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# Piece: https://leibnizlegible.com/api/records/25988/text
# Catalogue record: 25988 — [De sublatione terminorum ex aequationibus fragmentum]
# Incipit: x_5**13a_2xx+14a_3x+15a_4=(1)=0
# Date: 1683-05
# Other printings: Knobloch: Beginn der Determinantentheorie, 1980, S. 181-182
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=25988&katnr=56677
# Work: https://leibnizlegible.com/work/00068201
# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folios: Bl. 187 (from the shelfmark LH 35, 14, 1 Bl. 187): 2 pages, canvases 373–374, page ids 00068201:0373 to 00068201:0374
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=373
# Lines: 103 recognised on 2 of 2 pages, mean confidence 0.75
# 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.
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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 187r — 00068201:0373
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000373.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 77 lines, status machine
 NCX X X X (X 13a XX + 14aX + 154f
= (1) =0
sit X + 2IXX + 22aX + 23aa = (2) =0
Sex multiplicetur aequ. 1. per form. (3) utam XX +314
+32a et aequ. 2. per form (4) utam X+ 4IX +42aXX
+43aaX + 44a Ex 1 per 3 fit X+ X X 13acX+ 1X
+ 1saXK 
X X X 13aa X + 14a X + 15a XX
e
2XX
327
+13,31a.. + 1431a.. 4 154, aX
ra1 X +21. 4(F + 22. 41ax + 23. HIaX
207
+1332a. 4 14. 32a. + 15. 32a
Ex 2 per 4 fit.
X +UXtZIME + 23aaX_
+4241+ 21. 424. + 12. 12a an +2342~X X
+43aa +2. 93aa. +22. na XX + 2342a∞
+. 4aa. +21. 49a. + 27. 44aX +23. 444)
et quia (5) ∞+6) aeg. 5 ∞ aequ. 6. Inveniantur
sollantur literae 71, 32, 41, 42, 43, 44 habebitur aequ. in qua pro 43
L
ponatur 232y. et epe 1g9. 2229, 21, trestermini tollantur.
3T. 13 23
27
21. 22
t15423
14.1
13, 23
13. 3
23. 29
Forma aequavis 13.2421
st
uis
22. 21
22. 1
24
21, 21,21
2F2I.H
21. 12
21. H. 1
22
2
e
2
13
152Z2
6. 22.22
a
19. 45. 22
2
2. 2
2
12. II
23
22. 21. 1
An a. hoc semper
per ∞e4. nj .
non altio vin
tertio gradu
praestare liceat
tu
21
223271
15
22. 2
221
X iC13
LL L1.1
2L.2
113 1
Lf.
q
t
21. 41 9
d

## Folio 187v — 00068201:0374
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000374.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 26 lines, status machine
aequalio
X etc. habet  radices. aequalio
X etc, habet 4 radices; ex quibus una est communis
quaetadi
triqe. Ergo agta summa id ergo fieri pt quinque modis; seu
cum unaquaeque prioris possit reperiri in posteriori. Si jam
trium
quaeramu jummum harum quaor radicum, productum 23. id
uique quatuo modis pt assignari; ubi porro efficiendum ut horum
productorum, et rectang ulorum, et trireorampuilorum
summa sit aequalis nihilo. Haec ergo profundius
meditanda, retrum nempe praevideri possit
ad quem gradum hiz positis assurgat sumulatrium
radicum ex quibus una est cois prinae aequationi
et summa restangulorum, etc. Haec enim si
probe ratiocinemur videntur posse praevideri
ante calculum.
F(1aX + 19a = ( o sit X + WX F 22aX + 23 aa 7
cotux x
134X
=21X+21, 2 (+ 2. 22a. + 21. 23aa.
22Z
A22a P- XtaX - 22. _ a a X - 22. 23a
= 214)
-217
= 21. 2122a - 217,23aa