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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 71, page id 1047377675:0087
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 49 lines, status machine
# Lines: 49 recognised, mean confidence 0.81
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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DF ese aequalem rectangulo cuius balis es perimerer hquu
xa AB e alricudo circumferencia radii P C. manifestum eAt
Supertciem erlinari geniti ex roratione rectanguli FTK cir-
CaIl equalem ese rectanculo cains balis est circumterentia
xadii IK _ alcicudo CKEuna cum IR, hoc es rectangulo cuius
balis circumferentia radii OL e alcicudoeotus higurae am-
Bicus HIO,F CKKI III, quod idem est cum rectangulo
cuius balis est rectanguli IIK ambicus ee alcieudo circumte.
rencia radii OL: sed superticies cylindri geniei exrotacio.
ne rectanouli AIK circaFII estad superticiem Colidi rocundi
genici ex figurae AB rorarione circa DF inrarione composi.
ea exproporrione ambitus tgura FIK ad ambicum Agurae AB
ec exproportione rectae OL. ad rectam F C. seu circumteren nuiusi
rix radii OI ad circumterenciam radii F C; aeque rectanou.
lum cuius Ba(S eR am BiEuS AgUIEX FTK X altirudo circumte.
rentia radii OL, Seu superficies crlinari geniei ex rocacione
rectanguli HR circaHII, eAt ad rectangulum cuias DalIS CA
ambicus sgurae AB e alcieudo circumterentia radii F C in
eadem ratione; de ideo superticies cxlindri geniei ex rota.
eione restanguli FIK circa HII est ad rectangulum, cuius balis
ectambicus foura AB de alticudo circumterentiaradii P C
ve idem laperheies ad superticiem solidi rorundi geniri ex
xocacione higurae AB circa axem roracionis D F; X proinde
Superticies Colidirorundi orri ex rocarione Rourx AB circa
DE aequalis est rectangulo cuius balis est ambitus Agura
AB de altirudo circumterencia radii P C, quod demonstrare
Oporruit.
Non dissimili fere merhodo demonstratur haec propolicio
eciam si perimerer hgura non sic clausus.
P kD1. 3).  HI EOR F M a.
Si cylinarieus rectus secetur plano ad basem seminormali: truncus
inferior aequalis erit cylindrico cuius basis eadem est cum cylin
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