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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1131, page id 1815201908:1188
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er AD R AEVR A CTRCVEI
Dico Corpus genicum ex ddctumuruo parabolarum lubalternarum
maius cse londoeasorcsato Parallelepipedorum quod producicur ex
rectangulis omnibus C p, l8, _cc. in scripeis parabola An B, ductis in FC-
ctangula omnia C a, IO, ec. parabolx ABC circum (cripta.
Demonstratio.
Scensum est in praecedenci segmentum Ce s2O in sesmentum C X Z0, produ-
ceremius solium quam omnia rectangula C D Id, eec. in omnia rectangula
Ca, I0, _C. Acqui parabolacora AN B ducta in subalcernam eoram EB A, maius
corpus efficie quam seomencum eC B na in seomencum C = ZB. Eroo parabola
Ax B in parabolam EB A maius Colidum signit aspcegaco para Ilelepipedorum pro-
ducto ex omnibus rectangulis C D, Id, _c. in scripeis parabolae An B, in rectansu-
la omnia C a, IO, _ c. Parabolx CB A confcripea. Duod crac propolicum.
renio candem ad demonstrationem Theoremaris supra proposici.
PR OP OSTTIO LI.
Vincparabole (ubalcerna ADC, F C A binis inscripex quadratis circa
A COmmunEM aXeM AC, sivc (quod in idem recidit, ve in propol. 45.
ostentum est) quarum aris A C laceri recro axeos sic aequalis: S (uper A C
diamerro describatur lemicirculus AB C, quem eorum inera parabolas
cadere patec ex 126. de parabola.
Dicocorpus produccum ex alccupatabole ABC in lubalcernam pa-
rabolam L C H, a Guals Leicylindro, cuius balis est Semicirculus ABC,
alcirudo aurem axis parabolarum AC.
Demonstratio.
123I
laequalia non sunt IIIa corpora, exie exlindrus corpore parabolico maios aul ht
nor. Ponatur primo exlindrus esse maior corpore parabonCo GuAHCTALO AIIGV2
C. sececur axis AC bitariam; ex bina axeosscementa in cor ex aeque mulcas aequa
lesparces subdinidantur in punctis F, F, ve dudtis per F parallelis rectis BL, HOI-
malibus ad AC. complecilque rectangulis F I, rectangula F B L ducta in alciru-
dinem cplindri AC. Cxlindro inscribane axcrepacum parallelepipedorum haben. 2 Pait
 rectanea CC  chrnbenoq
ips0
Au  i GIILIIIMI