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# Piece: https://leibnizlegible.com/api/records/25448/text
# Catalogue record: 25448 — [De tollenda litera legibusque divisionum]
# Incipit: nx_5 + px_4 + qx_3 + x_2 +sx + t [(1)]= 0
# Date: 1693
# Other printings: Knobloch: Beginn der Determinantentheorie, 1980, S. 311-315
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=25448&katnr=56698
# Work: https://leibnizlegible.com/work/00068007
# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 10
# Folios: Bl. 8–9 (from the shelfmark LH 35, 4, 10 Bl. 8-9): 4 pages, canvases 15–18, page ids 00068007:0015 to 00068007:0018
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068007&page=15
# Lines: 210 recognised on 4 of 4 pages, mean confidence 0.79
# 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 8r — 00068007:0015
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 9v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068007/jpgs/default/00000015.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 66 lines, status machine
nX + pX + gX + rX = x + t = (0 aXt bX+ xt dx +y = 0
Tollatur X, habebitur aequatio in qua b, c, d, y, ascendent ad  gradum stum
et quoniam si besset = y, vel aliter nihilominus ascenderent, sic, sequitur non
seu
posse esse aequatione in aequatione aliter dari nisi , bt, et, 48, y
2
y, 5b Yb, 5bc yb, ybc ybcd, yb, ybc ybc ybed ybidhe
v, yb etc. y ib etc. f, yb  y; et idem i haeleris
facias a
d
Haec aequatio in qua y
d. esse auius dimensumis, TC duaeum d trium, y, quatuor
designavitur per u, 12, 13 14
rabeE etd
Rursus P, 4, Y, s, t assungent ad
quatuor dimensiones. Ad huc amplius si B, et S, dem q et Y se habe
it
bunt eodem modo. Quod si _n tollas seu ponas agneat
seu ponas n =0 tunc p et F,, g et 5 se habebunt eode modo et
ita in reliquis. postre habita scil in terminis, ubi atest n.
Inventa jam aequatione Y. etc. ponatur ut robique
_Et sit jum y + ey + f9+ gy + hy+ K = Y et ullobius
t, phahatur radix quinti gradus. comparando Y+ et et cam
formula excilata ex Y+h dactur atssi
d
ex + 11X + 12 X + 13X + 14 X + 15 =0
21
i
_X + 21 =0
fit 21 = 1121 + 12. 21 - 13. 21+14
2X) = 21
4 H.L
X+21
i
21.2t
+H. X. 21
= 21. 721S
1c. 2
12.
21. 2. 21
Filort. 2t
l.
13.21
= 14.2
4122 +13. 21. 21
=t2. H. 21 -13. 21. 21.21
4 1. 2_. 2 471. 21. 21, 21, 2)
a21. 21.212)  EI. 2.21.21. 2)
X + px + g =0 sit X = ay rab X = a y + sabustioabG ab9 + ab gu ab
+C
fit + ay L5a b15 + 10 a by + 10 à by + 5aby + ab
+9y +59Cy +104cy 419e +59cy +4c
apis +aac ut +bapeus +aapey +ay
X + pX + q = 0
apb +gasbe +6apbC +40ub + apbe
X Inx y y- ne tux +pX
2.2
+ui
=1. 21. 2) =H. H.H.
+21. 2. 21 4 21. 21. H. 21
y + Sl9 +10cC y + 10Cy +5Cy+C
y +acy 46ccy3t4
yi
y +acy 1sces talis
+ b + abest
vin

