# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00067996:0017
# Permalink to this reading: https://leibnizlegible.com/page/00067996:0017?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 1
# Folio 9r, page id 00067996:0017
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 10v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00067996&page=17
# Source image: https://digitale-sammlungen.gwlb.de/content/00067996/jpgs/default/00000017.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 49 lines, status machine
# Lines: 49 recognised, mean confidence 0.84
# 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.

X + iBx + bx _ -
X + dX + ab -
ay r0
Satet op hasduas aequationes facile
esse resolubiles, sed jam alias
ex ipsis faciamus: componendo fiet:
Ergo X + bB y
Ergo V ⊓ X +d X + ab
Ergo Xp, X + dX
Ergo X Y) a - d
multiplicemus quamlibet ex ipsis per arbitraliam, fiet.
B X + 2 B bx + b B - y β 0
VX + VdX +Vab - Vay.
Conjungendo fiet aequatio talis.
c
= V + 2βb X - 7 a ys.
+ Vd
)+Vab
Esto jam aequatio data huic factitiae similis:
Y + MX + n X + py + ql 10.
conferendossheminos terminis respondentes quaeratur valor ipsarum.
(3. Y. b. d. a. ante on
Na e P. Ergo
N m. Ergo
P
3)
p
m
Ergi
am
D+
l-mp
+ dl-dm p C
sive
ent
dm dl ut
b Restat ultima aequatio
sed quae exitum universalem nega
quia b assurgit ad quadratum
Obiter annoto cum no
non nisi semel duae aequationes conjunguntur
sufficere unam multiplii, et artitrariam qua altera multiplicatur
superfluam esse, ut hoc loco patet, Rati est quia duae arbitraariae
tractari possunt instar ductum numerorum ac proinde intelligi possunt
se metiri, ponendo ergo Vp 55. p
Patet totam aequationem
dividi posse per β3. et solam  ex arbitr arii usauz. Verte,
b - ut
1- m