# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068104:0005
# Permalink to this reading: https://leibnizlegible.com/page/00068104:0005?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 9
# Folio 3r, page id 00068104:0005
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068104&page=5
# Source image: https://digitale-sammlungen.gwlb.de/content/00068104/jpgs/default/00000005.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 113 lines, status machine
# Lines: 113 recognised, mean confidence 0.85
# 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.

Hic nota ada pro diversis
summovibus ejusdem
Lex. Homogencorum
replicatioprima ida
3tia
lx) ddx dddx ) ddddX)
2
dx d(i)x d0)X
= 2
((3) X
XddX et dx X dddx et dx Xddddx et x et. charrcter est o.
Haec igtur  ducta in formulam angent gradum non characterem
idem est si in ex, de etc substituas pro dx, du, et. eoum atorem
X ddddx et X dddx et ddx Xddddx et dddx esc homoy. charautex est ∞)
sed quia non est idem numerus literarum, adque = xay +y dx
ideo tantum semi hogegenea sunt, seu non accurrunt adaque- Xadus + Edxdy Fydax
in calculo Idem est in caeters hujusmodi
X dd ddX et dd
adttZ. Xalbys Ayexddyst Sddx lus Liulx .).
Non est opus examinare
feupas cub uti abest x nam eadem prodit
foruntat in quibus plane abest X nam ut in
iis appareat rex homogenectum sufficil maximam
scim Nam x sequentem pro albissimam sumi pro X
proxinam pro ax etc
 X 
ix et dx Xdex et dx
LH et d: Ad  et doX
X desx et doX
Ka up (XdB) X et dlB)X
char.0 char. 2
X d (IX et dC)X
X d3)X et d CZ
X AOX et dcos
X d 5) X et diE) X
X ABIX et d6
X d5)X et
X d5) X et 2)X X d(8) X et d
X
char. 4
X d(gX et d()X
4. 1.
X d(1) X
coi danscendentu
Nobis in calculo nostro non est opus
ire ultra d(2) X seu dddx. Nam
_ tollendo y imus ad ddx, tollendo du ad dddx,
ubi ponendo ddy =0 sublatae sunt affectiones ipsius y.
opus est calcula summationum
dx = 16)X dX = 2 X d (o)X dX = 3X d (o)X eu
dsex = d (uX daoX = 2 d oX d()X d d( )X = 3 dbX dl. IX etc
et C
ArgaZ =. Xy
=C
etL
di dex = X ds)X + d C)X dX d CoX = X d ()X + 2 x doX c(X d (esx = X db) X + 3 X LC)X et
dX duX = X dE)X + dlgX d(X dx d6)X = X d(3x + 2 X d(oXdeX d X deyx = X diX + 3 illox dyx et
l
ec
d X dxx dG)X = X e X d(2) X + X dC)X + d(X d C)X
L
Generaliter analysi effici poterit, oblato Cummando, ut
reperiantur 908 ipsi adjungenda, ut bimul omnia summari
possint d de (s, =  d ()(5) d d(f +1)
 d dex d(SXD = h a (esX  d (etIX, d (f) x D + 9 a(eX, d(f+ 1) X, d (3 
Et eodem modo facti ex tribus gentraliter; quaeri pt differentia. Hinc colligitur
otiam feri posse ut idem summetur pluribus modiso.q. d(1) X  explic per ale
fer (VX doX explicestur per d(es
()Xd a (+ CX. st sit dxh L 5) Xd = d (1) X3. fiet h Ia et D = 3 et f = 1
posteniore casa fit e- it sit d ()k d sosx =  A()XD. Ergo h = 2 et 421 1 922 (verte)
X d4)X et a b)X
X il7)X et d (3)X
char. C
a X ddx = X dddx + 2X dx ddx
et 2Xdk ddx homog cum ex
Ergo X addx homog. cum du
den q =X dddus +3 dxdaytgaes
Et ita pooro
Tabula Homogene.
tatis Tanscende–
fium
X dBiX et d (O)X etc Homognitur o.
etc
etc
ubi varius possunt
permini homogenet
pro quaris potentia
alicuius differentialis
nostiinendo valorem
explicando eam potent.
X toto vel parte
ale sX = X al X dlX = d  y
d
= X d(1)X = dX
=X dosty E ale)x d CeX
Item Eadem fabula linasmutam pt
omn
reuttates ingredientes literas
commuu o charactare multando
t videntur etiam nunquam
nemyle
binari termini per altum
et
imnes multes
amtate, seu deprimas tunc par
NCcpir X
d(o)x d)x eci
stabunt d(o) d()X, a(2)X et
id ea est in lolo hoc argumento
X = d(- 1) X
a(t X a(tIIX
 debet esfe d 1et 1)X vel ox vel duyX. Priore casu sit e = -1
ica