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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 967, page id 1815201908:1024
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V N CV L A CYLAHDRIC A.
Demonstratio.
FIEISIS DEILCS _E HETTO, inscribaneur
prramides super eadem basi FT C, crune
txpreamides incer se aequales, cum alcicudi-
nes neaquales; similicer X quabanEUE e py-
ramides, qua in Frustis ITTOC _ HTTOL,
Cuper eadem bali constiruentur, cum alcicudi-
nes carum etiam sine aequales, e quia omnes
similicer figurx inlcribenda Fructo IIOTD,
aequales crune fguris que eadem constru-
ctione inscribentur Frulto HTOK, CruNE
Frusta illa equalia. 2 pari modo quia onnes
quoque figura tructis TIICC, TITOT in-
Scribende Fucura. sinc aequales perpetuo, ct-
jam hxc Frusta aequalia CruIHE; CunEigiEVE qua-
cuor illae parces Colde aquales incer le, ac
proinde solidum ROL aequatur Colido
DOCTV ITC: ostensum quoque est
DTHLC Xquari DHTK. Pgicur communi
addIEODEBL ID, CTIEDKIL B aquale
DTCB: addIcisergO KGP, DGCTDTI.
qua ance ostendi esse ae qualia, torum D C CB aequale erit cori DR C L. B. Ouod.
fuic demonctrandum.
PROPOSIFTO AMII.
Aca BE vnga BD AC, in cuius bali de Vatos diametrum AB, X-
Aquidistet CF, qua bilecta in C, per C _ axem cstua ducatur vlg-
num taciens in cflindri luperticie sectionem C D. lumpro deinde in C D
puncto aliquo R, perillud sccundum AB diamerrum hac ingulatisle-
ctio BL. KM a. Denique per rectam FP. asC planuu ani aquidistans
FLHIME,
Dico parremrnoularem F I. LM L
ad vngularem partem FTTDIF eam
habererationem quam haberrecta C. H
ad rectam CD.
Demonstratio.
cam habere rarionem quam habce. CD ad
CK: eodem aurem discurtu octendi porest
vngUIA BD A, PaTECM BFFTTF. A, ad paF-
EEIM BFLME A vngula BR A, candem 
habere rationem quam FFT ad FL, hoC CA
CD ad CR. isicur relidua duo F HD TF,
FL KM F. eandem habene racionem, quam
CD ad CR. Duod tuic demonstrandum.
Corollarium.
Vmisicur per z. huius etiam eorae rngula
 B K A, BD A cacionem candem hab CanE
quam recte CR, C D, Sequitur vngulAS FOEAS
lesmencis eAle proporrionales.
967
b24. lovius.
Scenim ostensum c solidam magnicudinem
Longularem BD A C ad rngulan BK AC
a