# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00067996:0001
# Permalink to this reading: https://leibnizlegible.com/page/00067996:0001?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 1
# Folio 1r, page id 00067996:0001
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 2v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00067996&page=1
# Source image: https://digitale-sammlungen.gwlb.de/content/00067996/jpgs/default/00000001.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 110 lines, status machine
# Lines: 110 recognised, mean confidence 0.68
# 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.

Septembs. 1614.
in numeris exequenda. Methodus solvendi problenuta
+c
+ c
e
co
(10) co
HI
Lc
4470
t
e- rect.
4 +cy.. appellemus per brachylogiam Z.
1 +  seu X + d+ Ey HZ
Unde ut tollatur Terminus 2du fiet:
Quadrato, quod quadratum, memse pristam
primem aequationis 5. latus, per trachylogiam vocabimus, v.
2
q +9l
+
C+2 -
3l-
a
3
2. 7
2
GI
-et et
3
g 2c et
ad
=f + 2cdl 1 V.
eorqu
4c3f 14a
e =2ec r 7
+ fr- 4cdf + 4C
fiet:
+f4cdf1 400
2e 90 +gl- d 2xe, +f 1cd5 + 4e2d
1
+E
11) Ergo denique A co +CZ
(12)
(3)
+ad.. + qu
Appelleme X +d X +.
Ergo ex Aeq, 2. et 3, fier:
Ergo ponendo
(10)
s
in integris
 + dX +C YX + e y + fy + gl p0. und fier:
(2) . X +dX (+ 4 1 - y - f y -gl
+ cy 1 9 + 2dY
) Et tiet:
2
(8) sive v
XXXV, vol N 1hr.
Aequatio quadratica duarum incognitarum,
acds
(6). Nempe t ponamus:
s
+=
m per brachus lgiam.
ml.
.
  (1)
(4
Ponamus Co ri 2l., et ZH. 7 L, et En d et (15)
e
A
P
(16)
9
em rt
A 5
Namesi Nuneri explicati, co. Z. e.  c. m. sunt interri, divisores aequantur
unitati, et in datis omittentur, in agnotis calculus ostendet omitti debere in fine
si sunt fracti, nominatores corum atque numeratores hac ratione exprimendo,
2 1
omnia ad integros reducemus, et fier ex aeg. 11. sequens
pi
cet a
v
a
 H ~H, sive (18) ~ 235n4 + Lh95i5 3. p 2 p
+ heod
ut
H rSenqu
Hujus aequationis 18 cum ingredientes omnes sint interri, facile
ptre pertes puoinua cigutita mulipes esse heant maguit
1.
a
u
acdF + F
+ qu
-2e +
seu dexterior
Ergo posterior aequationis hujus pars aequatur
f
(1). Eono 
pued
1+C
idea
u
ELELIOLL:5. C. 1
AFCLA
CHANNOVRRa
e
 B.VX