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# Catalogue record: 41839 — De Ambiguorum valorum expressionibus generalibus
# Incipit: Si x=a vel x=b fiet x-a=0
# Date: 1698-04
# Akademie-Ausgabe: AA VII (assigned, not yet published)
# Other printings: Couturat, Opuscules, 1903, S.574.
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=41839&katnr=39119
# Work: https://leibnizlegible.com/work/00068253
# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 3 (shelfmark LH35, 3 B 3)
# Folios: Bl. 3 (from the shelfmark LH 35, 3 B 3 Bl. 3): 2 pages, canvases 5–6, page ids 00068253:0005 to 00068253:0006
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068253&page=5
# Lines: 62 recognised on 2 of 2 pages, mean confidence 0.80
# 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.
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# 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 3r — 00068253:0005
# Source image: https://digitale-sammlungen.gwlb.de/content/00068253/jpgs/default/00000005.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
De Ambiguorum valorum expressionibus generalibus
1
si X = a vel X=b fiet X - a = 0 vel x - b = 0 ergo ductis duobus in se
invicem utrobi utrique aequatio; satisfaciet aequatio X a+ ab XX - a X + ab =0
Hinc extrahamus radicem, ut valorem rum uiq ambignitati seu utrique casui satisfacientem
inveniamus, fiet XX - aX + haa + Zbb + ab = Zaa +  bb (  ab ( ab) = 0
seu fiet x = 5 a + b + L a - b seu X = Z, a + b + a - b. sive erit
si quantitas (X) habeat duos valores disjunctivos,  (ut valeat
jui
aut a aut b;) erit valor generalis ipsius (X) conflatum ex summa
et residuo duorum valorum dispunctiporum. seu q
ambiguae valor communis duobus valoribus disjunctivis
est summa ex summa et residuo duorum valorum disjunctiborum
Hinc jam procedi potest ad valores disjunctivos tres, et quatuor, et
plures Nam valor communibus ipsie Nam x valeat a vel b. vel C
et valor communis ipsius a et b sit l, quaeritur valor communis ipsis
et C  et fiet X = = IFC  (+)+ IrC. Et
X = 4 a +bC
seu X =
a - b + Lc
a + Z a (+) qa (+
4b
3C
4 Zb
LC
+
4
La
(7) 2 a +b (+) + L a - b (
si ++
Se + 2+
fit
1LC
1si t-, si 4--
unde is est valor aequationis factae ex X -a, X - b, X-L, X- c =o. Ita ut
esa
evera
sint 4 casus, et c occurrit bis; et a quidem ac b se habent eodem modo, sed non 
xedC a+b-cona hec vel a+ b -c
Quod si vellemus omnia tria se habere eodem
ut c. 
modo esset n adt hibonda aquatio cubica X- a X2 + ab X - abc =0
atb+c
ac
quae ex pegulis cubicae aequationis resolvenda est, quia hoc casu oporte
ut habeatur
extractio; etsi interveniant, imaginariae in speciem. Et sic pulo haberi
posse expresionem generarem Triplecis ambignitatis. Quin et simpliter sed
quadruplicem molenietur ope aequiq biquad palicarum resolutarum
Et videndum an mon sic appareat processus in infinitum
pro embigulit
quantum libet multiplicata. Qui deinde fortasse et lucemprae=
hoec
beret, pro radicibus irrationalibus altioribus
resolvatur
actu ipso

## Folio 3v — 00068253:0006
# Source image: https://digitale-sammlungen.gwlb.de/content/00068253/jpgs/default/00000006.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 6 lines, status machine
1
e
nu  s
t
ui
1