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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 3 (shelfmark LH35, 3 B 3)
# Folio 3r, page id 00068253:0005
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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