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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 102, page id 1047377675:0118
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=118
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 34 lines, status machine
# Lines: 34 recognised, mean confidence 0.88
# 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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# After the first blank line: the recognised lines in reading order, one per line.

29
O2
CYI= FY2XND; e proinde pohrea P. Y prima de C, Y EeCuN:
das erie NO quarea concinue proportionalium, et ideo Agu
eaDOT eA ad rectanoulum DV, ve conois parabolica (cuius
basis est circulus BC2O) ad cytindricum parabolicum ille
conoidi circum (criptum, cumque dentur proporcio conoii
dis parabolicae ad cxlindricum sibi circumscriprum et re-
ctangusum D V, dabitur quoque houra DOT. e ideopun-
ctum quoque Z; de ideo dacur in lemicylindribase eius cen
erum aequilibriis de proinde semicylindri cenerum grauicaris
eric in data perpendiculari ad balem c centro aequilibrii ex
cicaca, atque idem gravicatis cenrrum est in rect a O a ducta
inter punctu e a mediun punctum rectae A B ex punCtO B
buins, bdsBC. perpendicularis, suppolica nempe cylindrum ese
seaum a plario baseos planum in rect a PO secaDEC; AEigIEUK
DERC ad CZ ica Da ad as, erit dlemicylindricenerum graui,
catis, quod inveniendum erat.
In huins 62 docebimus aliam mechodum inveniendi pro;
DOrTIONEM INEEF DV _DOT.
PROP. 54. ZFI FORF M A.
 Se paralelOgTaMUM ABIK, AEquE curvA ACI calis Na-
curX, Ve (duca recta quacunque DF Parallela et ae quala
rectae AB CurVam sECANEC in C) racio AB ad FC SC mulcipli
caca racionis A K ad A L inratione P ad . dico parallelo
Bramum ABIK eNC aa SgurAM ACIKVEP it Qad O. produ
tacur reCta IB in C RE IUASATUF CUrUA A HI C caLIS NATUTK, VE
ductarceto CF tangenec curuam AC I in quolibee puncto
C e ductis, parallelis FC, FH) recta C HIlic aequolis de pa-
ralleta rectae FF: manitestum est ex huius 7 rectam AL ad F FD
Teu LC adHC esse vEP ad O cum que hoc lemper AaE, CuI
dens elt Aguram AC IB esse ad Fcuram AC IC TIVC P 2d3
aeque ex huius 12 Agura ACIOHI CA ae qualiS ABUTX ACIR3
e ideorsura AC IB est ad Aguram ACIK vE P ad C de com