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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 52, page id 1047377675:0068
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
# Lines: 37 recognised, mean confidence 0.86
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circa axen Locationis IK. esse guancirares magnicudine d
Grauicare analogas, quoniam eadem proporcio quae demon
hracur esse inter rocas, eodem modo demonstraeur esse in
cer partes carum proportionales.
e A O P. 25.  _ F O R F M A.
Eisdem politis, supponendo anculum inclinationis; Plani secantit
cum base cylindrici (sopus est) producta, esse semirectum: Dica
quadratum semidiametri circuli aequalis superticiei (olidi rotun
di duplum esse superficiei trunci.
Sc enim ex praecedente, re alcicudo cylindrici ad circu-
a Ferenciam circuli cuius Cemidiamecer eA radius rOcan
cionis, ita superhcies crunci ad superticiem Polidi rocundi s
in hoc aurem casu, quando angulus inclinarionis eR Pemire
aus, altirudo cylindrici es aequalis radio rocarionisi d ideo
in nostro casu; re lemidiamerer ad sui circumferentiam, ica
superficies erunci ad superficiem Colidi rorundis ve AUFeM
Temidiamecer ad circumferenciam ica semistis quadrari se-
midiameeri ad circulum; de ideo re lemistis quadrari semi
diameeri ad circulum, ita superticieserunei ad superhciem
Folidi rocundi; e convercendo e permutando, circulus eAt
ad superficiem Colidi rocundi ve semissis quadraei semidi-
mecri ad superticiem erunci; se d circulus supponitur xqua
lis superticiei solidi rocundis de isicur Temistis quadrari lemi
diameeri illius circuli aequalis elt superticicitrunci; et ideo
quadracum Pemidiametri est duplum luperticiei eruei, quod
demonstranaum CraE.
Duxe praecedenres propolitiones eodem prorsus modo
demonstraneur de superhciebus rocundis genicis exrocus
tione rnius vel plurium linearum quarumcunque sive recta
rum, curuarum vel mixearum, Aguram non claudentium:
semper enim ad superficies exlindrisirecti sup er linea vel li
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