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# Piece: https://leibnizlegible.com/api/records/60553/text
# Catalogue record: 60553 — Reductiones quadraturarum irrationalium altiorum ad inferiores
# Incipit: √(a+bx+cxx) + √(l+mx+nxx) = y
# Date: 1676
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=60553&katnr=57451
# Work: https://leibnizlegible.com/work/00068196
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folios: Bl. 178 (from the shelfmark LH 35, 13, 1 Bl. 178): 2 pages, canvases 351–352, page ids 00068196:0351 to 00068196:0352
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=351
# Lines: 40 recognised on 2 of 2 pages, mean confidence 0.74
# 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 178r — 00068196:0351
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000351.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
Hoc bene
ductione
quad
pturarum
irralue
rrationalium
altiorum ad inferiores
seam videntur.
sic optime
a +bX + CXX + AI + mX +nxx = y. quae libet
pari summabilis exgue et clocume tollno sumura–
bilis per notas en ventiones, ergo et totam jam
Tollamum irrationales, fiet a+bx +CXX ++ 21. V. = yi
e a + b x + CxXL+
q
C
assungunt +
y = 2 y+
et y=
et y
A
l in
y a+bx+ex= atet exx mlamx erp
. Seu seu per ompend. splo
1
Lm
D. ergo V = 1DC
D+ (2
1
d2 +O.
similiter datur
nut enim paeden radice
) D+ C etitrito non pt fieri C
am  s doer
 si fierer 
 uitu
c

## Folio 178v — 00068196:0352
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000352.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 3 lines, status machine
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