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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 458, page id 1815201908:0515
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18. huius.
acMomranaum.
huirs.
imiliter aBIL a Guas ALF.
CFI ixicur dimidium eAt eocius P F
eede hcte at dit
Aenr, erir AC in I e K, divila, vt
ti t auita cE iM C∞ HI: WditLa
La alurctula elt a C. ece
eR OPOSITIO CCXZ.
IIdem positis, penarur per B diameterL. NI.
Dico esse ve B ad BHI, (ic L. B ad BM.
Demonstratio.
Voniam A L est Contingens, L. B cA ad BMI, veb AM ad MC, hoc est F B
Lad BF. ICd ve F B ad BF, Sc C B cA ad BFT, igicur ve C B ad BF, ACL, B
eAt ad BM. Ouod erac demonstrandum.
PROPOSITTO. CCKKI.
AdeMMABEMECAgUTA, dUCAHEUTFECLX M C, MFT.
 Dico MD esse parallelogrammum.
Demonstratio.
S Sc enim ve HB ad BG, liCM B ad BL; Per PExcedenEem et permucan-
dove HB ad MB, sic CB ad B L: sunc aucem anguli ad B laceribus proportio-
halibus concenci xequales, criangula isitur MB FI, ETB L c Similia CunC: _C M FTd pa.
rallela EL: eodem modoh R FF producatur donec cum AD convenise, octendi-
cur CM aequidiltare ipsi DHI. pacalleloxrammum isicur est DM. Quodfuic de-
monctrandum.
PROPOSITIO CCXZII.
Ademmanence tgura, ducantur AB, BC.
Dicorriansulum AB C xqualc ese para llelOSFAMMONI D.
Demonstratio.
IStC DEM Clangulum criangulo AB M aequale. similicer crianioulum B FM
sequale BM C criansulo; isicur rocum criangulum P. M P cori criangulO ABC
CAxqualc. CA aucem F. M F criangulum duplum erianguli OMI FI, (quia balIS E F
ex 2rg. duplacestbaleos C FI.) isirur M D paralleloerammo xquale eAt criangulum ABC.
Ouodtuic demonstrandum.
eR OP OSITIO CCXXILI.
AdaM manente houras aemicratur ex D diameter DVI. (10
Dicolincas CI, FIV simul Sumpras, xquari rectae D NsdiC
394. hrvius.
E3
nei
Ex
pentis.
B0
Demonstratio.
iam AC, B O sectionemi cd.
recta F C a Gqualis cB
equidi
Demon.
( e i u    1  . p   .  . Au  .   A  u H .       M     titu   t          a   t put