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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 708, page id 1815201908:0765
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VCTVS DLA
Praerex balim quadrataM, BIG L. L. DBC Planx lunc d criangulares ad punerum
908
erac demontrau.
C concurrences, unde de lxurapyramidalis olt, gux balim habet quadracam. Ouod
1.dofon.
DSIxIO IV.
ducic quae balim habet rrians atalem.
Rianculum rectangulum in se ductum subalcerne, pyramidem pro
Demonstratio.
Riangulum rectangulum AB C, duccun
in se lubalcerne, id est in criangulu BCD.
figurami producat L BC D. dico illam esse
prramidalem, gua bauim habeceriangula-
rem. erisacur ex B linca L. B, recra ad plg-
num ABC: ee AB linex xgualis: ponan-
curque quoruis F. F C+ ParaIlelx AB. linea
P F ducra in FO recrangulum producie
EIF F C, rectum  ad planum B CD; quare
FF, FIG lincx quoque rccEX lunE, ad
planum BCD, _ LB lince parallela.
quia veco LB, FF aequales sune re-
Cris AB, E F; ve AB est ad FF, id eAt BC
ad F C, SCF B est ad R F; in direccum ixi
THT SUNE L. F, C, _ L BC superticies plana
est de criangularis cuius lacera BI. _ CL.
concurrune in L. Smilicer ostendetur, L, H.
D puncca in dircerum eNe et L BD Superh.
eiem ese planam ec criangularem desinen-
cem in L: BE quia LF C, L FTD linca rC
cex sunc e P. H aquidiltar FC, adeoque
 CD, FCCEX E FI, C. D quoque in codem
suncplano _ CL D criangulare planum de.
snens in L. quare cum illa superhcieserian.
criansularem. Priangulum isitur rechlgulum duccum in se lubalcerne, de c. Quod
Riangulum reclatigulum ductuminse
lubalcerne aequalc est dimidio prra-
midis qua resultar et ductu ciusdem trian-
Demonstrario.
Tcrriangulum AB C. duccum in BC D crian
sullin Ceiplumce DC B B prramis orca ex ducu
AB C in se lubalcetne, dico prramide AFF BC
duplam esse pyramidis CB F. D; planum ABC
duccum in se B exhibee prramidem, quadracam
AB E F basim habencem. quia vero angulus
ABC reccus assumitur, eric BC alcicudo prra
midis ex criansulo ABC in se ducco extribicat
dueta
eral demonctrandum.
gulares sinc e concurrenc esin L. prramis cA Aixura L. B C D, habens balim BCD
61. Feninus.
PROPOSITIO. V.
suli in le
culum xquale d Mle, subalcerne policum:
sICq; F F B C Apyramis Orta ex duCtU A B C crian