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# Piece: https://leibnizlegible.com/api/records/406/text
# Catalogue record: 406 — [Aufz. zur Integration irrationaler Integranden]
# Incipit: ∫dx√[a4+x4] quaeritur. fiat xx = aalω + aqam et fiet
# Date: 1676
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=406&katnr=57982
# Work: https://leibnizlegible.com/work/00068199
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folios: Bl. 136 (from the shelfmark LH 35, 13, 2c Bl. 136): 2 pages, canvases 271–272, page ids 00068199:0271 to 00068199:0272
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068199&page=271
# Lines: 81 recognised on 2 of 2 pages, mean confidence 0.69
# 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 136r — 00068199:0271
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000271.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 50 lines, status machine
a4)
agar
dx a + quaeritur. fiat XX = ColCo 3ijuo +4
et fiet 2X dx = (Pc + a9) ldco = (Lco + am) pdio
deu ax
e
alg-amp, du
Multipl. per
EX  ( peo + a9
sax Va+x =
2
t
Ppcocd F 2p9ci + aa99
Ergo sict
. ia
aoo +2aab9 a ag +alloutmamraam
 V
se
Apcotaqu
1 sit B
ad proco +a lgco + aM
2
qud
aetripco
u
alqamp (pco + ag
2
sed taq
ed s
seu 1o v amil
el
4 Halov(-a Elamta namnitraam lV Camam taan ao
fiet pdx 1a +X
multi per
a9, lv
du tel
aa
Xi R 1099+1y712,:, 20l99+29+22 = X: a fint
10a+ 20X yy. + 21XV t 22. X ∞0 qundio 31gy 43294357
10a. = n a y = 12a seu 31 yy 431. 329+31. 3320
seu 31gy + 32 319 + 232 = 4352-31.
ist
e
seu 214+ =32=
e
sou
in y= V432-31. 33 = 2 32, : 31 =421 X - =11. 21aX + G11a. Luy
20.221 4 12, 20 aX = 10. 1a 2 
410.22 ax
20 X = 10a

## Folio 136v — 00068199:0272
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000272.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 31 lines, status machine
2
 b10+20 ∞0  bu +21
 0
20 = 10 8)- b.   21 = = u s-bC
ab 10 V, = 6101
aC 20
∞
hhv
e
102
a
∞
Tolt.
CEI
+ aharo et akk
h =1, ab 10 + ac 10bb:cc = 102 abce + ac bb
K = ab 11 + ac 11 bb cc = 1 sabectac b
3. 10n = hK  dabit..
e
20. 2p
a
3. 10. I1
(
il
em
3(10 b in (si b seu) 3. 10. 1V = 16 il ab
se
C
ita ubi evanescit 10. 11
nec
EaCb