, page id 1815201908:0590
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# After the first blank line: the recognised lines in reading order, one per line.

ae
sel.
al.
1
lo
tum
Cta
CuI
Htes
unes
id1.
in-
12-
Une
Y
e-
TH
um
itet
 e
ee
12-
ap.
A.
de.
HI XD F R B, OL A)
aequalibus acaritur plana parallela rectae = Lexhibentia communes insersectiones AC, DF,
erecta deriqs. C+ II per L quae sit parattela FL, Y L aequales interse, s C I, FI L aequales fue-
rint:imo e A C, D Ii bifariam dinisa in LL ex C, ex ellipses AB C, D F. F aequales ac simi-
les: unde cum rectangula D L. F, A K C aequalia existant vii ex rectaneula V PZ, SR T.
eriam quadrata P L, K B, de O P, R C) aequaliu erunt inter se, vt ex ijs quae libro de Ellips di
eta sunt manifeste collicitur. ex consequenter eriam hyperbolae in hoc casa similes erunt habe-
buntG larerakB, P. L, d R O, OPaequalibus intervallis a punctis NI, ex V distantibus, a
qualla prorsus, ur in priore scemate quodiubebas sectionem axi parallelam fieriostensum est.
5 1 TIO 1V
icarum sectionum ABC, PD F diameter sCBD, qua bita-
riam diuisâ in G ponatul pet ( linea occuttens a BC hyperbodi.
(52 (12CI
Dico quod CO proopolurx uose eemte enominE.
Demonstratio.
urnito
Ca IM L
Desita ex C ordindet a CLL aet ctame-
crum BD, hac HC aequalis Crl, d Cx LOF-
rens CG linca in F: quoniam igicur HIC, IP.
lineae in oppolicis sectionibus ad candem diame-
erum ordinacim policx sunc, aequidistane h HI C.
F. I adeoqne anguli CFTG, OTF XQUAHEUE.
tunc ducem ansuli ad C, oppolici e IG, (I
linex Guoque aequales, xqualia igitur lunc crian-
sula OTIC, WHL. aHC, LI linex aequales:
quia vero BC, 6D aquales sunc ex hypoches,
DI quoque aequales luho: quare LF linca DrOUE
hypelbolxoccurrie, b equalis est HIC: eadem
tixpeldolae, e prouc CC lince occurrie: unde
punctum P in PerimeliD eA Byperbolx, _CC
producta oppoliex occurrielectioni in P. C uoc
21S2OMBCC  Cc MI 3153C
cs e
Corollarium
A D CLCIL.SILM IBC 1~. IBI
Ine sequitur A per e punctum quo B D diameter bissecacur, alia duearur, hy-
verbolis dccurrens in C _ F, _ ex C ex F, ordinarim ad diameerum BD pO-
nancur CHI, D P illas, vei etiam DLS BTP eAc incer se aequales: anifectum est ex.
eLAE F1 F
dlinacim ponacur lL. aelliameerum BD occur-
_ BHI, CIper conteractionem reliqua IIB.
igltur est TF ordinACM posita, prout occurrie
etac demonstrandum.
21
1et
priori demonctrarione. ui mrii
ingrecile:
PROPOSITIO V.
ciorolli go
2cerBI
Adem BoSFa Roura: Si B D vria diameeroruni bilecetur in C.) V. Jnv
Dicorectass pet C allaod petces in 
bitariam leCari.
Demon-