# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/382/text
# Catalogue record: 382 — [Aufz. zu Differentialgleichungen]
# Incipit: 0 = (1) 100dx [+100]dy + 110xdx [+110]ydy + 111xydx [+111xydy] +
# Date: 1676
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=382&katnr=57958
# Work: https://leibnizlegible.com/work/00068199
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folios: Bl. 108–109 (from the shelfmark LH 35, 13, 2c Bl. 108-109): 4 pages, canvases 215–218, page ids 00068199:0215 to 00068199:0218
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068199&page=215
# Lines: 60 recognised on 2 of 4 pages, mean confidence 0.76
# 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.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# 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 108r — 00068199:0215
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 109v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000215.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
+1IIXy 
() 100 dx + 110 Xdx + 101HdX + 120X dx + 102 y dx + 121 X ~dx L II2XIy A + 13OX dx +102V ay etC
dy
dy
d’dys
ydy xdys ytu Xdy Xy dus Xydy
O= 400 + 210X + 21IXy +220X + 221Xy +230X +2ZLXy +231Xy + 240X etc. Et differentiando aeq2
y
fa
ay
( ixyqXy
gay xay ydy xdy qidus xydy ay
Ex aequ. 1. quaerendo culiem dy. ax fiet
suar
dy (4) 100 + 110X + 101 1 120X YVor  + 12I Xy +U12XY + 130 x + 103G. Et eunem quaerendo ex aeq. 3
dx 1p0 + 110y + 101X2Oy+1O2 X HIUIXI + 112Xy + 130 y3+ 163X3
liet. dy=. 210+ 2. 220XFny +3 eoKC Hmy +3 23, Xy H2 Vx 44. 240X + 231 y3. Et aequindo valores
ruxus
ruxx
dx 20 + 2. 220y+ uX (13. 90y + rux +3. 4Xy +2 22 Xy + 4. 1407+ 251 X
Et ae quando valores 4 et 5 fiet
1BD W La WXL IVI. Voy F uL. 2WXyL 1O H oy Mnoxy 
100. 210+ 110. 210X + 111. 20Xy + 120. 20 X + 121. 210Xy + 130. 20X
+102. 210y +112. 210X y +103 20y
+101. 210y
2.400. 320 +2to 10 x12 i  2 no 1 no 1 2o
 et 5. fiet
2.220. 100y +2. 2010 XyF2. 2IB. 101y t2 NO IXy + 2120. 10274 2. 220. IIX y + 2.220. IXy +2. 220.1037
192 Y
ti. 220. 130Xy
.211. 100X + ( 2H1. Worry, L. 2HI. HIX +p. AII II Xy + X1I. 12O X + A2II. 112 X9 +2II. 121 Xy + 211. 130X3
xy
2. 220. 12
duris
Gerurxy
F2II. 103∞13
der Cal calus est ghoest aust gum bogus arhasit, utione
und  Calculus cortinuandus in plagula in fol, in versa a
collocato. prodibit aeq. (6) quae divisa per X4y dal aeq. (7.) quam, coparire
oportet cum 6q. 2. exaltata e in comparatitiis. sunt sola constantes si ergo exaltetur
c9. 2. per formula generalem ex X et y factam prodibitaequ (8) comparunda
cum 69.7. Ubi vicend aeq. 1.  finienda est, mod nunc in primo, nuncu in secundo
punc in tertio gradu, dt fiet erc. Et ita cognoscemus quid sit possibile. Quodsi
iis sit impossibilis, propimum erit, ut in aeg. 2. pater X et y. assumamus Z,
(az:q eac vel similes
∞G 
formatam si placet exeodem moto se cabentibus X et y v. b.
tamatas ipse Z formata eodem modo ex X et y. Quod si differentcandrores
illam trauscendentem vel transcendentes, oportet duos differentiales coincidere
non aequari. sed nobis sufficiat, hac n methodo investigare reductionem
Utile duprimis erit pro Quadiaturis hoc atsolvi, ita enim certo scimus,
ad ordinaria
quousque ascendere possit aq2 debedt ag. 2.

## Folio 108v — 00068199:0216
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 109r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000216.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 7 lines, status machine
14
ei
en 
+015. et 2
p . 9.2
001 11C
DERSACHSISCHE LANDESBIBLIOTHI

## Folio 109r — 00068199:0217
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 108v); this page is its right half.
# No recognised text on this page (recognized).

## Folio 109v — 00068199:0218
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 108r); this page is its left half.
# No recognised text on this page (recognized).