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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 3, page id 1047377675:0019
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=19
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 38 lines, status machine
# Lines: 38 recognised, mean confidence 0.85
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2
EC
10
Est
RBL exceNUM LECGTIK supra rectam RI maiorem eNse ex.
CENU OMMIAM LCCLAAU RFS. FF, CA, Emul suprA CurrAM RB.
producantur tangences AC, F F, ad proximas perpendi-
culares versus Kin C d L. Cx primo propoliros AC est maior
CVErA BC, FF MaIOE CUrVA FC, _E FIK MAIOT CUIEVA KF; e
ideo omnes simuIRII, FF, CA, Cune maiores incegra curra
KB: deinde ex secundo propolico BD, hoc est, RI minor cR
CurraBC; _ C C hOCCR, C A minor eA AECU FC; _E LF,
hoc eA, FF minor eAarCU R F; _ ideOOmnes KI) FL, CA.
limul sune minoresinteora curra RB; e ideo maior est ex-
CetuSreCarUM KHIB FF, C A, SuprA rectaS HI, FF, C A, quam
Lupra curram XB; (ed rectE FF, C A, sune communes urrique
rectarum summe; e idco excessus rectE KHI Cupra rectam RI
ek aequalis excesui lumma reCtarUM XHI, FF, CA. CuPEA
summam rectarum RI, FF, C A; qui demonstrarus est maior
excellu rectarum XII, FEs CA. Cupra curram RB, quod de-
monstrandum erot. Si vera curva fuerie conrexa ad rectam
Mes ve in secunda AgurA, X deDCE CNC pUNCtUM CUEVK a FC.
etaMP maxime remocum, de aliquoc demonstracionu ver.
ba Cunc mucanda, licur per (e incellis ee inductrius L. ector.
PROP. 2. YH FORPM A.
lecurra quaecunque 79C D simplex, Ccu non linuola,
(Ei enim Fueric sinuoles oporcet illam in plures simpli-
ces diuidere) super qua imaginetur superticies cylindrici
recti, cuius alcicudorecta X. 2 puncto quolibet curuxe nem
Deo in quamliber rectam nempe 26 demicratur recta per
pendicularis 93. e dueatur in eandem 26 recta 9B CUrVaM
perpendicularicer lecons in puncto 9. producarur rect a 38
in S, Uc 35 Anc aequalis recte 96, idem quoque suppONIEuF
tieri in omnibus punctis currxe 79CD, ita ve ex rectis in cur.
ram perpendicularibus per propria sua curre puncta ad re-
Atam 26 normalicer prorraetis consetur sparium RV d2a
CIEVA
1.