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# Piece: https://leibnizlegible.com/api/records/1225/text
# Catalogue record: 1225 — [Aufz. zur Differential- und Integralrechnung]
# Incipit: √[dx²+dy²] = ω = dx/v. seu dx² + dy² = dx²/v²
# Date: 1676
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=1225&katnr=58765
# Work: https://leibnizlegible.com/work/00068076
# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 4
# Folios: Bl. 2r (from the shelfmark LH 35, 7, 4 Bl. 2r°): 1 page, canvas 3, page ids 00068076:0003 to 00068076:0003
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068076&page=3
# Lines: 72 recognised on 1 of 1 pages, mean confidence 0.66
# 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 2r — 00068076:0003
# Source image: https://digitale-sammlungen.gwlb.de/content/00068076/jpgs/default/00000003.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 72 lines, status machine
Co
dx + dus 
et
da
Ax 
. seu Ax+ dy=
a
s
e
dx + vdy = dx. fiet dy = dx - Ex v, : r
e
1
d
seu dy L dx V1 - D: v. Efficiamus _ ut 1- v aequelur
quadrato 1_ZNa 1∞2ZV + ZZ vV. fint v = 2
e
et EC V= 2
et S1-
seu
a
dy
et
 17
5y
etu
70 = 1 = 2.
es 
99
y. 1499= 1
le
(1 -vv = 1Z= 1: Z+1 et dividendo per v
en
1.Z seu dy: dx =
AX 2L 1
dm
G= Vdx +du=L
dari
+ Z
2
a
a
ev
prodibit
1
n
Itaque posito
ipsius + Z invenire per curvam, seu ipsi invenite
fier
se
carvam edementis proportionatea
indin
Xa +1
mmumnt
ddem
= AH
= l= 2Z
2
per X. patet si quis velit summam
es
opus ee ive summa ipsius
a id
finc patet autem
C. YXX+I. LAX+
ut obiter dicam, culivit parabolocidum et Hyperbolociolum
excepta prima Hyperbola, et excepta recta posse exhiberi
curvar proportionalem per communem Geometriam.
grsq 
++ fiet
a
eetrc
+
t