# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068200:0487
# Permalink to this reading: https://leibnizlegible.com/page/00068200:0487?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 243r, page id 00068200:0487
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068200&page=487
# Source image: https://digitale-sammlungen.gwlb.de/content/00068200/jpgs/default/00000487.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 66 lines, status machine
# Lines: 66 recognised, mean confidence 0.82
# 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.

Jam quia Y = ax. hnic auferatur addatur
p latus curvae parabolice ad Contirasm
relatie axemrelatae
2Z = X. seu 2y = X. Ergo differentiae Applicataram hicinci
a
sunt Triangulo Homogenea. Eaum quadratum
a - 1. fiet V4Y + a latus ejusdem curvae
a
a ad basn relatae
ponatur ea differentia esse: E= W erii ejus 
a
addatur a, fiet, s2ga-G Ercae ergo vsus spicatam circuli. Confrmad
paulo aute demonstrator a
a
fet jan
Contra Y +3Y+
a
2
Ergo.
parabolic
parabilicae,
addatur
s
a
eli.
ya
a
vide pau. .
monis.
Ia forte ago Curva Parab,
aequalter divisa per per
a basi secta videtur, circulo
ab axe secta Hyperbolae
sgntomos. Quod foret
maximi momenti est enor
vax sax paxta- tax.
=y. Ergo. y= ae+a+gX-
a
a
ax + a + aX - 2Va X + aX
Ergo 2aX + a - 7 =, a X + aX
ambobus quadratis.
~ a
ak a 17+ a 27 et
N
C
a a
tax +tax. Ergo
V
et
a
-a723 +3 = 4a X +4aX
a
a
Et rejectis nimis parvis, fit: e
ul
1X + X = 0. enZ L
a
a
eu 4y = X. seu 4y = aX.
In y = ax. Unde sequitur diffe
a
parexa
rentras applicataram hyperbolae ad axem
esse ipsismet dindiatis homogeneas quae
est intmorabilis proprietas ad Tangentesa