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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 215, page id 1815201908:0272
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HC.
161
Otit
est
t
CIR CV V Y Si
propolicionis Archimedex vericacem de comparacione circulladrectonsulum a X
quale alirer hinc porse demonstrari.
PRODOSEDIO ZO.
TatHeCtO CtCai A BC insistac ad rectos angulos recta B D, iungacut-
Dicorectansulum ABD, ad A C D rectangulum rriplicaram eius Ha-
bererationem, quam obcinet linca DB, 2d DC lincam.
Demonstratio.
Via DB normalis est ad dlame.
Ltrum AC recta CB, BD, B A,
icem CB, CD, C A per clemenca
in concinua lune analogia, onde cum
prima BC verique seriei communis lE,
eric 2 eacIO AC ad AB cerrix ad
cerriam duplicata eius quam habet secunda CD; ad D B SccM LCAFAEIOFC, sionibne
Etanguli AB D, ad rectangulum AC D composica cA ex ratione AC ad AB,
hoc est duplicata D C, ad DB, _ exrarione D C, ad DB, parecigicur rationem
ABD rectonguli ad rectangulum ACD; triplicatam cAC linex D C ad DB. Juod
fuir demonstrandum:
eR OP OSITIO ZCI.
Emicirculo ABC criangulum inscribatur AB C, ècuius verrice ad
balim demissa Bcnormalis BD.
Dico rectangulum D AB, ad DC B rectangulum, criplicatam rario-
nem habere eius, quam linea AB ad BC.
Demonstratio.
um enim BD normalis sic 2d dia-
WMCEEUM A C, CFUnE deMUOETeS AC;
AB, AD, _ AC, CB, CD in conci-
nuaca ratione: quia vero communem ha-
benc primam AC, crie AB ad DC, in
riplicata rarione AB ad BC; scdD AB
ectangulum ad D CB rectanoulum ta-
ionem haber composiram exrarione D A ad D C, id est duplicata AB ad BC e
X AB ad B C, isicur rectangulum D AB, ad V C B eriplicatam habet rarionem
LB ad BC. Ouoderat demonstrandum.
PROPOSITIO XCII.
tmicirculi ABC diametto A C in F e Foccutamnorles l 13
O, TaHSanturque AB, AD
Sico L. AB rectangulum, ad F AD rectangulum, rarionet abele
ciplicatam rectae AB, ad AD.
127. Eib
deproeres
que DC.
Demon