# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068037:0010
# Permalink to this reading: https://leibnizlegible.com/page/00068037:0010?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 19
# Folio 5v, page id 00068037:0010
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068037&page=10
# Source image: https://digitale-sammlungen.gwlb.de/content/00068037/jpgs/default/00000010.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 51 lines, status machine
# Lines: 51 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.
# 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.

LC aequ. LB: 
Est autem PB
simplex
LB autem quae curvam secat in duabus punctis
CB
ubicuculus radio pB descriptus eam secat, est
duplex. simplicem Bp vocabo S.
t
ipsam LB vocabo B. fiet  d aequ
y - X a
seu B y -x aequ. ns. Quaeritur an liceat
fingere D y -x egu _d et scribere o aqus.
aco aequ ns. Et jam fingere aequationem
AP appellando v. Fingere aequationem inter
v. co. 5. talem, ut ejus differentialis (positis
v. et co simplicibus adeoque dv et s exist
existentibus 0) exhibeat aco aequas. quod
non difficile est. Jam ope aequationis fictitiae
et inventae, et ope relationisu inter 8. v. P. ed
ex natura curnae inveniomus tandem rela
tionem inter y. et X. sed vider jum difficu
talem non potest, hoc modo inveni
sed quia haec methodinimium effeceret
et fere semper problemata solveret, ideo
accurate examinanda restringenda ex
corrigenda est videtur tamen in ea
latere utile nescio quid. Nota
videndum utrum problemata sunt determinato
ad certas curvas et quomodo id cognosci
queat. Uentemus rem in curvis jam notis.
rax aequ ry in paratiolu ABX.
BC, Y. BP, a.
equ +a
AP, v. PC, S.
 Veqo X+ a.
2ax r. x.y
nosit saequ 2ax +v- 2 X + XF quae ad
maximit; o
 vaego atx.
2a 0 -2∞ +2x restituitur
ax AV. XX
aequ2ax + YV = 2VX + XX. pro at ponend XV
siet. Saequ. 2XV - 2XX + vV - 2VX +XX seu 
saeqo a +xxF vo unde fieret: 2X aequ. 0.
quod absurdum est. Itaque supponendum relationem
si
illam fictilitjam inter L X. v. C. non esse quam
libet sunt enim in data qualibet infinitis modis
varialiles sec tatem quae nascitur ex aequatione
generali ad qualtei curvam et Eperial, exalicantua
nan cuca