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# Piece: https://leibnizlegible.com/api/records/1226/text
# Catalogue record: 1226 — [Aufz. zur Differential- und Integralrechnung]
# Incipit: √[dx²+dy²] + √[dv² +dω²] = e
# Date: 1676
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=1226&katnr=58766
# Work: https://leibnizlegible.com/work/00068076
# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 4
# Folios: Bl. 3 (from the shelfmark LH 35, 7, 4 Bl. 3): 2 pages, canvases 5–6, page ids 00068076:0005 to 00068076:0006
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068076&page=5
# Lines: 47 recognised on 2 of 2 pages, mean confidence 0.77
# 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 3r — 00068076:0005
# Source image: https://digitale-sammlungen.gwlb.de/content/00068076/jpgs/default/00000005.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 46 lines, status machine
pavuamum
VAx + dus + Ydv + dco = e
= 2
dx + du + Lv + c + 2 Ax + d7  dvada = C2
et
14
a
4
e2e  xadi + dr + aes  dx + dy  dp+ de +
= 2, XX. dus a (dx 8y) de da)+ dudu a dus dest duded
L
2
(a dx du rldes lys dv +y dco
u
Vatb CO + D = C.
2
- 2C0- 208 + O7+ ) + + 0D = 40
seu e
= 2CO
+ ODB) ∞- p = 0
odx + dy fidnaded
e  do
et Sex+ dy = esdv+ dc + (Sav lade
am an
2
dx + dus = d_ + 2d co + co. et dy = dx - c5 : 2c0
et dx = si cd set dya et c = 2l et dx = El m. fiet
pu
dy = Allmm- 4+ll : 4l. seu du = Cmin = l. Ergo
4
dx + du = (DU mm + l m = 2Ilmno + 14
seu
seu
suptum
dx + du = ImmLl a Vga mnioe
quod si jam faciamus lmm+ l = el. fiet M = de- 1
cujus summa datur
Ergo posito l esse infinite parvum n ordinariam
fiet se 2 fla et flne y = (Mm - 1l = (C 2l
= 2 ml = 2(+e il. Si  Si vero
eta
faciarum lum + lnn = enn existente n quasi unitate
intinitesima fit 1= enn: nim+nn et dandae
sunt hae summae ( ennmm - ennt nimtnu
et
ennm: mn +nn =X

## Folio 3v — 00068076:0006
# Source image: https://digitale-sammlungen.gwlb.de/content/00068076/jpgs/default/00000006.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 1 line, status machine
nee eoouon