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# Piece: https://leibnizlegible.com/api/records/60036/text
# Catalogue record: 60036 — Johann Jakob Ferguson für Leibniz: Annotationes Algebraicae
# Incipit: Si dentur aequationes
# Date: 1680
# Sender: Ferguson — Addressee: Leibniz
# Akademie-Ausgabe: AA III,3 N. 045
# Other printings: Knobloch: Beginn der Determinantentheorie, 1980, S.21-25.
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=60036&katnr=41746%2F2
# AA III,3: its series at leibnizedition.de: https://www.leibnizedition.de/de/reihen/reihe-iii/
# Work: https://leibnizlegible.com/work/00068011
# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 14 (shelfmark Lh 35, 4, 14)
# Folios: Bl. 5–6 (from the shelfmark LH 35, 4, 14 Bl. 5-6): 4 pages, canvases 9–12, page ids 00068011:0009 to 00068011:0012
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068011&page=9
# Lines: 296 recognised on 4 of 4 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.
# 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 5r — 00068011:0009
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 6v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068011/jpgs/default/00000009.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 54 lines, status machine
Aonorationas Aegebrnica.
l, der. tur aequationes 12. Z+ 13, 3+ 14∞0
et 22.L 4 23. 5+4∞d
Habebitur 22. 13. Z + 13. 24∞0.
23. = 12. 24
Tandem inveniatur
etem
2. 23. = 23. 14
.3 + 22. 14X d
Si dentum aequationes 12. C+ 13. 3+ 14. 4+ 15∞0.
22. 2 +23. 3+ 24. 4 + 25∞0.
32. 2+33. 3+34. 4+ 35 ∞0.
12. 33. 24. = 13, 34. 25
= 23. 14. 35
+23. 34. 15
+ 33, 14. 25
= 33. 24. 15
22. 13. 34.
+ 22. 33. 14.
+32. 13. 24
- 32, 23. 14.
12. 23. 34. 2 4 13. 24. 35 ∞0.
+ 12. 24. 35∞0
=12. 33. 24. = 12. 34. 25
22. 13. 34. - 22. 14. 35
+22. 34. 18
+32. 14. 25
= 32. 24. 15
12 23. 34.
+ 22,33. 14.
+ 32. 13, 24.
- 32. 23. 14.
12. 23. 34.4+ 12. 23.35∞0.
= 22. 13. 35
+ 22. 33. 15
+32. 18. 25
232. 23. 15
Si dentur cequationes 122. 2. 24133. 3. 3+123. 2. 3 +12. 2 + 13, 3114∞0
22. 2+23. 314∞0
Inveniemus 122. 25. 23. 3.3+ 122. 23. 24. 3+ 122. 24. 24∞0.
+ 133, 22. 22. + 122. 23. 24. + 22. 22. 14
125. Cl. 28. - 123, 22. 24. ~ 12, 22. 24
= 12. 22. 23.
+ 13. 22. 22.
- 22. 13. 34.
+22.33, 13
+32. 13. 24
-32. 24. 13.
-12. 33. 24. - 12. 33. 25
Sidentur aequationes Arei. Ecilicet:
122. 2. 2+133. 3. 3+144. L. A+ 1238. 31124. 2. 4 + 134. 3. 4+12. 2+13. 3+14. 4+15 ∞0.
22. 2123.3124412588.
32.2+33.5+34. 4+35∞0.
Sandem invenitur ut requitur:

## Folio 5v — 00068011:0010
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 6r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068011/jpgs/default/00000010.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 70 lines, status machine
122. 24. 24. 38. 33. 2. 2 + 173. 22. 25. 34. 34. 2 + 173. 26. 25. 34. 34∞ 0.
= 122. 23. 24. 33. 34. - 133, 22. 21. 34.35. -133. 24. 25.34. 35
= 122-23. 24. 33. 34.
+ 122, 23. 24. 33. 34.
+ 133, 22. 22. 34. 34.
= 133. 22. 24. 32. 34.
= 133. 22. 24. 32 34.
= 133. 24. 24. 32. 32.
2 141, 23. 23. 22. 32.
- 144. 22. 23. 32. 33.
= 144. 22. 23. 32. 33.
+ 144. 22. 22. 33. 33.
+ 123, 22. 24. 33. 34.
= 123. 24. 24. 32. 33.
= 123. 22 29. 34. 34.
+ 125. 23. 24. 32. 34.
