# Leibniz Legible — https://leibnizlegible.com
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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 27, page id 1047377675:0043
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=43
# Source image: https://digitale-sammlungen.gwlb.de/content/1047377675/jpgs/default/00000043.jpg
# 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.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

IOOratAMMa ABGO, DEHS, _ prOduCANEur reCtX AO, NS, UE
concurrane in 1. dicocraperium AD F. B maius essemixeili-
nEOADLO. ducatur HIKEparallela ec ae qualisrectae AB; m2-
niFeCUM CA EFAPCZIUM ADEB eNC Xquale ErAPCZIO ADMR
IECM _E EFADEZIUm A D MR maius cNCErAPCZIO AD L O, X
ideo mulcomaius mixtilineo ADL. O; PATeF ergO ProPOlI-
Tum nemDCErEDeZIUM ADEB maius ese mixcilineo ADL. O.
PEODUCLEUFRECta D C in C: dicorectilineum ABF Id C
minus esemixeilineo A D SO. ducacur recta C F. parallela
rectis AB, 1DE, _ C R parallela rectis AO. DS: PAFCEFrapC
Zium ABF C esse aequale craperio AC R Q d craperium
CFFD eRe aequale trapezioC BL I; ee proinde rectilineum
ABEDC aequale eAt rectilinCO ACDLIRC, quod minus cA
rectilineo ACDSO; _ ideo rectilinCUm ABELC. mulcomi
nus estmixtilineo ABSC qua demonstranda erant.
P R O P. FT. Y H F O R P M A.
Ie spacium mixeilineum quodcunque ABKI comprehen
lum a curva BR, recta AI e duabus rectis parallelis
BA: X I; SEque Curra M Y calisnacurX, ve (Cumpeo in curra
Bk quoliber puncto C de ex eo ducta recta C. F purallela rc.
etae AB, _ reCtA C Z CUIFVAM BR CONEINOCNEC FeFMINATA A FC-
Eta AB si opus ect, producta in L.) recta PZ semper (ic ae qui-
lis recta CS ParaIIelX reCtE A Z _ Terminaca d CurU. Y M.
dico mixcilineum BRM Y, comprehensum e curris BK, i Y.
_ rectis BY, KEM, rectae AZ Parallelis, elle aequale mixcili-
neoB AIK. Si non (unc aequalia; sic eorum differencia X; _
dividacur currilincum BRM Y a FOFreCtIS CS, CFP, KM, rectX
BY parallelis, re (ductis rectis OM, IN, FR, Y V. paralle.
lis rectae AB) omnia parallellogramma O N, O Z, IV, limul
minora line quam X, hoc enim hieri porest ab indetinico p2-
rallelarum numero. ducantur subcendences recta BC. C C,
vk, e cansenres in punctis B, C, Cn R, BD, DF, F L, L. K: ma-
2
nitectum