# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/175905688X:0091
# Permalink to this reading: https://leibnizlegible.com/page/175905688X:0091?run=74
# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 69, page id 175905688X:0091
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=91
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000091.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
# Lines: 45 recognised, mean confidence 0.82
# 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.

IC la
ce
LInCaMC
DEOPOTI
2
L IBE R T E R F F e 5.
construendo Problemate aliquo per genus linearum
simplicius, quam nacura ejus permittie, deludaret.
Duocirca ut hic adducere possim resulas qualdam, Denacura
GuiDUS UEFII GHC DCCCAEII CVIECEUF, Opus CAt, ut in sC- Equario
nere aliquid dicam de natura sEquationum; hoc est.
desummis, quae ex pluribus cerminis sunt compoltae,
partim cognitis, partim vero incoonicis, quorum alii
aliis sune aequales, vel potius, qui omnes simul consi-
derati nihilo sunt aequales. Ouippe Exepe praectat illos
hac ratione considerare.
Sciendum itaque, quod incognita quantitas in qua- Quor habe-
libet Equatione, toc diverlas radices seu diverlos va ripossinera-
lores habere postic, quor ipsa habet dimentiones. Nam qualibet s
A, exempli gratia, x supponatur aequalis 2, Teu X = 2 quatione.
aequalis nihilo; _ TULLUS X ∞ 3, TCW X = 3 ∞ O; _ MUI-
ciplicetuE N = 2 ∞ O PCF N - 3∞ O: habeDIEUE X X -- 5 X
f 6∞ 0, TCUXX ∞ 5 X = 6. Qua AEquatio est, in qua
Quancitas x valet 2, ex praeterca etiam 3. Ouod sIruI-
lus AaEN ∞ A, aFquCx = 4 ∞ O multiplicCEUE PCL N N-
SN. F 6∞ O, PEOdUCCTIE X3 - 9 X X -1- 26X - 24X0.
qua alia est AEguatio, in qua x habens eres dimentio.
nes, tres quoque habet ralores, qui LunE 2, 3, e4.
Verum (xepe accidic, quod quaedam harum radicum
t
linctallae, seu minores quam nihil: UE, (I SUPPONaEUE X Duenant
delignare quoque defectum alicujus quantitatis, UE. Sine falsa
Duta 5, ita uchrabeatur x- f. 5 ∞0, quae multiplicata per
X3 = 9X N - f - 26X = 2 4 ∞ 0, TaCIaC Xt = 4 X3 = Z9X X
106X = 120∞ 0, PrO SEquationC, in qua QLLaLLIOF
CunEradices, niMIFUI EECS VerX, QuX LLINE 2, 3, ex 4, 2F
Quc una Falla, guae CAt 5.
racices.
Inde liquido constat, quod Aquationis summa, n
oux plures radices continet, dividi semper postic Per posstamen
binomium, quod compolicum cA ex quantitace inco- sionumnu-
Enita, merus ali-
num.
aices in
diminui