+ 1C4. 23. 24, 32. 33.
= 124. 22. 24. 33. 33.
= 124. 23. 23. 32. 34.
+ 124. 22. 23. 33. 34.
+ 134, 22. 23. 32. 34.
- 134. 22. 23, 32. 32.
= 134. 22. 22. 33. 34.
+ 134. C2. 24. 32.33.
+ 133. 22. 34. 34. 25. -133, 24. 25, 34. 35
- 133. 24. 25. 32. 34. 4133. 24. 24. 35.35
- 133. 24, 25. 32. 34. +144, 23, 23. 35.35
+ 133. 24. 24. 32. 35. -144. 23. 25. 33.35
= 133. 22. 24. 34. 35. -144. 23, 25. 33.35
+ 133. 29. 24. 32. 35. +144. 25. 25. 33. 33
+ 144. 23, 23. 32. 35. +134, 23, 25.34.35
- 144, 23. 25. 32. 33. - 134. 23. 24. 35.35
+ 144. 23. 23. 32.35. - 134. 25. 25. 33.39
= 141. 22. 23, 33.35. +134. 24. 25. 33. 34
= 144. 22. 23. 33. 35.4 13. 24, 25. 33. 39
+ 144. 22, 25. 33. 33. = 13. 24. 29. 33. 35
= 144. 23, 25. 32.33, - 13. 23, 25, 34. 34
=144. 22, 25. 33. 33. + 13. 23.24. 34. 35
+123. 24. 25. 33.34. + 14. 23, 24. 33.35
- 123. 24. 24. 23. 35. - 14. 24. 25. 33 33
= 123. 23. 25. 34. 34. - 14. 23, 23. 34. 35
+123, 23. 24. 34. 35. +14. 23. 25. 33. 34
- 124. 23. 24. 33.35. +15. 29. 24. 33. 33
- 124. 24. 25. 33. 33. -15. 23. 24. 33. 39
= 124. 23, 23. 34. 35. -15. 23. 24. 33.34
+124. 23. 25. 33. 34. +15, 23. 23.34. 34.
+134. 23. 25. 32.34.
= 134, 23, 24. 32.35.
+ 134. 22. 23. 34. 35.
= 134. 23. 24. 32. 35.
= 134. 22. 25. 33.34.
+ 134. 22. 24. 33. 35.
= 134, 22. 25.33. 24.
+ 134. 24. 25. 32. 33.
+ 12. 24. 24. 33. 33.
= 12. 23. 24. 33. 34.
= 12. 23. 24. 33. 84.
+ 12. 23. 23. 34. 34.
+ 13. 22. 2433. 34.
= 13. 24. 24. 3233.
= 13. 22. 23. 34. 34.
+ 13. 23. 24. 32. 34.
+ 14. 23. 24. 32. 33.
= 14. 22. 24. 33.33.
= 14. 23. 23. 32. 39.
+ 14. 22. 23. 33. 34.
Si dentur aequationes. vilicet
122. 2. 2+133. 3, 3+122. 2. 3+ 12. 2+13. 3+14∞0.
222. 2. 2+233. 3. 3 +223. 2.3+22.2423. 3 +24 ∞ 0.
envinienms cequationem eequlletem.

## Folio 6r — 00068011:0011
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 5v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068011/jpgs/default/00000011.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 104 lines, status machine
nem 3.3t 122. 2. 210. 5. 53
d. D35. 33. S. d. d.d +r22. 2. 23. 133.3.3.3+ n2. 122. 24. 233.3311210-2221.541. la 29 24∞0.
+222222 133. 133.
+222 123, 123. 233.
122. 222. 133. 233.
=I22E.
= 122, 123, 223, 235.
+122. 135. 223A23.
-222. 123. 123. 223.
Si dentu ceq
+C. 22. 27. 233.
ACcL. 12. 123. 233.
+CC 12. 123. 233.
Cc2. 123. 123. 23.
L122. 2. 13. 239.
122. 222. 13. 233.
12C 222. 533. 23.
= 122. 222. 133. 23.
- 122. 22. 122 232.
-122. 12. 223. 233.
- 122. 23. 123. 223.
+122, 22. 133. 223.
+122. 22. 133. 223.
+ 122, 13, 223. 223.
+222. 222. 13. 133.
+222. 222 13. 133.
- 222. 12. 133223.
-222. 22. 123. 133.
222. 13. 123223.
+122. 122. 25. 28. +122 122. 23. 24 4222. 12. 12. 24.
