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# Title: [Vera Circuli Et Hyperbolae Quadratura] Vera Circvli Et Hyperbolæ Quadratura (shelfmark Leibn. Marg. 98)
# Folio 114, page id 834940469:0198
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=834940469&page=198
# Source image: https://digitale-sammlungen.gwlb.de/content/834940469/jpgs/default/00000198.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 36 lines, status machine
# Lines: 36 recognised, mean confidence 0.84
# 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.

14o
x14
naturX, ve (ducta recta FC tansence currum HIF. D in quoli
bec puncto F _ ducris parallelis FF, BC) recta F BGIF aequa
lis e parallela rectae C F: manifeltum cA ex huius7 rectam
CF seu BF eNe criplam rectae L:O, cumque hoc semper AaF,
evidens es Aguram IIBDE CNecriplam AgureHIODE, acque
ex huIUS LZ AOUEBHIBDF. CA aequalis ApurA HIEDR; ac pro-
inde EOura HIEDK eAad Aguram FIOD E in racione 3 ad F,
dividic ergo curra HIFD quadrancem circuliin rarione 3 ac
23 Quod demonttrare oporcuit.
Ouod si rario OIad FI essee quincuplicata racionis CI ad
OI curra H F D quadrancem circuli dinideree in ratione 5
ad 3; li oucem sepeuplicaca inratione 7 ad5; de sic in gene-
res liracio CIad ElEc mulciplicaea rationis Cl ad Olinran
rione cuiuscunque numeriimparis ad vnitarEM D CUEYAHEL
diridet quadranrem circuli in ratione ciusdemnumeri im.
Paris ad numerum imporem proximeminorem, quae omnia
demonstrantur sicur hoc cheorema. Fodem prorlusmodo
demonstracurno Colum illa Vallibi incerpolicio qua spacium
cissoidale mensurat inlibro de creloide. sed eciam omnes
Forcalsis alix quae imaginari poctune, suppolica primxe inter-
polcatisurae mensura. Quod sratio C l ad E l lic mulcipli.
cacaracionis CTadO linracione numeri cuinicunque paris
ad rnicatem Cacile daretur Rgurae R IIF. D quadracura opc
huius 54, uc docet Vallihus in lua Arichmecica infinicorum;
ee ideo innorescie in recta DK cenerum aequilibrii Agura
DEHIA opChuius 37. Ilinc eriam eridens eltDFF eandem
semperhabere racionem ad D E.O quam habet DP HIH ad
LiL(O, quod summopere nocandum nam (praecer multa
ala pulcherrim a proBlemara) S secetur conois parabolica
Plano adarem porallelo, ex data ciuldem ab axc distantiad
dabicur huius ope ucrumliber conoidislesmentum.
e
nonias
.c.