# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068200:0192
# Permalink to this reading: https://leibnizlegible.com/page/00068200:0192?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 95v, page id 00068200:0192
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068200&page=192
# Source image: https://digitale-sammlungen.gwlb.de/content/00068200/jpgs/default/00000192.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 54 lines, status machine
# Lines: 54 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.

5 May 1698
Aequatio differentialis data verb. gr.
dy: dx (1mo) = Xx tuy: aa
fiat X: a = dz: dv et 36ro) y: a = dv: do, et ex aequit fiet
ido
fiet dx: a = du adque - dzddv,: dodo et (5to) dy : a = dudaro - dudav,: dudy
atos
ergo du: dx= doddw -dv ddo,:, duddz - dzddx  t, mo) = d Zd Z + dudio,: dodo
Ito)
Hic possumus jam assumere duas aequationes, unam qua  aliqua
referatur ad reliquas v et Z, sed ita tamen ut non
detur relatio ordinaria inter du, do et dz alioqui per 2 et 3.
literarum ut W,
daretur relatio inter a xia et y:a; et alteram possumus
assumere, qua formula quaedam differentialis assumatur pro
ontante, cujus differentiatione habebitur nova aequatio differentio
differentialis et harum duarum ope tolli poterit tam duo quam
sane possumus facere ddio = 0 seu du constantem
possumus et facere.  di = dodv: dZ; sed ita
daro.
 non tantum poterimus tollere dio, sed etiam nova orietur ad huc
determinatio, nam crietur verbgrdy dodan - dvdvadzu = 0
ita ex aeq. 7 non solum tollerentur du, et daro, sed etiam poterit
tolle de evel ad huc una ex ipsis 1z, do, daz, dev quod
nescio an non reddat nimis tractabilem. Itaque praestabit
imo video jam in quo peccatum: non licet assumere dio = dudvrae
vel aliquid simile, decretur
enim relatio inter
haptes X: a
quod si ergo velirans
i velumue intervenire W, verb. gr. scribere du: W, non licet ejus valore
et y: a per ∞g. 2 et 3. Oporbet ergo
interven haberi nisi per da vel dazue, ergo non licet toller W
differentiando, nisi descendendo ad dda: ergo non oportet adhibere
W absolutam; id unum ergo superest ut fiat du: de= dd: dav
vel aliquid simile, ita enim nulla timenda nimia determinatio, nadi
haec differentiare non lcet, isi vel unus discendere ad ded. sit
ergo ex. gr. ∞ (8) daro =0 et dio = (quo) dudap: d dav ergo
ex 69. 7 fieb - dodaz: do ddzue - dz ddv = dZdZ ddnddx + dvdo ddzdZ,:do
otuo
ddvtor
quae est aequatio quadraturabilis, ed. Et spes est hac ratione posse
es. non dum rei fidere ausim, donec absolveum
in eximplo. Ex aeq. 7. feri polert d posilo ddio 20 fieri potent: du ddo dvdo
e
obtinen quaesitum
ap
vZ de daz + dibdu dvadz - dZdZue dz ddv-drodiodz ddx et poterit fieri
(amo
B
-dio dd vdrdi  d io dio doddz - dio clio de ddo = dxdodz ddzue
fiet
et fiet ex ((7mo)
bomo) dudrqdazdzapdv d27 ddo