+ 122. 122. 233. 24.
+222. 12. 12. 233.
+222. 12. 123. 23.
+222, 12. 123. 23.
+222. 123. 123. 24.
- 122. 222. 233. 14.
= 122 222. 233. 14.
- 122. 222. 13. 23.
-122. 222. 13. 23.
122. 222. 133. 24.
- 122. 222. 133. 24.
-122. 12. 22. 233.
- 122. 22. 123. 23.
-122. 12. 23. 233.
- 122. 123. 223. 24.
+122 22. 22.133.
222. 12.125. .Ml. C2. 14. Cn.
+222. 12. 122 24 -122. 12. 22. 24.
- 122. 222. 23. 14. 4. 122. 22. 22. 14.
= 122. 222. 23. 14. +222. 222. 14. 14.
- 122. 222. 13. 24 - 222. 12. 22. 19.
-122. 222. 13. 24.
- 122. 12. 22. 23.
- 122. 22. 123. 24.
- 122 12. 223. 24.
+122. 13, 22. 22.
+122. 22, 223. 14.
+222. 222. 13. 19.
+ 222. 222. 13. 14.
= 222. 12. 13. 22.
+122. 22. 13.223. -222. 12. 223. 14
+122. 22. 13. 223.
+ 122. 229. 223. 14.
+222.222. 133. 14.
+222. 222. 13. 13.
+222222. 133. 14.
-222. 12. 22. 133.
- 222. 12. 13,223.
22. 13. 2123
-222. 123. 223. 14.
= 222.. 22. 123. 14.
+ 222 32. 12. 23. -122 222. 14. 24.
1222. 2. 2. 2+ 1353. 3, 3,3+ 1223.2. 2.3+1235. 2. 3.3+ 122. 2. 2 + 133. 33 = 122. 2. 3 f 12. l+ 13.d +1400.
2222. C. C. C+ 2333. 3. 3.3+2223. 2. 2. 3+2233. 2. 3.3+222. 2. 2 +213. 3.3+223. 2. 3422.4c3. 5+24∞8.
Dit 1222
1223. 3+122
1233. 3. 3+123. 3412
1a
0 1b
ic
1333, 3. 3.3 + 123. 3. 3+13. 3+14 ∞ 1d
2222
2223. 3+222
2233. 3. 3+223. 3+22
dd 20
∞ 2c
2333. 3. 3.3+233. 3.3+23. 3+24 ∞ 24
et hrabebimus 1a. 2. 2. 2+ 1b. 2. 2 +1c. 2 + 1d ∞0.
2a. 2. 2. 2+ 2b. 2. 2 +25. 2 + 2c ∞ 0.
Quae aequationes i reducantur ad unam, invenietur.
1a- 1a. 1a. a. 2d. 2d 2d. 2d - 1a. 1a. 1a. 2a. 2d. 2d. 2d. 1 d = ra. 2a 2 a. 2a. 2 d. 2d. 1d. id
= 1a. 1a. 1 a. 2a. 20. 2d. 2d. 1d + 1a. 2a. 2a. 2a. 2d. 2d. 1d. 1d
= 1a. 1a. 1a. 2a. 2d. 2d. 2d. 1d + 1a. 1a, 2a. 2a. 2d. 2d. 1d. 1d
= 1a. 1a. 1a. 24. 2d. 2d. Erl. 1d + 1a. 1a. 2a. 2a. 2d. 2d. 1d. 1d
- 1a. 1a. 1a. 2b. 2d 2d. 2d. 1c, + 1a. 1a. 2a. 2a. 2d. 2d. 1d. 1d
+ 1a. 10. 1 a. 2b, 2d. 2d. 2c. 10, + 1a. 1a. 2a. 20. 2d. 2d. 1d. 1d
+ 1a. 1 a. 14. 2b. 2d. ad. 2c. 1d + 1a. 1a. 2a. 1b. 2d, 2d. 1d. 2c
= 1a. 1a. 14. 2b. 20l. 2d. 2cl. 2c. + 1a. 1a. 2a. 2b. 24. 2d. 1d. 1c
- 1a. 1a. 2a. 1b. 2d. 2d. 1d. 2c
= 1a. 1a. 2a. 2b. 2d. 2c. 1 d. 10
+ 1a. 1a. 2a. 1b. 2d. 2d. 1c. 2d
- 1a. 1a. 2a, 26, 2c. 1d. 1d. 2c
1a. 1a. 2a. 2b. 2c. 1d. 1d. 2d
∞ 2a

## Folio 6v — 00068011:0012
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 5r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068011/jpgs/default/00000012.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 68 lines, status machine
+ 1a. 1 a. 2a. 2b. 10. 10. 2d. 2d - 1a. 2 a. 2a. 2a. 1d. 1d. 1d. 2d + 2a. 2a. 28. 2b. 20. 1d. 1d. 1 d q
= 1a. 1a. 2a. 1b. 2c. 1d. 2d. 2d - 1a. 2a. 2a. 2a. 1d. 1d. 1d. 2d - 1a. 2a. 2a. 2b. 1c. 1d. 1 d. 2d.
