# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/834940469:0135
# Permalink to this reading: https://leibnizlegible.com/page/834940469:0135?run=74
# Title: [Vera Circuli Et Hyperbolae Quadratura] Vera Circvli Et Hyperbolæ Quadratura (shelfmark Leibn. Marg. 98)
# Folio 51, page id 834940469:0135
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=834940469&page=135
# Source image: https://digitale-sammlungen.gwlb.de/content/834940469/jpgs/default/00000135.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 34 lines, status machine
# Lines: 34 recognised, mean confidence 0.92
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

PKOP. 24 YHEOREMA.
quae in antecedente; superficies trunci erit ad super
ficiem solidirorundi orri ex ejus base rotata circa communem se-
ctionem baseos (siopus est) producta  plani secantis, ut altitu-
do cylinarici ad circumferentiam circuli cuius (emidiameter est
radius rotationis.
sura e praeparatio uint cadem sicur in ancecedentes di
co superticiem crunciR DDC esse ad superticiem colide
rorundi orci ex rOtAEIOnC AGUTR DE FC CirCa IK axeM FOTa
cionis, re OP alcicudo crlindrici ad circumterentiam circuli
cuius semidiameter estradius rorationis L. P. in anceceden-
te demonstracum est OP esse 2d circumferentiom circuli cu-
Ius CemidiAecer PL., VE HIE ad circum ferenciam circuli cu-
jus lemidiameter F V: acque haec proporrio codem modo
demonstratur de omnibus rectis in superhcierrunciR aDC
ad basem BE FC perpendicularibus, ad omnes circumteren
cias circulorum ab eorum punctis intimis in circumroration
ne descriptas; atque ex omnibus illis rectis condatur ipla su-
perhcies crunci, de ex omnibus circumferenciis circulorum
ab intimis rectorum punctis seu a baseos ambieu descripeis.
consatur superticies Colidi rocundi orri ex rotatione balcos
circaaxem lK; ee ideo verna encccedencium ad rnam con-
sequentium nempe O P alcieudo cxlindrici ad circumteren-
tium circuli cuius semediamerer elt L. P radiusrocationis, ica
omnes anrecedentes, hoc est, lupertcies trunci RODC, ad
omnes conlequenres, hoc est, superficiem solidi rocundi or-
ti exrotatione baseos DFFC circa uxemrorationis IKC, quod
erac demonstrandum. Hoc eriam cheorema demonttrarur
eodem modo decrunco superiore si Rgura A B concipiAEVE
rotaricirea rectam MN.
Pater ex demonstracione superticiem rrunci R OD C de
Cuxerticiem Colidirocundi orri ex rocarione baleOS DEPL
CITCa
Eildem postis