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# Title: [Vera Circuli Et Hyperbolae Quadratura] Vera Circvli Et Hyperbolæ Quadratura (shelfmark Leibn. Marg. 98)
# Folio 71, page id 834940469:0155
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=834940469&page=155
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 33 lines, status machine
# Lines: 33 recognised, mean confidence 0.91
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DF esse aequalem rectangulo cuius baHS eA perimeter hgu.
rae AB e alcicudo circumferentia radii RC. manifectum est
Superticiem exlindri genici ex rotarione rectanguli IIK cir-
CaTIIegualem esse rectangulo cuins bahs est circumtereneia
radii IK de alcieudo CK vna cum IR, hoc esrectangulo cuius
Baliscircumferencia radii OL. _ alcirudo totus Agurae am-
Dicus HC, FCK .KI.F.TII, quod idem cst cum rectangulo
cuius balis est rectansuli ITK ambicus de alcieudo circumte-
rencia radiiOL; sed superheies crlindri geniti exrocario.
herectanguli HIK circa TII estad supertciem Colidi rorundi
geniti ex hgura AB rocatione circa DF in ratione compoli.
ea exproporeione ambitus AGUTX FIK ad am bIEUM AGUTa AB
s ex proporrione rectae OL ad rectam F. C. Peu circumterens nuius.
rix radii OL ad circumferenciam radii F C; atque rectangu.
lum cuius baHS est ambitus Aguex FTK e alticudo circumte.
rencia radii OL. Ccu superticies crlindri genici exrocacione
rectanguli HK cirCATII, elt ad rectangulum cuius baAS eA
ambicus Agurae AB e alcicudo circumterentia radii F C in
eadem ratione; de ideo superticies exlindri geriti ex rOtA-
eione rectanguli HIK circa CM est ad rectangulum, cuius balisi
estambicus Agura AB e alcirudo circumterenciaradii F C,
ve idem supersicies ad superticiem solidi rorundi geniti ex
rocacione Aigurae AB circa exem rotarionis D F; de proinde
Superticies Colidirorundi orri ex rotatione Agurae AB circa
DF aequalis es rectansulo cuius basis eAt ambirus Agura
AB e alticudo circumferencia radii P. C, quod demonstrare
oporcuie.
Non disimili Fere mechodo demonstratur haec propolicion
eciam si perimerer hsura non siE clausus.
PRO P. 37. E ZI EO R F M A.
Si cylindricus rectus secetur plano ad basem seminormali; truncus
inferior aequalis erit cylindrieo cuius basis eadem est cum cylin.
drice