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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 468, page id 1815201908:0525
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e A R ABO
Corollarium.
AdeM POLTRABUFa SequitIF eNe vEC F parallelogrammum ad para lleloorammum
IE, hc A C, B parabolam ad pacabolam AD C: icem convexum AHB F ad
convexum ABC F.
A C: ducaNEUTGUCCMaLIIM BF, CD.
PROPOSITIO CCXLIV
DArabolam ABC cuius diamerer A C Secen vecun que linCX AP,
Dico spacium parabolicum F. BL. D, quadruplum esse spacii C ABC
Demonstratio.
Voniami parabola D A BC quadrupla est a segmenti ABC
CF AB parabeta qladrupla segmeci A B, parabOIAD ABC
est ad leomencum ABC re F. A B parabola ad segmencum AB.
isicur cum parabola D ABC ad ABC, corum ad eocum siE
VE B AB ablacum ad ablacum AB, eri religuu E BCD, 2d
reliquum AC. B A, bE D ABC corum ad cocum ABC: quare
EBCD figura, quadrupla est figurx lineis AC, AB d Para.
bolica BC concelsea. Quoderur demonstrandum.
P R OPOSTTIO CCXLV.
TOntingat AB C parabolam liIed quae cunque AD conveniens cum
mecris quibuluis DC, lBIn D _ F. IUNGANEUEGUE AF, AC.
Dico concauum E. DCGF duplum
CNTEpaTtIS AFC C, linCIS AF, AC COn
TCHEX.
Demonstratio.
Oncauum ABCD A b duplum est Para-
bolX ABC: _ concauUM AB Fi F A du-
plum cs seomenti ABF; igitur residuum
F. DCCF duplum cAt rCsdui AF C C A.
Ouodcrac demonstrandum.
eROPOSITIO CCXLVL.
DArabolam AB C suBendar linca AC, qua divila in D _E F, vi
AD, AF, a C commue propales sinE, erigantur diametri DB.
L. I, C F. e peL DLLLPHHCLA Cx A RECFR PONANEUE AG, A F SCCANECS C F
diametrum in F _ C7.
Dico F LCC ad spatium quadrilarerum Bl eriplicatam habere ratio-
nem AC ad AF.
lincis AB, AC et parabolica BC concenti.
demonstratio.
EX COrO
b242. Bu-
Voniam AD, A F, AC Bonuneur continue proportionales, NE C A ad FA,
cI. DCprO. LACC CF, 2d F. D. Ccd ve CF ad B D, liCC elt ad 6f; igieur ve C A2d A
cressionibus. (C C C+ 2d CrF: visc CaI CA C de C HF ATAHSMIAII, CMM CL uu
ADC da IC LA ad L IC L ad HII: est aurem  AF
. lale itlolta