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# Piece: https://leibnizlegible.com/api/records/9952/text
# Catalogue record: 9952 — [Aufz. zur Dyadik]
# Incipit: Si a, b, c, etc sint qvantitas qvarum potentiae sunt opsismet aeqvales
# Date: 1693
# Akademie-Ausgabe: AA VII (assigned, not yet published)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=9952&katnr=39181
# Work: https://leibnizlegible.com/work/00068255
# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folios: Bl. 56 (from the shelfmark LH 35, 3 B 5 Bl. 56): 2 pages, canvases 111–112, page ids 00068255:0111 to 00068255:0112
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068255&page=111
# Lines: 56 recognised on 2 of 2 pages, mean confidence 0.84
# 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 56r — 00068255:0111
# Source image: https://digitale-sammlungen.gwlb.de/content/00068255/jpgs/default/00000111.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 55 lines, status machine
si a, b, e, etc sint lite quantilates quarum potentiae
sunt ipsismet aequales,  nempe 0 vel 1, quoedum
circa potentias utiliter observabuntur. Nempe omnes in pon
po in iis omnia reducentur ad unignes biniones teniones ese
et opers pretiam eut Tabulam exhibere aalium potentia mm
ifferentiae potendiae inter a et b, potentiae impares sunt a-
l
nam cubus verb. gr est a - 3 ab + 3 ab = b. idemque est in caetens
imparibus, ubi media destriuntur. sed in impa paribus conservantur
atque in unum summari debet  quadratum differentiae est a + b - 2 ab
qtum est a + b, + 6 ab - 8 ab = a + b - 2 ab = a - b posito a esse
majore unbe 2b - 2 ab = 0 seu ( b - ab = 0
sbicubus est a+ 6 + a + b ∞6 + 6. 3 _ 6. s. 4 + 6. 5. 4. 3 ∞ 6. 5. 4.3. 2
1.2
1. 2.3
T. 2.3. 4 1. 2.3.4.5
a - 6ab + 15 a bb  20 ab + 15a a b - 6 a b = b = a + b - 2ab
30 -32 =2, e Notandum differentiam inter numerus sedium imparium
si differentia detur inter a a et b Cllatb, situs ea differentia
et parium emper facere 2.
+
a 1b et quaeratur differentia incer hanc differentiam et C, fieb
C
Hic non tractantur
omnes literae eodem modo. sed ut tractontur eodem modo
  t (+) + a (+) L b
+
a
efficitur potentus. Nam quadratum ac - 2 ab + bb est
potentia differentiae inter a et b. Assumatur jam C, et seribatuo
(aa = 2 ab + bb) - C fiat -, a a 1bb + c.  20 fea 2 ab +bb) - y
Erg  et Et aa - 2 ab + bb = y y + cc - 2ay
b
(9- 6) - 2 = 1
9 - 6 - 4) - -
2
2 =
7- 6 =
9-6 - 3
4 - 1 =
9- 4
4-3 = 1
(9 - 2) - 6 = 1
9-
2 - 1 =
Itaque non semper idem prodit
1
sed si dit differentientes sint 0 et
semper prodit idem
nam qu(a + b - 2 ab - c) = a + b + C + 2 ab + 4 a b - 8 ab - 2ac 
Ergo prodit a + b + c - 2ab + 4 abc
bc
et
radice) aequantum
Nempe ibi potentiae hb

## Folio 56v — 00068255:0112
# Source image: https://digitale-sammlungen.gwlb.de/content/00068255/jpgs/default/00000112.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 1 line, status machine
Caoisce ronue