+1 a. 1a. 2a. 1b, 1c. 2d. 2d. 2d, - 1a. 2a. 2a. 2a. 1 d. 1d. 1d. 2d + 2a. 2a. 24. 16. 2c. 1d. 1d. 2d
-14. 12. 2a. 2b. 2c. 1d. 1d. 2d - 2a. 2a. 2a. 2a. 1d. 2d. 1d. 2d - 1a. 2a. 2a. 1b, 1c. 1d. 2d. 2d
+1a. 10. 2a. 2b, 1c. 1d. 2d. 2a - 1a. 2a. 2a. 1b, 1c. 1d. 2d. 2d, - 1a. 2a. 1b, 2b. 1c. 10. 2d. 2d
+ 1a. 1a. 2b. 26. 1c. 1c. 2d. 2d +1a. 2a. 2a. 1b, 2c. 1d. 1d. 2d, + 1a. 2a. 1b. 2b. 1c. 2c. 402d
- 1 a. 1a. 26. 2b, 1c. 25. 1d. 2d - 1 a. 2a. 2a. 1b, 1c. 1d. 2d. 2d, = 1a. 2a. 1b. 2b, 10. 2c. 1d. 2d
= 1 a. 1a. 2b 2b. 1c. 2c. 1d. 2d - 1 a. 2a. 2a. 2b. 1c. 1d. 1d. 2d - 1 a. 2a. 1b, 2b, 2c. 2c. 1d. 1d
+1a. 12. 2b. 2b. 2c. 2c. 2d. 1d +1a. 2a. 2a. 1b. 2c. 1d. 2d. 2d - 1c. 2 a. 1b. 20, 1c. 10. 2d. 2d
+1a. 2a. 2a. 2b. 2c. 1d. 1d. 1d 4 1a. 2a. 1b. 2b. 1c. 2c. 1d. 2d
+14. 2a. 2a. 1b. 2c. 1cl. 1d. 1d + 1a. 2a. 1b. 2b, 1c. 2c. 1d. 2d
= 1a. 2a. 29. 1b. 1c. 1d. 2d. 2d - 1a. 2a. 1b. 2b. 2c. 2c. 1d. 1d
+2a. 2a. 2a. 2a. 1d. 10. 1d. 1el ∞ - 1 a. 14. 1a. 1c. 2c. 2c. 2d. 2d +1a. 1a. 2a. 1c. 2c. 2c. 1d. 2d,
+2a. 2a. 2a. 1b. 1c. 1d. 1d. 2d
- 2a. 2a. 2a. 1b. 2c. 1d. 1d. 14.
+2a. 2a. 2a. 10. 1C. 14. 1d. Et
+2a. 2a. 1V. 1V. 1c. 1C. ed. 2d
- 2a. 2a. 10. 10. Ic. 2c, 1d. 2d
+1a. 1a. 1a. 2c. 2c. 2c. 1d. 2d = 1a. 1a. 2a. 2a. 2c. 2c. 1d. 1d.
+1 a. 1a. 14. 1b. 2c. 2d. 2d. 2d 41a. 1a. 2a. 1c: 1c. 2c. 2d. 2d.
=1a. 1a. 1a, 28. 2c. 1d. 2d. 2c = 1 a. 1a. 2a. 1C. 2c. 2c. 1d. 2cl.
+ 1a. 1a. 24. 1C. 1c. 2c. 2d. 2d.
- 1a. 1a. 24. 1c. 2c. 2c. 1d. 2d.
= 1a. 1a. 2a. 1b. 10. 2d. 2d. 2d.
+. 1a. 1a. 2a. 2b. 1c. 1d. 2d. ed.
- 1a. 1a. 2a. 1b. 20. 1d. 2d 2c.
