# 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 104, page id 1047377675:0120
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=120
# Source image: https://digitale-sammlungen.gwlb.de/content/1047377675/jpgs/default/00000120.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 38 lines, status machine
# Lines: 38 recognised, mean confidence 0.81
# 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.

C
P_6 P. 55, E HE O _ E M A.
lldem bheis, quae in ancecedente: dico rarionem Boure
RACIK ad Aguram ACF eNe mulciplicaram racionis IK ad
C E in rarione P,F. ad P. Fx anECCCderE ABIK CC ad AC IH
re PfO ad Beodemodo ALCF est ad AC F: ve Pus Pad
 idco ABIR eA Ad ACIK VEAL C F ad AC L, _ p. Fmurando
ABIR CIE BA ALCE rE ACIK Ad ACL, AErATIOA BIR ad AL
CF el COMPOSEA CK PAEIONE AK ad AF _E ex raFIOHE IK ad
CE ee proinde ratio AC IK ad AC F componitur ex cildem
racionibus; ac ratio IX ad C F est inulciplicara rarionis AK ad
AE in racione P ad O e converrendo, rario AK ad AF Cl
mulciplicacaracionis lR adC E in ratione 9 ad P, e compo
nendo, racio compolica ex racionibus AR ad AF _ IK ad
C F (nemperatio Agurae AC TK ad Aguram ACF) est mulci.
plicaca racionis Ix au CE in ratione P 9ad P, quod de
monltrare oportuit.
P ROP. 56. 2 TI FO A F M A.
repolico ABIK rectangulo _ reliquis posiris ve in ante
a cedente, li super AOUrIS ABIK, AC IK, suppOnantuE CY
lindrici recti, cuius veriu (que alticudo A B, icem suPPOSitO
cylindricum super ACIK sccari a plano ipli bAC A C. IR (C,
minormalis de cam secance in recta AK: dico parallelopipe.
dum super ABIK eNe ad inferiorem cruncum cxlindrici su
per ACIK rE qP, f. 20 3d9. dupponacur planum (CcanS CY.
lindricum super ACIR produci uc lecet etiam parallelopi
pedums manifectum esteruncum ejus inferiorem ese prisimd
criangulare parallelopipedi dimidium. Deinde hc rectan-
BULUM AMTK cum inscripea linca ARP ealis propricCAEIS,VE
(lumpeo ad libicum puncto F s ducta recta DF. O ipsi AR
perpendiculari ee lineas ARYI, ACI, secarC in punctIS R, C3.
iem
Mu
AE
c
W
SuI
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