# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068198:0295
# Permalink to this reading: https://leibnizlegible.com/page/00068198:0295?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 148r, page id 00068198:0295
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 149v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068198&page=295
# Source image: https://digitale-sammlungen.gwlb.de/content/00068198/jpgs/default/00000295.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 80 lines, status machine
# Lines: 80 recognised, mean confidence 0.79
# 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.

Z dy
e
5) + deo t
19 = e
Assumta aequatio, in qua, b, c, e, deo sunt con-
stantes, differentietur, fiet: dusa
cy
d2dy b7 + Zddyb7+ deo D + +Zdy cdy b + deo dtb7 + deo tcdy b = 0
lc
cy
S
ricu
dividendo per (3 atque ordnando fit duoat + Cdco F dy + cdydus + ddy =0
Aequatio ergo quae hiic iventifican.
 +1Z d9 pr ole 
sit aequatio data V dxdx + cdydus + ddy = 0 posito V dari per N
dxax
Unic aa ddZ = C dcode, et fiet aa ddz:
erit v
et
agLadt:Z et quia abest dus,  in data, fiet in praecedente C + deo + aadZ =0
potest, poterit solvi.
e
 C
aa dcodt: vdxdx) seu d: den - - C vdXdx
Sia Z progressionis Geometricae, erit dZ: dq = dq: Z et ddzue = d Z1Z: Z et ddz: 7 = dZdZ . 2
 (L andcod Coco de:
-+ a
y = - cvdxdx et fit dZ: Z = e dx 1 - cV. Et habetur
per quadraturas ex, X adeoque et  et proinde et c revera enim dz: Q =d(3
Et habemus dz dur Z2
ded
ydyb + deot b =e solvi potest, nam transformetur in
Habita autem Z et deo habetur et C
porro aequatio
C
scy
=C, et pro t7 ponendo  fie L
= e, uti omnia habentur praeter , adeoque et
Icy
1  cdy b + deo F B
hanc C
quia ergo solvi potest aequatio V dxdx + Ac dydus Hanas
y d + ded F
seu Vdxdx + deoC gdcodso + adcod es =
liet aa vdx cet
siu de=
dx
A
cc 4V= a
Y-CV
C
cc8- a
Vdxdx + p axdy + cdy dy + aa ddy =0
et quia da=
a Yt(V): V
7 d((rdx) X MdxdZ = aa dd7,: Cd co)
sed ibi incommodum est, quod
a
nam
tus tc dydus + ddy =0
y = acco at; vdxdx et cdio et deo + aa dZ =
y v da
dx 1- cV: 
Sed talis aequatio aliunde solvi potest
nam fit
(id si hy in data non abfuisset, v. g. si habuisseruns vdx dx + B
fieret vC 44 dcodb. Z7
fieuet L
en
dy: deo = c: a et Ady: deo =: a, e his valoribus ubstitutis
 fit vdx dx + AC  dco dco 88: aa taadcod8: a =
ponatur
a
a
etiam itar ad ddx
ZaE
yndx
nam b habetu
exs