+ 1a. 1a. 2a. 2b. 2c. 1d. 1d. 2d.
= 1a. 1a. 20. 1b. 2c. 1d. 2d. 2d.
+ 1a. 1a. 20. 2b. 2c. 1d. 1d. 2d.
+1a. 1a. 1b. 2b. 1c. 2c. 2d. 2d.
- 1a. 1a. 1b. 2b. 2C. 2c. 1 d. 2d.
= 1a. 1a. 2b. 2b. 1c. 2c. 1d. 2d
+. 1a. 1a. 2b. 2b. 2c. 2c. 1d. 1d.
- 1a. 1a. 2b. 1b. 2b, 2d. 2d. 2d.
+ 1a. 1a. 1b. 26. 2b. 1d. 2d. ad.
+ 1a. 1a. 1b. 2b. 2b. 1d. 2d. 2d.
=1a. 12. 2b. 2b. 26. 1d. 1d. 2d.
= 2a. 2a. 2a. 1b. 2c. 1d. 1d. 1d
=2a. 2a. 1b. 1b, 1C. Ec. 1d. 24
= 2a. 2a. 1b. 1b 2c. 2c. 1d. 1d
= 1a. 2a. 2a. 1c. 3c. Cc. 1c. 2d 42a. 2a. 2a. 1c. 1c. 1c. 1d. 2d.
= 1a. 24. 2a. 1c. 1c. 2c. 1c. 2 - Ea. 2a. 2a. 1b. 1C. 1d. 2d. 2d.
+1a. 24. 2a. 2a. 1c. 2c. 1d. 1d +2 a. 2a. 2a. 2b. 1c. 1dl. 1cl. 1dl.
+1a. 2a. 2a. 1b, 1C. 1d. 2d. 2d = Ea. 2a. 1b. 2b. 15. 1C. 1d. 2d.
- 1a. 2a. 2a 2b, 1c. 1d. 1cl. 2d, 4 2a. Ed. 10. 20. 10. 2. 1d. 2c
+1a. 2a. 2a. 1b. 1c. 1d. 2d. 2d, = 2a. 2a. 10, 10. 10. 1d. 2 d ed.
-1a. 2a. 2a. 2b, 1c. 1d. 1d. 20, 4 2a. 2a. 1b, 16. 20. 1dl. 1dl. 2c.
+1a. 2a. 24. 1b. 2c. 1d, 1d, 24, + 2a. 2a. 1b, 16, 2b. l d. 10, 2d.
=1a. 2a. 24. 2b. 2c. 1d. 1d. 1c = 2a. Lu. 1V. 20: 20. 1d. 1d. 1d.
= 1a. 2a. 1b. 1b, 2c. 2c. 2d. 2a
+ 1a. 2a. 1b. 1b. 2c. 2c. 1d. 2d
+1a. 2a. 1b. 2b. 1C. 2c. 1d. 24.
2a. 1b. 20. 2c. 2c. 1d. 1d
=1a. 24. 10. 2b. 1c. 1C. 2d. 2d
+1a. 2a. 1b. 2b. 1c. 2c. 1d. 2d
+ 1a. 2a. 2b, 2b. 1C. 1C. 1d. 2d
= 1a. 2a. 2b, 2b. 1c. 2c. 1d. 1d
+1a. 2a. 1b. 1b. 16. 2d. ed. 2d,
+1a. 2a. 1b. 16. 2b. 1d. 2d. 2d
=1a. 2a. 1b. 1b. 2b. 1d. 2d. 2d
2a. 16. 2b. 2b. 14. 1d. 2d
=1a. 2a. 1b. 1b. 2b, 1d, 2d. 2d
= 1a. 2a. 1b, 2b, 2b. 1d. 1d. 2d
+1a. 2a. 1b. 2b. 2b. 1d. 1d. 2d
+ 1a. 24. 2b. 2b. 2b. 1d. 1d. 1d
+1a. 2a. 2a. 2a 1c. 2c. 1d. 1d - 2a. 2a. 2 a. 2a. 1c. 1c. 1dl. 1d.
-1a. 2a. 2a. 1C. 1c. 1c. 2d. 2d, 42 a. 2a. 1b. 1b. 1c. 1c. 2 d. 2d.
+1a. 2a. 2a. 1c, 10. 2c. 1d. 2d, - 2a. 2a. 1b. 1b. 1c. 2c. 1d. 2d.