# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/27357/text
# Catalogue record: 27357 — für Johann Jakob Ferguson: [Beweis eines algebr. Theorems]
# Incipit: Demonstratio hujus Theorematis a me reperta: quodomnis aequatio cubica
# Date: 1680
# Sender: Leibniz — Addressee: Ferguson
# Akademie-Ausgabe: AA III,3 N. 056
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=27357&katnr=56808
# AA III,3: its series at leibnizedition.de: https://www.leibnizedition.de/de/reihen/reihe-iii/
# Work: https://leibnizlegible.com/work/00068124
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folios: Bl. 84 (from the shelfmark LH 35, 8, 30 Bl. 84): 2 pages, canvases 167–168, page ids 00068124:0167 to 00068124:0168
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068124&page=167
# Lines: 55 recognised on 2 of 2 pages, mean confidence 0.76
# 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 84r — 00068124:0167
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000167.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 52 lines, status machine
a = b
a + AAh. + V a = + b
ae
X
- gna +. rX - 5∞0
n + Va + 1
X + S... y.
X
X2 + 2 ax +6
3X - pX  c
X+axL.
= b no
Demonstratio hujus Theorematis a me
o
+ Yd
+
Yad
reperta: quod omnis radix aequatio cubica deprimibilis) XSc
habeat radicem rationalem.
Nam radix aequationis (ubicae
est: + V: 9+ 1 494 - = p
+
9- 3
V)
quod si ergo deprimibilis est, necesse
est ex his binomiis radicem cubicam
extrahi posse. Extracta autem
cia 
radice fientbinomiutu a + sb
et a - sb. uli quid quorum
summa erit 2a quae erit radix
X. X
rationalis. posito a esse rationalem,
ipsam a autem esse rationalem patet
seriqibus
-
7
9- L
cubrea
+ L
ex e eo quia in binomiis extrudts cabicis unde radio extrahenda est
binomii exsitrahendi
Ccubr
P est quantitas unde radii
extrari potest, nempe ea est.  p, cujus Tadix est = P Ex tali autem binomio
si modo radio extrahi potest, semper una pars est rationalis. Ergo ut
in in additumento ad schotenii lom. in Geom. Cartesi
1
2
r+
+.
27

## Folio 84v — 00068124:0168
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000168.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 3 lines, status machine
FRIED WILHELM LEIBNIZ
eeeeeeeeeeeeeeeeeeeeee
FDERSKCe VSIOOTICK