# 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 19, page id 1047377675:0035
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=35
# Source image: https://digitale-sammlungen.gwlb.de/content/1047377675/jpgs/default/00000035.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 recognised, mean confidence 0.85
# 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.

la
sid
2M
10
Ast
mixtilineo IDEL, sed de maius est, quod est absurdum; d
proinde recta RC incra curram A O non cadic versus verri
cem: S heripoces, cadarrecta C Kintra curram vertus ba-
lem reliquis se habencibus ur inpriore politione; cricqueuE
IK ad D E ica mixcilineum I A F. L ad mixrilineUm D ALF,
aC IK ad D E maiorem haberrarionem quam ad Da; e ideo
mixcilineum I A FL. ad mixcilincum D A L. F, maiorem ha-
bec racionem quam IK ad Da Peu IC ad D C: e ioitur mix-
cilineum IA F I. ad mixcilincum D AL I maiorem habce
rationem quam rectangulum 12. ad rectangulum DI, de
invertendo, per convertionem racionis e rurtus inver-
cendo, mixcilineum IA F L ad mixrilineUm IDFL maiorem
haberracionem quam rectanguium IZ. ad rectangulum IX2
de permutando mixcilineum I AF L ad rectangulum IZ. ma-
iorem habet racionem quam mixtilineum IDFL ad re
ctangulum IX, cumque mixcilireum IA F L SC aequole re-
ctansulo IZ. eric rectangulum IX maius quam mixcilineum
IBFL, Ced _ minus est, quod cs absurdum: non cadic erso
reCCA C K inera curram A D verlusbalem; e ideoreceaHC
Curram A G ranSIE In PUnCEOK. rCCTE CKGF perpendicularis
RCCEAKEECCCA AO OccurrenS in T; manifeltum cAClCAC ad
CXUCIKadRP; acque C TCK ad C R urMII ad NI, quoniam
rectae lI. IM. IL, eficiunt criangulum reccangulum limile
eriansulo C LI, cuius lacera IM, INi, Cunc homolosa laceri-
buSC. L, C. R; de proinde ue IK ad R Iica lM ad LN; cumque
hoc eodem modo hiac in omnibus punctis curvae A CB, mani-
Feltum est exhuius 2recram AO eNC ad CuErAM A G VErC
ccungulum OB adhguram ABSO, quod demonstrare OpOE-
Cltbo
S C H OL TV M.
Vius proposicionis invertum Facile quoque demon.
Lacur; nempe, lirecta AO sic ad curram A Dvere
ud OB ad tisuram ABS O, irem si curra A P calis
 2
si