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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1004, page id 1815201908:1061
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1004
YNCVEA CYEFNDRICA.
corpora rnoulas continentis. se d rario pyramidum est composira ex ratione quadra-
si baseos ad quadratum baseos, hoc est ex duplicata racione diamerri ad diamerrum,
e ex racione Cemidiameeri ad lemidiamerrum, quae cadem est cum racione diamierri
ad diametrum, ac proinde criplicata est raeionis diamerri ad diametrum. ergo eriam
corpora quxe rugulas continenelunc incriplicata ratione diametrorum balium rneu
larium. quod demonstrare oporrult.
PROPO5
5
Ilindro parabolico recto CD AF. L
E conseriprum lic prilma, cuius late
BA, BC, Fe;tE cansanc pacabolas
quae sunebales exlindri.
Dicopyramidem cuius balisrectansu-
lum Cub. C A, ordinatim polica ee dupla
alticudinis cxlindei parabolici, alcicudo
vero axisiple HID, cylindro parabolico
elle a qualo
Smonstratio.
CVmatur AK dupla ipbuS A E, quae es alciri-
do cylindridaci. Fst demonstracum libro de
parabola a criangulum ABC CACIC(quiALECRUME
parabole AD. C. rudcociam prilma AC B F F
Cst lelquialceru cylindri parabolici ADCIOF.
Posico deinde plano per C A de F: exic pri(ML
ACBF P. Cs criplum b prramidis cuius bass
AC B, verrex B, ac proindo sesquialcerum que
que cs partis reliqua, qua eAtporamis balum
habens C AR G, verricem F. CrSO pYFAHIS
C AF C, F, aquatur cylindro parabolico. sed
Pyramidis C A F. Cs) F, alcicudo est HI D B, quae
12. Parab. cdupla est axeos parabolae HD. ergo prramis C A F C F, daequalis est pyramidi,
19. duodec. cuius alcirudo sC F(D dimidia prioris alcicudinis II B. balis vero rectansulum C AK
quod ex constructione duplum est baleos prioris C A F G. Acgniprramis, cuius al-
eicudo est FTD, balis vero rectangulum C A. K CC illa ipla prramis de, qu2 agic a Per-
eio, cuius nimicum alcicudo lie axis IPD, balis vero rectangulum, quod (uB CA ordi-
nacim polica ex dupla alcicudinis exlindei parabolici concinerur. Manifecta igirur eAt
vericas Theorematis.
D.R O DO S P, T, IO L ∞X V 1.)2r il 53
VTcongula KHTI à cylindro recto abscilta, alcicudinem habens parem
A diamerro batis KI, quam eingane plana cansenria l A. D, B AC B.
C. e se e  soeni noe vescluil sl 203n seradila
Dicocorpusrnoulam includens, quod planis cansenribus de duobus
polrgonis, lemicirculum IENLI, _e semielliplim IFT K ambiencibus con-
cinecur, mulctarum duabus laceralibus pycamidibus hoc est solidum
E L. AD FF, aquale esterneula
211 5t.) cl e
Demor: