# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/40107/text
# Catalogue record: 40107 — Über Determinanten
# Incipit: [Formel] [Text:] Ergo ad formandos coefficientes novos
# Date: 1678
# Other printings: Gerhardt, L über Determinanten S.422-423.
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=40107&katnr=55174
# Work: https://leibnizlegible.com/work/00068250
# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 37
# Folios: Bl. 3r (from the shelfmark LH 35, 3 A 37 Bl. 3r°): 1 page, canvas 5, page ids 00068250:0005 to 00068250:0005
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068250&page=5
# Lines: 99 recognised on 1 of 1 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 3r — 00068250:0005
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 2v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068250/jpgs/default/00000005.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 99 lines, status machine
Unde oritur regula generalis salis palchra. si duae sint aequationes ejusdem
liters, et multiplicetur una per formula qua um grau sit sit gradus proxina
altera aequatione inferioris; poterunt poterunt in  aequatione ex productis
composita tolli omnes ittermini diteram tollendam continentes
10 = 22 +2, X +20
Multiplicetur
aequ. 1. per form. 31 + 3oX A et aq. 2. per form. A2 + ~1X + 40 X
o = R 13 + 12 X + 1X +10X
13. 3) + 12, 31 X + 1. 3IX + 10. 31X
+ 13. 30 +12. 30 -+ 11. 36 + 10. 30
= 10. 13. 21. 4+
a 01, = +13. 13. 20. 4
abei = +10. 12. 22 - 191 21
- 20. 42 - 20, 91 -20,40
XO2 = +12, 13. 20- 10. 13. 22
12 = - 10. 13. 2)
1722 = + 10 11. 22 - 1B. 13.20
30 2 2040: 10 31 = 22. 42: 13
Hi galores substatu ducti ex terminus
extremis aequationis 3. substituantur
intterminis mediis. pro 30 substituendo
13, 20. 40, et pro 31 substituendo 10. 22. 42
et ubi absunt ambo, multiplicando per 10. 13
unde fit 01. 12. 23
02. 13. 21 = 02. 11. 23
703 = +11. 13. 20 - 10. 13. 21
713 = - 10. 13, 20
(23 = (r10. 10. 22
Or. 13. 21 = - 16. 10. 12. 12. 15. 13. 20. 20. 22 +10. 1050. 12. 1915. 20. 22. 22 +10. 10. 12. 13, 15 (20. 29. 2) = 76. 18. 10. 15. H. 19, 20. 4. 22
01. 12. 23 = 210. 18. 18. 13215. 13. 20. 21. 22. 8
03. 11. 22 = = 18, 10. 11. 11. 15. 13. 20. 22. 22 +10,10. 10. 11. 13, 13. 21. 22. 22 + 16. 1. 11. 13, pt. 20. 20. 22 = 10.76.16. 15, (5. 13. 20. 21. 22
Op. 13. 22 = (. 1b. 10. 13. 13. 18. 1. 20. 20. 22 + 18. 16. 985. 15. 13. 13. 20. 20. 20
03. 12. 21 = .: 16. 16. 11. 12. p5. Bh. 20. 21. 22 f. 10. 16. 16. 12. 15. 15 21. 21. 22 + 19(16. 11. B3 15. 13 2021 248. 10 16. 18. 19. B5. 1. 21 21. 21
02. 11. 23 = B: 10. 16. 1  1. 15. 20. 24. 22 + 1d. 16. 16. 18 B. 13. 22 22. 22
+10, 10, 22. 22. 22
=10. 11. 21. 22. 22
2210, 12- 20. 22. 22
+10. 12 21. 21. 22
= 10. 13. 21. 21. 21
13. 10. 13. 20. 21. 22
+ 11. 11, 20. 22. 21
- 11. 12, 290. 21. 22
L2. 11. 13. 20, 20. 22
+FeC 12. Loc 2022
+ 11 13, 20, 21. 21
+ 12 12. 20. 20. 22
=12. (3. 20. 20. 21
+ 13. 13. 20, 20, 20
= 21. 42 - 21. 41 -21. 40
= 10. 13. 22. 41
A YII =- 10. 13. 22
22. 42 = 22. 91 - 2240
+ B. 10. 12. 22. 42.
+ 13. 13. 30. 40
Ot 10. 13, 21.
1 3 26. 20
oc 0= 11 + 10X
to lo 22 222
le t 21 2222
a nannt
HI. H. 21. 21. 22
12. 12. 20. 21. 21
harum combinationum
sed nec onstat salis degignis, nec de numeris coefficientibus
Nondum apparet ratio exclasionis
videamus an ex sub atia ex reductione multiplcationibus
per formulas artitrarias aliquid generale duci possit. Et
redinchoemus rem ab initio
Oi 11, 21, 0r 12,27
fit 0 11, -21 0 10, -2
Sit 0= 12 + 11X + 10X d= (B 21 + 20X
ex petr multi lin es et opopitis fit 11 8+ 1o 20 fiet
eago Ex 11. 22 - 1 2. 21-
fit -11. 20 + 10212
+ 12. 30 + 11. 30X + 1O. 3DX
per  desolutionem aequatio
num multiliteralum
simplicium 1C
110-y. 40- 6. 11 pre-
sit _ n 30 20. 40 - n1. 41 (70
1030 2040 20+1 = 0
saX=0 olqs neaniso aro l ro narbisiC
Ao octo - 21. 41 pro 13a + 23bF33C
11, 21, 31; 12, 22, 32;  B, 23, 33
na 1e 20 a
ut in multilitererum simplicum Canone  oca  sunt literases et aequationales. Ita hoc loco
11. 3 40 -1811 - 0
qu cefficientes quamndm. literarum, ut hic 30, 31, orc. si adscnt, habent notam dxtram. 1. ruque  reliqueua
Nota dexta vero
teque nota lleralis itaque adE coefficieptet canonis multiliterarum simplicium habeatur coefficien
Quod ad notam sextram
omnum, ut 40, 4, erc. habent notam et simistram 2.
praevis, primum sinistra nota illius semper mutabitur in 1 vel in 2
attinet  ea in aeq. Canonica est 1 vel 2 vel 3; in aeq. nova est 0, vel 1, vel 2. dento gradio
utera literae. Ergo si  aeq. camoniae nota sit n, in aeq. nove fiet nota n- 1 - et p est nota gradus literae; sed nota gradus
literae ex nota simstra aeg. canoniae nosci pt. Nempe notasi hoc loco notae sinistrae  lamonicae 1 respondet 0; 2 et 3 respondet o et
tmpe a noti sinita lamonica ditolemise prontatum s oeu eti iamante  undem defioiente
quod signa atfuse omnibus comonicis dicholocgrio posterioribus evefficientitus praefigitur-
constate on seetut aest asr