# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1047377675:0058
# Permalink to this reading: https://leibnizlegible.com/page/1047377675:0058?run=74
# Title: [Geometriae Pars Universalis, Inserviens Quantitatum Curvarum transmutationi & mensurae] Geometriæ Pars Vniversalis, Inserviens Quantitatum Curvarum transmutationi & mensuræ (shelfmark Ms IV, 377a)
# Folio 42, page id 1047377675:0058
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=58
# Source image: https://digitale-sammlungen.gwlb.de/content/1047377675/jpgs/default/00000058.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
# Lines: 37 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.

P ROP. 29. Y H EO R P M A.
 lefigura quecunque AB super qua imaginetur cxlindris
cus rectus seccus a plano transeunre per rectam LC de
planum baseos AB seminormaliter seCanEe. AF reCTAML rC-
ete FC parallelas eque superrecta MI. mixrilineum MOL.H
TalisnaturE, VE (dueta recta quacunque EDCNO rectXFC
normali ee Aguras AB, LOMI secance in punctis D, C, 1, O)
recta aBionaca P SiC ad mediam ariehmericaM INCEFDP, CLs
VEDC ad NO. Dico cylindricum rectum cuius ba(S MOLH
de alcitudo recta P ese aequalem inferiori rrunco eylindrici
super AB secti re suxra dictum est. Quoniam enim P elt ad
mediam arichmericam incer D L, C E, ve DC ad NO, igitur
rectangulum P in NO aequale cA erapezio a rectis DC, CFr
DE. rectangulo ad D a C. led cale crapezium eM communis
sectio plani super recta FO ad basem AB recti cum trunco
interiore cxlindrici; cumque hoc semper hat rbicunque du-
CatUT reCTAF. D C NO, manifectum est ex doctrina ductuum
Cregorii a S. Vincencio cylindricum rectum cuius basSMO
L. N ec alcicudo P aequalem esse crunco inferiori cylindricire)
Ai supeF MOLM lecti ve supra dictum cR, quod demonserare
oporruie.
Hinc quoque pacet cylindricum cuius ba(S MOLN _ al-
ricudo P esse magnitudine ee grauicare analogum dicto eru-
co; cumque cylindricus AE lua bah analogus, parec eriam.
cruncum elle cidem basi magmitudine ee grauicare analogi.
e RO P, 20. Y H C O R L M A.
Tidem politis quae in ancecedente, screcta FZ rectX F
L Cnormalis, super qua sicmixcilincum OT VR calis ne-
TUTa, VE (ducta recta qua cunque RTDS recta FRnormaliee
figuras OTVR, AB, incerlecante in punctis T, D, 5) rectaal-
signata Phc ad DS,rerecta RE ad rectam RT. dico cylindri,
CuI
CF
ne
10
Eta
ri