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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 681, page id 1815201908:0738
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LOPOSITIO XII
medis 2.4. applicatur parabola
romprehentum a ipirali ex prima revolurione nata et prima linea
(Ab) quae principium ettreuolurionis, spacium cerria pats est primi
EPPLIC AYIO.
AOB prima voluta cuM Io circulo B FI, ex pTIIa recta A B; descri-
Dbacur aurem paraboda acM habens Al ac proinde cansene AB,
ultaque BC parallela axs tunse A C. Manifectum igirur est ex ijs que
diximulsr. _ 3. propolic. alem a paraBola Segmento AF. C, circulum
vero a criangulo AB C represencari.
clatelle parcem, cranculi ABC.
circuli.
Ii
DicoAF C scomentum parabole rer-
Demonstratio
ZIIcca DI D, iunzcCD, d _IC DF P4
ralletam dd BC, HOC eIt ad Al. PCF G. AF-
chi. de quad. parabol. D K CAt ad RF, ve A F
2d F C, hoces ve A D ad DB. Ouare cum AD
sIE ParIPE D B; CrIC _ DR ipARF. Ergoper
33. I. Conic. C Deansit parabolam in C: REqui
parabola A F C est duxe cerrix crianguli AD C
cuius duo laceracansime parabolam, (p ex pro-
Pol. 237. libri nostri de Parabola) ae proinde vna
cercia crianguli AB C, quod duplum est alce-
rius. Tgicur eriam haecnobilinim a spiralium pro-
prieras convenir parabola. Qund erac demon.
Arandum.
SITIO XII
LapptEL. B. A. dsb Parabota.
ppus 1. 4. Locctortum Machemati:
Cacum prop. 2l. acloccat ouolu,
quod secle Archimedes, torum spacium
cem ccu pe t. eaClen prur
piolpua Lcaca riemueute decenir
Spirale primum B C F AB cerriam esse par-
A per C delcripio circuloP C PI, spaciuM
pitale ta cclllata CC Pallelateclo
1to t2C0
681
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