# 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 115, page id 1047377675:0131
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=131
# Source image: https://digitale-sammlungen.gwlb.de/content/1047377675/jpgs/default/00000131.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 27 lines, status machine
# Lines: 27 recognised, mean confidence 0.80
# 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.

qu
e
edt
1
Dt
Eccurrae cycloidis primaria semilts C BAeiuS BaHSCC; avitu du
acirculus
genitor AF. C: basem tangens in puncto C, a
diameero CA. dico curram C BA duplam eNC reCtR A C. RIC
AILC quadracum, SiEque Agura NACLN calis naturE, ve
(ducta recta quacunque PM parallela rectae AI) rario AI
vel AC ad FM sic Cub duplicata racionis AF. ad A C: manife.
PRO P. 63. Y E EO R F M A.
RuM eA ex huius 59 Fguram inAnicam NACL. N esse duplam
quadrati AIL.C. per Ldiamerri A C punctum quodlibet du-
Cacur BM rectE AL Parallela Cyeloidi _ CurVX L N OCCUrrCNS
in punctis B, M. Secans circulum de rectam IL. ve in hgura;iun-
DanEuF recta A E, F C, d illis parallela DB, BH: ex huius8
Patet BD rangere cycloidem in puncto B de BMI contingenci
esse perpendicularem. nE BF adBIT ItA EF ad FC: SeuFA ad
AE, acque racio AF ad AC duplicara es racionis AF ad AF,
e ideo ratio A F ad A C est duplicaca rationis BE ad BHI,
sed. ratio AF ad AC eA eriam duplicaca rarionis AC ad FMI,
Ridcoue BE ad BFT ita AC VeI FK ad FMI, cumque sCMPCE
iCA sIE, PATCE ex hHIMS 2 rectam A C eNe ad curram AB C. IM
P. 2
F4