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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1127, page id 1815201908:1184
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 30 lines, status machine
# Lines: 30 recognised, mean confidence 0.91
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QV ADRAFYRA CIRCYEI
eROPOSITIO XLV.
DOnantur super A B duo quadrata ABC, B AD, quibusinscripex due
R semiparabola AC C, BITD Situ Cubalterno circa communem axem
AB, e super A B diamerro Temicirculus describatur AF B.
Dico corpus quod producir parabola AC C dueta in parabola BHID,
aequari Lemicy lindro cuius balis est semicirculus A E. B, alrirudo AB.
DEmonstrationem dedimus libro de ductuplani in planum propolicione 143. illic
enim octensum est parabolas subalcerne policas, quarum communis axis est X
qualislaceri recto axeos producere solidum aeguale semicrlindro cuius basis eAtse-
nicirculus axe eanquam diamerro descriptus, alticudo vero iple axis; sed parabola-
rum AOC, BFFD quadracis inscripearum axis AB x quatur laceri recto aXc05,
aquod ordinarim pOSEa A D Sc aqualis ipR A. B. ergo solidum quod produCIEUE CK a 9. Parab.
ductumuruo parabolarum ACC, BITD aequacur Cemicrlindro super semicirculo
AF B in alcicudinc AB.
Verum cum hoc cheoremasieonum ex primariis huius operis, proximeque in AuaF
in circuli quadracuram: sic aurem demonstracio propolic. 1 a3. libri ductuum allaca
Forcasse srictior quam ve omnibus Pacistaciae: pleniorem huius vericaris demonstra.
cionem exhibebo propolicionibus aliquor sequencibus.
P R O POSITIO XLVI.
VIE AB axis parab olarum subalEerNE POLITATUM AKB, ABMI, _ axebi-
lectoinE, itemque AF, B F. bilectis C _ D, per diuitionum puncta
C, E, D ducantur recta ad axem normales, compleancurque rectangul a
tam C P, P. Q in scripea parabola AHB, quam C I, F. L. circum (cripea Pa-
rabolae ABM.
Dico Colida que OriunEUE ex TPHT In CENM; d exHOK in
FNOD, limul Cumpea maiorem molem exhibere quam Colida que hunE
ex ductu plani MNL in F C FP, e plani NOL in PE. D Q, simul
CumPEa.
Demor