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# Piece: https://leibnizlegible.com/api/records/3677/text
# Catalogue record: 3677 — [für L.]
# Date: 1690-09-16
# Addressee: Leibniz
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=3677&katnr=42059
# Work: https://leibnizlegible.com/work/00068196
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folios: Bl. 306v (from the shelfmark LH 35, 13, 1 Bl. 306v°): 1 page, canvas 608, page ids 00068196:0608 to 00068196:0608
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=608
# Lines: 126 recognised on 1 of 1 pages, mean confidence 0.75
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# 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.
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# After the first blank line, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 306v — 00068196:0608
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000608.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 126 lines, status machine
11 410
120.
20dl1)
21d20
+ 10 209e
=100. 20. 20(+110. 10. 20) +1011 20d,0 20 = 002n + 101. 10. 11p, : 101. 1) p = 1( 120:100
 10d2 100s. ApP + 12ONA I = 0On, Sed ita sit 12OHL H
2. d120. 10. 11
120. 1010
-120. 11. H- + 120. 1L. _ = 00n, seu evasteseit 11. Eig
non licet tollere d10. in aeg. 3., si absit 110, et retineamus dio, nectolam
neque adeo explicemus.  P, fint 11. = 00 S(00n: 100pe +126)
proenietur secundum 10 ad aequationem non minus data difficilem
sit s hZ X = G
XY a dy: dx = x + y: 4X = Z
sit ddg: dx - adx dy dx = Xdxq X191
Elo
(ax + dy ( dx) + ydx.
E
et
en ddya = ddX Z = 1 dp dy: x + ZdX. x dx
s
u
ddu A - Y u tX =. dx dy +Zd- di
Z= + + X dd
et 7= de
(2)
XZ = y +X
n
und
ect
XdZe + Z dx = dytap
Xdy + 7dx =  dy+ du una differentralis
essi
L
alia disperentia
du dr tu dyXt Axx = ydx-xax x
seu X de = dy X - y dx
Ex 2 fit y = XZ- X ex 5 sit yx dy. dx
ex.
Xdz. dx excsibXZ X dz. dx
quae dude6 et7 aequando fat
= X = XZ- X az: dx
ose
seu
du  lx: X seu Z= BL = fax: X = ytX: p
porla
nam dx: X = dy X - ydX, : X
seu dxX = dyx = ydx, seu dix Lydx = Xd
via X 49d. Z-1
eud:Z-
 sit AC  o 5M gy: p- 1 = y dy. Z. - y dx
seu y2 Z- 1 dy: dZ - Z. 2 dp: dZ
rursi ob 3 fit ydZ. 2-1 + 2x  dy + dx se
19
seu X+G, : X = dy: dx ut desiderabatu
ed sollendam literam X
seu du alsa
dy + dx = Z dx  21: dZ
aequando valores 18, 19. destinitur dyniaeus (22)
aequadem
 iee adsedeattad utcus
Hinc discimus Caronem generalem, si sit aequac
quae cunguium literarum (ut Z  q) ejusque quaeruntur
duae differentiales 3 et 8 et har ope harum ac vg. 2. follantu
mempe az et habotu n hec soctam ax. d
X
potanda in de varis modit nabus diffentat
et difficentio disterentralis cn combinabiles. posum
ersi opt mescheda m s 1 21 sept 1b90
4x dx 105 dy 4.7
y ex
a
1y dy 20
hX + a dx + b ay + cxdy + e HaY = C
addx + liddy X CX ady + sexd e_ ddx F edx dy = c
seu Nempendio Faddx + +b ddy 1+ e de dy = 0
et sidmando teg.
+Cx
compentio aut sit, et E h. fiet dux + A ddus + h axdlys L.
et b + cX = Y it  a+ exL v
et ex ag. 1. fiet a d t eg ex v. dx + Zdy 20
tolli pe v adeoque y, ope aeg. 7 et 4 et fiet
1)
=Zay ddx + Zdx ddy +hax du =0, uti abest n vel y
quaeratur ad huc, alia ubi similiter absit, ex nempe
ex aeg. 7 fiat v = a dx. -Z dy. ax fiet
edy ax +_ e Ye y F dx ddy + cdx dis 4 - Zdy ddx
C0K
sed coincidunt agg. 10 et 8. explicando hper c+ e. itaque
non et tolli nisi uina, ut y, vel ex ex his qua aod
y, X, dy de oordinetur aeg. 8. secuma y
52
fiet +h dx dy + Z dxddque B seu
a Z ddx 
tag: y = +dx: q dex  xt. Unde ddx
pro inbibrio explicundu per X et ax habetur
to relato du t. ex, per quadraturas
si tollatur ay ex aequatiae 2. dasitur acys dex
per de fiet alx addus: dxe ta dx in R. y + Xda
at 
addus = ex in X, y + ed addx in X, yarationem
et quia hes lantor homogeneae, datur ddy: dax per
ax dddx, interventa rationum duanum copo dat
t inventam compotitam ex nga
si y sit sublata restabunt q homogener nempe ax, du) anty ait
et dabitur days: dixper dx: adex et du: adde, interventur
rationum lium
a
sis
no quislum s alu adusolis
a ida
s. manat dduo
indeterminalae a. Ponatur
reclired i si prnatur dax= ep, hassetur aadginetus
addus: et et du beu ates
si faciamus ddy =e habetur diu non d sy per dxa a
Eujgloqventu x se perrex.du dxd
si faviaumm ddus= sponatus ddX ax prsiabit relasio para
inter adx, du ildys et tiet e d
aut - t
xddy: ay per ardax. u interventa e  sed nihil horum irem abso
u
lite
Einptur
seu aditus :dus ret du: aD) et Ox: a seu ta per + et X