# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068201:0533
# Permalink to this reading: https://leibnizlegible.com/page/00068201:0533?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 267r, page id 00068201:0533
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 268v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=533
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000533.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 92 lines, status machine
# Lines: 92 recognised, mean confidence 0.75
# 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: the recognised lines in reading order, one per line.

 2m +3 ma t b. m  smn B FI c.
Multiplicetur aequatio 1. per _ m fiet: 2M  ma 2m b m p - 2n 2, 5 mn, + ZC
3
m b - 2n -3mn f c - 4 n3 - snin - 5 mu. et ex collatis valoribus ipsis in, 3, er 4. per,
Am
+bm - 2n m - 3nm ( 2C - 2, 4, n3 - 2, 5mn - 2, 5 mn, adeoque fiet, rursus
M H +bm -em- 2c + 2,4, n =2, 5. mu., huc
3n = 2, 5n
+bm + 2,5 nm + 2A, 13 -2C
274
∞ + 3 n
sive 4 2, 4, bm + 2, 5 N m (+ 2, 4, n) EC H +2 bn - 2, 3 n3(-
22,+
4bm (= 2, 4 n in) - 3, a n m
5
M2,
+2
+a n
+24 no
225..
i 27 4,...
qui rator si in xg. 1. niseratur, fiet
aequatio gradus septimi, sed quae ponendo
210. fiet cubici per quadraticum prri.
Videamus, quid det tifct trium literarum combinatio.
3 nB
Amo) 2m 8un omu iomnum
-6mnv - 4n
B
pt n ne
e
v m
adeoque reducendo fier
v
no m) 12C( 2, 5 m n - 25, n m = 2, 6mnv - 2, 4n
C = 25, B2 V
vn
X
es
f24
e
e
E  d 1 2, 4..
5an
- 2, 5 N V - 2, 5V n
3, + v 7 b, - 3nv-3n m- 22
unde aequando duos ipsius m valores, assurgem ad calculum,
sed nisi fallor nimis prolixum.
Rectius ergo utemur tam pro cubo, quam quo quadrato- quadrato; artificio Tabulae, quae
calculum in fallor contrahit: quam abulum alibi calculatam huc repetert imulile est, ejus ope
autem altiores in fallor potentiae aberunt.
2m 3mnD
p2
b
une fiet, DF
sint datae aequationes duae,
am mnC sit men tix. Mulliplicando aequationem 1per
m n21
fier: 2D + 2E, + 3E (+ O3F) p, bX
bx - 2E ∞2
Bx.
Li
3CX
c = 5E ∞4, sive 4bX - 2C 17+4, 2E
alqvi posita tantum radice bisecta, in in, et n. fiet EH mnx potitoque 2pop, statim obtinebimus 5
desideratum. Cum alioquin longius commode procedi non possit, nisi scribamus: +4 b
unde quadra ado utrobique fiet X
en., at ex aeg. 1. fiet : 2X-
duabus aequationibus tollendo N, fiet atrabique  restabit sola mu
pro quadrato quadrata, hisecando radicem habebimus aequationes:
b
 ima a
ix 1I
Smn m
5
4, 2 mus _X B C.
3,3
D= min 1 b. et collatis utrobiq
n  +6muC
nv m
nn
quae non difficulter invenietur.
n
+3
+ 2c
eritque Mp
2 +3,2,5
fiet m rjb -3
verre
b - 21
-
in