# 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 29, page id 1047377675:0045
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=45
# Source image: https://digitale-sammlungen.gwlb.de/content/1047377675/jpgs/default/00000045.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 34 lines, status machine
# Lines: 34 recognised, mean confidence 0.87
# 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.

micelcumala praceaato erapeulua Lab a alusel
mixcilineo BCSTicem d craperium CtlC maius essemir
rilineoC CP Q e traperium CTIIK maius ene mixtilineo
GRMO, e ideorectilincum A BC C RImaius est mixcilinea
BRMOPQST. Pater quoque ex ancecedence rectilineum
ABDCE minus esse mixcilincoBCVY _ rectilineu ECFOFI
minus esse mixtilineoC CrR S de rectilineum II C, R I minus
mintilineO GKNP; ec proinde rectilineum ABDEL RI minus
CAmiXFIlInCO BRHPRSVY: cum igitur mixcilineum BATL
Consistac inter rectilinea ABCOKEI; ABDFLEI e mixtiline
BXML Y consiltat incer mixtilineA R M OPOSTB, RNPRS
V Y B, icem rECtilinCA ABC GKI, ABDFLKI COnSStAMEIMEBE
mixcilinea BRMOPOSI, BRNPRSVY, monifectum est mix-
cilinea ABKI, KM PB, minore quancitare difterre quam mix
EiLInEA BKMOPQSTI RNPHSVYB, Sed horum differentia ex
suppolitione est minor quam , e ideo diftereneia mixeili
ReOTUM ABKI, BKM Y, est muleo minor quam X, quod elt
ablurdum, ponitur enim maior quam Z; nulla ergo est diste-
reNEIZ INEEF MIXEILINCa ABKI, BKMX, ec ideo aequalia lune,
quod erae demonstrandum. Eiadem ferc esset demonstrario
in duabus praecedeneibus, criamsi conrexitas currae BK eNCE
verlusrectam A I.
l
I F I N I T IO NL S
EIFuerit Agura AB F F comprehensa a rectis parallelis
 AB, FF recta AF Parallelis normali e a B F liner qua-
libet, item Agura CFIK comprchenlaa rectis HI, GR, (ita
HE EHI siE aequalis recta AB _ CDH reCtA L F) de linea HIK,
quae eriam aequalis est linea B F, hac lege, ur, sumpeis ad li-
bicum lineis aqualibus BD, HII, iuncta recta OT Aac aequalis
rectae DC. perpendiculari ad reetam AF: appello tiguram
GHR, Asuram ABFL inroluram; _ sipuram ABFB Aguram
DHK CrOLUFaMa
ppCl