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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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b. titim
VN CYL A C. Y LLHDRIC A.
Demonstratio.
Demonstracum enim cs rectangulum sub DC et
DF, aequale esse superticici vngulari ABD. DC-
monstracum icem est rectangulum lubDC. _ P. F, X
quari luperticici ATM B. oAtensum b quoque cA rectan.
sulum. DC, FC aequari superticiei IMNR, e re-
ctangului DC, C HIxequale exictere superticici RNOL.
rectangulum denique super D C e FTC, xquale esse
superticici CL O. Pacerisicur coram vngulx superticiem
diuitam eAC sccundum parces diameeri D C, cum qua-
deacum DC. sc divisum in rectansula qua clorciuneuT
andem racionem quam parres linCx DC.
DeOsiF1O. Lt
IYlindrusrectus A B D L, CuraS AICICHdO PAF
ctionem ongularem ABCD.
Oco luperticiem ingularem ad cyliiaau, cam obtinereracionem,
quam diameret clculi ad perimerrum.
Demonstratio.
no exhibe
Alic diamerro basis AD, Sccetur per AD pla-
Vpersicies cylindrirecti AF aequalis est rectangulo concento sub BC, hoc eA
DDA, e sub coroperimetro circuli ABD: quod eodem fere discurtu probabitur.
quo demonstrauic Archimedes criangulum cujus alcicudo est semidiamerer, balisre.
ro, circumferencia, aquari circulo. se d quadeatum D A est ad rectangulum conten-
cum (ub D A, ex perimetro circuli, ve D A est ad perimerrum circuli. Fr∞o e qu2-
dracum D A, hoc cs per 15. curua superticies rnigulae A CD, est ad crlindri su-
perticiem ve diameter D A est ad perimeerum circuli A B D. Ouod erac demon-
Bcanidum.
PROEOSIFIO LIV.
Noula ABCD culus alticudo BC, lecerur plano per AD ee quod-
idet fuliocuu e latbla
eotel