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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1130, page id 1815201908:1187
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QV ADRATVRA CIRCYEK
LAOPOSITIO XLIX
Esumplatigura propolicionis 47. lifuerint segmentorum axis AL,
LLBL, Subdivisiones Facex plures ac plures in inhnitum iuXTa Mentem
propolicionis 47. ac proinde plura semper ac plura reccangula inscripra
Fuerincparabola A a B, circum (cripea vero parabola ABE.
Dico nihilominus solidum quod producitur ex mutuo ZC OA,
C r EO Teomentorum lubalternorum duetu, maius esse solido quod se
ex omnibus rectangulis inseripris parabolae Aa B in omnia recrangula
conseripea parabola AB6.
Demonstratio.
DErEcietur eodem discurtu quopropolicio 48. Nam quo dilcursuillic Cx 46. Osen-
dimus solidum exseomentis PNKL, R P P. M, qux adiacent medio axis puncta
T in SCOMeNta RBOL, L DaM maius eAC solido quod hc ex rectanguliS RV, F X
in rectangula RV. I S, eodem quoque demonstrabimus ex 47. Colidum quod AE eK
sEGMENEIS NTDTR, RMFIF aequalirer a medioaxis puncto F remoris, in segmen-
ea IFBR, HICcoM, maius esse solido quod Hc ex rectangulis, Id, M X in rectangu.
Ia TO, MZ: _ Colidum quod signitur ex segmentis D eC I, s FFTO in segmenta
CxFI, ITOEO maius elesolido producto ex Cp, IIo in Ca, FIi. Focumigi
cur segmentum est C duccum in sermentum eorum C nZ maius solidumpro.
dueic quam omnia rectansula C P, Id, RV. I T. MX. HIo in omnia rectangula
C a TO, KL, L. S, A L. FLi. Duod erar demonstrandum.
LKOTOsITIO
Incpalaobraaea aeat de Mes AA B, ABC Ellatucom.
muniaxc  cto  paltes Al BL, In plurestemper ac plu-
res in infinicum parces xquales et x que mulcas, diuidancur, ducrisq. per
dinisionum punera parallelis lineis er, DF, ec. normalibus ad AB, in-
scribancurparabolae A a B, parabolae vero SB A cir cum scribanturrectan.
sula plura temper ac plura line terminio.
co