# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/26588/text
# Catalogue record: 26588 — [De modo tollendi literam ope duarum aequationum II]
# Incipit: Coefficiens termini primi Novi
# Date: 1683
# Other printings: Knobloch: Beginn der Determinantentheorie, 1980, S. 223-227
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=26588&katnr=56685
# Work: https://leibnizlegible.com/work/00068201
# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folios: Bl. 161–162 (from the shelfmark LH 35, 14, 1 Bl. 161-162): 4 pages, canvases 321–324, page ids 00068201:0321 to 00068201:0324
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=321
# Lines: 204 recognised on 3 of 4 pages, mean confidence 0.80
# 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 161r — 00068201:0321
# Scan: The same scan is also registered as fol. 162v; its text is given once, here.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000321.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
79 = - 21. 78 - 22. 37 -23.76,: 20
792 A.
79= P2(2. + 21. 22. 76 + 21. 23. 75; 20
10. 23
5+20. 2. 22 420. 22. 2. + 20. 22. 23
2+20. 2]22 420. 21. 23
H(2) 20. 2. 22
+ 20. 22. 22
= 20. 20. 25 +20. 21. 23
+20. 22. 23
79 = + 21 11. 21. 21. 75 + 21. 21. 21. 2274 +21. 21. 21 23 135.20 seu 79 = + 21. 212121 75 +, 21. 21.25. 22.74 + 21. 21. 21. 23. 737. 20
= 20. 20. 23
()20. 21. 21. 22. - (2) 20,21. 22. 22 1. (3) 20. 2. 22. 23.1
+ 20. 20.2. 23 11 + 20. 2022. 15.. + 2020. 23, 23.
. 20. 25. 21. 22 (= 20. 21. 21. 23
+ 20. 20. 21. 22 + 20. 20. 2. 23
(3)20. 21. 4. 22 . ()20. 2. 2222. 1) 20. 21. 22. 23
+(2) 20. 2021. 25.. - 20.21.21. 23 1. +1202023,27
+ 2020. 2232 11 42) 20. 20, 22. 23 1.
=- 21221.2.21. 21.74 - 21. 21. 2121. 22 72
19 = - 214 u1 21. 274 -uuu urrY3 - n 2121 23.72,: 26 ou. 1  2E Htout 21 ure
4 20. 20. 2. 23
HB) 20. 2. 2. 722 .v +po. 21 21. 22. 21. + 202.422. 23.
= () 20.20.2. 21. 231(2) 2020. 21. 2223 (2). 2020. 21. 23. 23.
(.- 20. 20. 4 2u2 . (= 20. 20. 2. 1. 12 = 10 2021 22. 23.
L+ 20. 21. 21222 = 20. 21. 21. 2. 23
-(2) 20. 20. 2. 1. 22 () 20. 20. 2. 2. 43
 20. 28. 11∞. 23 4 20. 202025, 29
+(2) 20. 20. 20 2. 25
() 20. 20. 2(.21. 23 (Po 20 21. 22 23
∞ 20. 207L222
(3y20. 20, 2. 21. 21
X2) 20. 20. 20. 22 23
+ 20. 20. 20. 2323
+ 28. 21. 21. 22. 29
78- - 2. 17 - 1. 16- 23. 15;. 20
78 = - 2127- 3. 76 -23.75; 20
71 = - 21. 76-2275-23.74,:20
76 = - 21. 75-22. 74-23. 74,:. 20
= 21. 21. 21. 21. 23
75= -21. 74- 2273- 23.79 20
= (2) 20. 26. L1. 29. 23
-2d. W a l2 13

## Folio 161v — 00068201:0322
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 162r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000322.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 83 lines, status machine
cvefficiens Termini primi Novi, fit ex primo prioris multiplicatopera et secundopnions per 20
tertii
sectinda
x
oterto ucce
Ny termini
Coefficiens AovZ terminu in valore sequenti
et primus pred valontersinedentus
multiplicatus per
vem
indicat lex homogeneorum virtualis
e valoris dat
ut ex pumo praecedentis
multiplicato per= 21,c
79 = - 21. 78 - 22. 77 -23. 16; 20.
78 = - 2177- 22.76-13. 13,. 20 79 = f21571. 47
P2. )6 seu - (1) 20. 22. P - (1) 20. 23
1. 15
0 2. ) 10. 1  - () C0
23. 76
17= 4. B-22. 75. 2614;   79= a (1) 21. 21. 21. 76 4) 21. . 2l. B 47 2121. 23.74, 20
(+ (1) 20. 21. 22 +() 20. 2222 +6) 20. 22. 23
l + (1). 20. 2. 22 4 770. 2. B
=(1) 20. 20. 23
dimensione
secundo
= 2
reb
ui ab
+2t a
(2)20. 21. ua
+2823 a
2021b
+20. 21. C
=2025. 2a
+20.EC a
+28. 4. 23
+ 20- 21. 226
28. 136
02
Qu. . ua
(20. 25 23a
2o. 21. n a
+20. 21. 236
+20. 21. 22C
1203. 21. 236
y2d H 23a
Or:  SL er t BgL. 22 12  Y LL12. 12 
tabee
+ 20. 1 0
ap
29a
2720. 2V. Ia
20. b
t 20. 2iC
+20 22 23 a
+20. 22. 23a
+ 20. 21. 231
3.23C
Eplicato pet
acedentis
tiplcalo
et ex prodentis tertio hmultaltelito pe 20
secuntus loc locusmedus fo
-21. 21. 21 - 20. 22. 2 - 20. 1. 22 - 20. . 2
i
- 21. 2 24 - 20. 22. 2
2a+200
tua ri ob + 20 cab
4 26. 21. 22b
. 1. 2b
eBC
+
02
3
5. 23C
+21. 23a
= 6). 20.2
+20. 2] 236
+2
1. 23 b
+ 20. 21. 2C C
a