## Folio 8v — 00068007:0016
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 9r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068007/jpgs/default/00000016.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 123 lines, status machine
XtuxI) +X + IX + 12X + 13X +14X +15 = 0
+x3
145
=X = 21a
- 2∞
= 11. 21 = 11. 2D
+21 +21. 2 F21. 2
+ 11. 21
2. 2
412
X + 21X + 22 =.
X +
Ergo X=
+ecy +5i
E_
ay- d
at 0b4 ex + dX
s-
seu compendio 
2
e + fx + EX
y
X Mlq X + AX + 1X + 14 X + 13 =0 X + 2IX + 22 = quadrando fit
N + 1 X + 12X + 13X, +14X + 1520
Et ex 3a per 2 fit. +
(seu XX = -21X - 22
X +21X + 22 = 0 fX = 213 2F = 2. 21. 22 + 22. 22
- 213XX = 21. 21 22X) +2.21.2 + 22822 fit X3= - 2IXX = E2X
Ex4 sit X = +2. 4. 2XX + 2222.
42. 2. 2
f 22.22.
e frI. ux +  Y. 2V
guu fel. 2. 22 (42. 1. E. 22.
-re
f22. 22
+ II. C + 11. 22CE
1, 146+ 4 - 2 -8
2l - 1 - 4 +2 +4
+ 2
X 6 XX
+21 X + 2P. 22
Aursus ex 5 per 2 fit - 21. 41 2: - 721. 2222
422. 22.
Et ex 6per 2 sib X = , 21. 21 X + 21. 22
Ergo ex aeq, 1. per 7, 4, 82. fiet
E 21.21 
12, 1+4 =2
13, - 1
614
5
- 22
 21 X + 21. 22
-321.2 . = 2.71. 22
+ 28
- 11. 23.
+, 1I. 21. 22.
+12. 21.
- 12. 22.
- 13. 21.
+ 14.
- 11. 21:22
+11. 22
+ 12. 21.22
= 13. 22
+15
(10)
142
(20 = 30X + 31  ypendio
34X + 35 =0
X+21X + 22 =0
tit _ 14- 21. 4 + 22
e
(1
seu 25.0- 21. 24. 35 + 342920
sit 20ux + ux=
dividatur 1 per 2fit residuus 36 + 21X = 0 et sit 1127 = st. Ed 14 22 operatio 30 + 3IX L LX a33X , qX ss 
Dimilendus 10 + uX+ X +13X +1 4X + 15K,
0
et fit 15.22 =35. 22 1 34. 2 Hinc 31= 11 Ex alibi a me calculatis
VXX+LXN =0 IXLuXtM=0
14. 22 = 32. 2 +33. 4 + 34. 20  dividatur 1 per 2. erit operatio 30X + 3IX + 32X3+ 33X + 34X+ 35
14. 27 = 34. 22 +35 435. 20
13. 22 = 3322434. 21+35. 20
(1. 22 Dl.2C+32. 21 +33 20
et siei residuns 34∞ + 35X 34X + 35 =0 lex,
32 = 10. 10. 2 - 10.19. 21 + 1.11. 20 - 10. 12. 20, : 102 103. 22 - 10. 1. 2s + 11. 11. 207: 10
10. 2 30. 22+31. 21 +32. 20
it lex operationis erit: 
erit
10, 20 = 10. 3
10. 21 = 10. 31 + 11. 3 1, 29
22 = 10. 32
+I1. 32 +12. 31+
10, 24 = 10. 39 + 11. 39+ 12. 326
10. 23 = 10.
10. 25 = 10. 35 + 11. 34 +12. 33
+0 26 10 361 H 35+ n 4
30 = 20
31 = 10. 21 = 11. 20, : 10
33 = 102.23 - 10. 11. 22 + 10. 152 21 - 113. 20 + 18. 1112. 20 - 10.12. 21 + 10. 11. 12. 20,: 18
seu 5 = 10. 23 = 18. nar +. 10. 1218. 30 =  11. 20, : 103
34 = 19. 24 - 10.1. 23 + 10. unr2, = 10 lin 12 20 + 1 20 seu 34. 1. 1. 1B 12p 1 . 1,. po  - 1 0. 1. t 1. 21 4 11. 20, . 10
2
= 103. 12. 22 4 16. n. M. 21 = 10, 12. 11. 11. 20
u
et 35 = 10.25 = 10. 11. 24 +1031. 21. 23 = 18. 11. 1. 1. 22 4 10, 11. 11. 1. 11. 21 = 15. 20.
1. 12.
1. 1. 12, 21
12. 23
1215. 22
p. 12. 11. 21
12. 12. 21 12. H1. 11. 21
itaque 2 = 20. 1031 = 10. 21 - 11.20  1832 = 15. 22 - (17. 10n. 21 + 15. 20
12. 2 210. 1. 12. 2) . 11320 10. 34 = 152. 24 - 1. 172 o. A. 12. 4
14.  + 10. 111. 23 - 10. 18 1. 22 4 10, 11. 11. 11.11. 21 = 1P3. 20 1 1212. 20
(0 12. 21 210. 11. 12. 20
11. 12. 11. 1.
12. 11. 11. 11.2
3.10. 11220
II. 2
21.21
= - 4+4
1F +t 2

## Folio 9r — 00068007:0017
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 8v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068007/jpgs/default/00000017.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 13 lines, status machine
1. 11. 12. 20
(L1. 12.11. 20
1212 20 r 1. 11. 20
rouni Iimmaus bly 2 dogato pe ast trot e non anierur a cor au ta erero avu e n rmet.
11. H1. 11. 12. 20 N apparet. quod prodiant omne
possibiles formo, et
numeri coefficientes seu
repelucon
ut in valode ipsius 35 occultunt (prraeter 1P inr2)
estin 12. 1
et B in 12. 12 et q2 in 1B3, qua
faciunt 4. 1B. 12. plura autem
non admittunt leges homon.

## Folio 9v — 00068007:0018
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 8r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068007/jpgs/default/00000018.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 8 lines, status machine
Examinandum quae lineae ex omnibus parallelas
fractione condirigentibus faciant quam dictinctissimam
ciant visionem, seu quam maxime radios ab unco punt
vementes colligant in aliud. RE  vemadmodum
ita hic quoque problema maximorum et minimorem institut
quoniam  den in purxi aptissima sunt sc circusi succe
rejumvis, puto p similiciter inquiri posset
inde ostitui potes