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# Title: [Geometriae Pars Universalis, Inserviens Quantitatum Curvarum transmutationi & mensurae] Geometriæ Pars Vniversalis, Inserviens Quantitatum Curvarum transmutationi & mensuræ (shelfmark Ms IV, 377a)
# Folio 7, page id 1047377675:0023
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=23
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 35 lines, status machine
# Lines: 35 recognised, mean confidence 0.90
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proindemaior eA differenria ineer huec rectangulas qua incer
superticiem cylindricam de mixcilineum; ledrectangulorum
differentia est rectangulum X in difterentium rectarum 7A.
q;ectaucem differencia rectarum  A, 7v. minor recta B Cx
Coppolitione; _ ideo differentin inter rectangula X in FC,
B9, A7, Simul, d X in FC, B9, V7, Simul, minor es quancica-
ee an nempetacro ab X in B, hoc es ex policione differentia
incer superticiem cylindricam de mixtilineum, quod est ab.
Curdum, ostensa enim est maior, superticiesisirur crlindrica
e mixcilineum (une aequalia, quod demonstrandum erat.
Duod S curus 7D non fuerie simplex sed sinvolas diriden.
da est in plures simplices, de demonstratio in rnaquaque
Peorum insticuenda:
Sivero tansens7 A Fuerie perpendicularis ad recram 78,
mixcilineum PHL. EIsE exrendecur in infinicum ad parres P:
hoccamen non obstance; dico adhuc mixeilineum PNL. IIS2
equale cse superkicici crlindrici recti super curra 79 Cil
cuius alcirudo X. Si non lunt aequalia, sic (si heri pocele)
mixcilincum maius (uperhcie, _ FCCEA NZ FCCEA HS P2PaI
lelta ablcindatur mixtilineum NLFIsS aequale superticiei
super curua gCD, hoc enim absque dubio heriporelt: co-
demque modo, quo ances demonseratur miscilineu HL. HIdS
aequale esse superticiei super gC. D; (unc ergo aequales, su-
perficies cxlindricirecricuius alcicudoZ, luper curvis gC V,
79C D, quod elc absurdum; mixcilineum erso PNL. HS2nOn
elcmaius dicta superticie cxlindrica: lic (si heri POcelE) mi-
nus; e abscindatur oD curva, ica uc superticies exlindrici
recti super gD exilcens, aequalis Eac mixtilineo PNLHS2,
ee ducacur 3 9 N reccae H d paralleIla: dCIOBSETAEUF VEANEC
superticiem cylindrici recti superoD existenrem, aequalem
esse mixrilineo HLHB3; sed ex suppolirione eadem lupeck.
cies cylindrici rectia qualis ele mixcilinEO PNLHdZ; mixri
InERErBOPHLHSES NLHS3, suncinter se aequalia, quod elE
ablurdum; ec ideo mixtilineum non ese minus superticier
sCd