## Folio 162r — 00068201:0323
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 161v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000323.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 78 lines, status machine
1
La
13tat -20 22
+2
21, 21. 21- 21. 2D.
13
+21. 2112
+22. 22 + 22.2
27
quid si sic, dissicmutando 20 et 20  et 50, da coracidere
20. 79 + 31. 77 + 22. 76 + 93. 75=0
+40. 77 +21. 76 +92. 75 + 33. 74=0
YI et 21 et 31 et
+40. 76 + 41. 75 4 42. 74 + 43. 73 =0
79 = - 11. 78 - 12. 37 - 13, 76,:10
78 = -21. 77-22. 76 - 23.75 20 79= + 11. 21. 78 + 11. 22. 76+ 11. 23.75, : 10. 20
- 12.20n = 13,20
47 = - 31. 76- 32 75, 83.745.3 b79- (112131. 76 - 11. 21. 32.75 - 11. 21. 33. 74, .10.20. 30
+ 120203] 4 + 12. 20. 32 1 412. 20, 33.
+ 11. 22. 30. + H1. 23.39..
= 13. 20.20..
∞ = - 41. 75. g2. 74 - 9373;: 4 79 = + u. 21. 31. 41. 75 + 11. 21. 31. 42,) 4 + 11. 21. 31. 43. 73, 310. 20. 30. 40
12. 20. 31.41  = 12.20. 31.42  = 12. 20. 31. 43
=11. 22.30.4]..-11. 22. 30.42- - 11. 22.3043.
+13. 20. 3041.- +13, 20.30. 42.. + 13. 20.30. 43..
211. 21. 32. 40 a = 11. 21. 33.40.
+ 12. 2032. 40u + 12. 20. 33.40.
4 11. 23. 30. 40...
75 = -51. 14. 52. B3, 53. p, . 50 792- 1. 21 31. T1. 51. 74 - 11. 21. 31. 41. 52. 73 - 11. 2131 41. 53. 72, : 1020.30.40. 50
+ 12 2031. 41. 52
+12. 20. 31. 41. 51
F11. 22. 30. 41. 51 + 11, 22
= 13.20. 30, 41. 51
+ 11. 21. 32.4051
12. 28 32,40. 51
= 11. 23,30. 40, 51
= 13. 20, 3071. 52
+C
1220 32, 40.52
= 11. 23.30. 40.52
+ 11. 21. 31. 42.50 + 11. 21. 31 4250
= 12. 20. 31.4250
= 12. 20. 31. 43.50
= 11. 22. 30. 4250 = 11. 22. 30. 43. 50
4 12. 20. 31. 41. 52
4 13, 20. 30. 42. 50 4 13. 20. 30.43,50
= 1. 21. 33.40.50
+ 12. 2033. 40.50
= 1. 25.) 40. 53
Noto autem in fine temini prim esse semper 1 et 0; in fine 2di semper 2 et 0, in fine yti 3 et 0
sed hioc non sufticit ad exclusionem, v. 9. in valvre , ubi ubi 7D est termini primi, reperio
I et 2 et D, ubi prangirte D, tamen non adest 1 2 et 1 et 0
praestitset forte sic scubere
10. 29 + 11. 38 + 12.77 + 13, 76+ 14. 95+ 14. 74 + 16, 73 ex =0
20. 79 + 1. 78 +277 +13. 16 + 24. 75 + 15. 74 + 26. 73 etc =0
et
+ I1. 22. 30. H. 53
Hujus combinationis Lex quaerenda est.
reque enim omnia membra absolute
possibilia adsunt, et invemienda
lex exclusionis. 2x. gi. in 77
in valore  2d0 ipsius 79 est
in coefficiente ipsius 77 est
+ e spectando notas
dextras (nam sinistrae semse
Sacul 1, 2, 3) habetur 1 et 1
item 2 et 0. sed non 8 et 
ibidem in 76 datur 1 et 2
item 3 et o; non lamen 2 et 1
eu
0 et 3
b
catur det 3, non tamen 3 ex c
= 13 ..H. 35
+ 11. 21. 33.40. 53
240. 5
= 12.2
10. 79 + _1. 78 + 82. 77 + 13. 76 =0

## Folio 162v — 00068201:0324
# The same scan as fol. 161r (00068201:0321), where its text is given.