# 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 49, page id 1047377675:0065
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=65
# Source image: https://digitale-sammlungen.gwlb.de/content/1047377675/jpgs/default/00000065.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine
# Lines: 39 recognised, mean confidence 0.88
# 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.
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# After the first blank line: the recognised lines in reading order, one per line.

U
et
Blat
Ad
rectaKP, e planum AB in recta MN: ee a puncto quolibce
recte IKnempeL, ducatur eidem I_ perpendiculare planci
OLP, Tecans plana IKMN, DF C normalirer inrectis OL, L
P; licque perpendicularis in L. P recta OP. Supponimus hic H
Lesc axemrocacionis; de rectam P L. illinormalem, appella-
musradium rocarionis. dicotruncum cxlindrici RDDC eNC
ad Colidum rocundum oreum exrocatione AgurEDF FC ciri
ca IR axemrocarionis, reoP alcicudo cxlindrici ad circum.
Ferenciam circuli, cuius Cemidiamerer es radius rocarionis
L. P. perbalem DE FC ducacur rbiliber recta P L, a ba lcos
circumterencia verinque terminata in L ex F, quae produccas
axi rocacionis normalicer incidat in punceo V: 2 punccis F, F,
excirentur perpendiculares ba(eos plano F: HI3 F.Cr, d plano
fecante terminacae in HI de C, qua necessario (une in superA-
Cic crunci ob erlindricum recrum, du-acurque VHrectar
qua necessario exictie in IK MN plano sccance: manifectum
CA eriangula OLP, TTEV, recrangula ad P _ F (cum habe +F
ansulosOLP, HIEV, aequales inclinacioni plani secancis lR
MN) esse similia; de ducca recra CV, ob eandem racionem
Similia sune eriangula HIF V, GFV, cumque C F SC paraIleIIA
recta HIE, de FF in direcrum F. V: Coincidenerecrx CIV, FIV
in rnam receam plani IKMN, cricque CII F. F communis in-
tertectio ploni CiFV, plano OP L parallellis cum cruncocy.
lindriciRDDC: pacec ergo OP ad PL. ese, VrHIF ad FV; de
ideoreOP ad circumferenciam circuli cuius lemidiamerer P
Lica LTF ad circumferentiam circuli cuius CemidiamererF
V; de re OP ad circumterenciam circuli cuius lemidiamerer
P L ica (reliquos rerminos in eandem alcicudinem, nempe
lemissem rectae FV, ducendo) criansulum HI F. V ad circu-
lum cuius lemidiameter P V: eodem modo demonctracur
ese, re OP ad circumferenciam circuli, cuius semidiameter
DL, ita criangulum CFV ad circulum, cuius lemidiamerer L
V: est igicur eocum criangulum G FV ad torum circulum
cujus lemidiamecer I V, ica ablacum eriansulum HF. V ad
abla-