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# Piece: https://leibnizlegible.com/api/records/618/text
# Catalogue record: 618 — [Aufz. zur Algebra]
# Incipit: (1) y = 10 + 11x + 12x² + 13x³ + 14x4 + 15x5 + 16x6 etc.
# Date: 1676
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=618&katnr=58195
# Work: https://leibnizlegible.com/work/00068201
# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folios: Bl. 151 (from the shelfmark LH 35, 14, 1 Bl. 151): 2 pages, canvases 301–302, page ids 00068201:0301 to 00068201:0302
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=301
# Lines: 58 recognised on 2 of 2 pages, mean confidence 0.86
# 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.
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# 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 151r — 00068201:0301
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000301.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 55 lines, status machine
= a 10 + W X + 12 X + 1 X + 14 X Y15X + 16 X erc
20 +2X +22 X +23 X + 24 X +25 X + 26 X erc
1020 + 10. 2X + 1022 X + 10.23 X + 10. 24 X +10. 25X 41. 26 X erc
+11. 20. 4 11. 21 11. 22 1. 23 11. 24 11. 25
1. 20 12. 21 12. 22 1223 12. 24
13. 20 13. 21 13, 22 13. 23
14. 20 14. 21 14. 22
15. 20
16. 20
Eodem modo, procedetur pro yuio. et ila porro. Et quilibet terminus habelit
coefficientem compositum ex omnibus combinationibus ex diversis seriebus, quorum notae
sinistrae aequabit termini exponentem
tantum
umerorum
sed investigemus divisionem seu Z. sit Z =Z. et sit
y = 30 + 31 X + 32X + 33X) + 34X +35 X +36X etc
fiet vZ  y seu fiet
(6)
y = 20. 30 + 20.31 X + 20. 32X + 20. 33X + 2. 34X eu
10
21. 30, 21. 31 21. 32
N. 33
22.30 32. 31 2. 32
aeq. , 3. 30 23. 31
24. 30
UX +MX _ + 13X   erc
fiet: 30 = 10 et 31 = u = 2130 seu 31 = 1. 20 -102 et 32 = 12 - 10. 1  4 21 112012110 21, :20
20. 20
seu 32 = 12. 20. 20. 4 - 14. 20. 8.21 =18.3625,: 20. 20. 5t 33 = 13 = 23. 10 - 211. 20 - 92.10. 21  21. 12. 20. 10 - 2.1 10. 14121 10 1. 5
120
20. 20
20. 20
20. 20. 20
Et Seu 3 = B. 2000. 20 - 12. 20. 20. 21 +81. 20. 21. 4 - 10. 20u 2
- 11. 20. 20. 22 +210. 20.21. 22). 20. 20.20
-. 19, 20. 20. 23
pergendo facile credo regulam inveniemque.
pergemus etiam ad radicem; et quaeremus Let y, sel yr, sel yvio, et cla porro
videtur semper Videndum et quatenus quin et pergi poterit ad Tel y et set ymon
et sel yn v. p2oe
jam sub v exempl. gratia continetur et  nam = = V
Satte ut Utile erit hoc artaficio uti, ut qua
posset huc alculus etiam utilis esse ad regressus si quandoliceret infiuntam
linfinities infinitam, reducere ad series simplices.
jungantur his Theoremata Nectoniana
lit 10, 11, 12 13, sint quanlitates factae se ordine progressi fiant ex
quantitatibus scire Arithmetica et Gconcehica procedentibus, poterunt
condi theorimata, ut si essetit  1, 2, 3, etc. vel 1, L, L, vel si essent
condi poterunt
1. 2. 2, 2, ac vel  L2 1, 22 3.E, 4.2, etc.
therremata pro ipsorum reductionibus ad quadraturas, quae deinde
prodermut p alia serieus ex his composita, ad quadraturas reducendas.
D=
VV ocugronae anx ons xXtio
yv=

## Folio 151v — 00068201:0302
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000302.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 3 lines, status machine
1C - 2
1
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