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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 90v, page id 00068195:0180
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 91r); this page is its left half.
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# Lines: 57 recognised, mean confidence 0.83
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10
Hinc dalis d, seu l, et dato D seu l+.. Pm dabitur etiam 1m
8
s
13
10
110
tandem dato E, sen l +..  n +. l m +. l nn +.. l’m’np, dabitur et emin.
a Tabilis
e
110 10
e
2
tis
Hinc tandim habitis l. Um, emn en datur l siven
sive n, sive p, per aequationem quarti gradus. Ex curus radiu
qualibet extrahendo radicem surdesolidam habetur L, vel m, vel n vel p
ita
Habeturque X seu l+ m + nF p, pure
16
20 
85
36 152
ita haec hypothesis suffint satis facit etiam alterio
semper-
ypothesi quam ratum consentaniam judicavi, ut radix su aequationis
turde solidae sit composita ex trabus quatuor radicibus aequationis
biquadrabicae, sunde solide extractis uti cubia componitur ex
duabus radicibus aequationis quadhatice cubice extractis, aliquid ifficiat rationale
ieu ethesis ridetur valie rationalis ut ip  irma nulla ex l, A
Ex act legitus combinatoriis a me dudum constitutis, 
exquirantum
posito X =  e l calculo expiruantur coefficientes ipsorm
20
(5, 1 m, l, etc. in valoribus XE, X, X, X
ut habeamus
quantitates O D, 0, 8.
Hinc jam ponendo B in n, p, etc = a + b + c + d
habemus a = O, hinc O = E +2 ab O = a + 3 ab +6 abc et
quas aequationes
34- a + 4~b + 6a b + 12 abc + 24 abcd
itas nunc aequationes conjungendo cum priribus .... = d
conju
= et ... = 9, habebitur a seu , et ab seu Vm, et abc seu Vm
et denique  abed seu lmErp
 leren
 In Aequatione cubica X = l + M
ib . sit aequatio X + gX + Y = 0 Cuit in X rationale nihil
In Xx rationale est sum Radices aequationis sunto X, E,  Aabemus X + Y
20
Ex=1
fiet XX = 00 +2 seu Xx = 29
habemus et Z XE seu X3 + xP +E∞ = q
et X3 = 6 + 309 + 6Y ergo X = bY. Erga in XX est rationale 24 seu 4, et
icex quia ergo in XX + ZZ + ∞x = 29, et quoad partem rationalem suam
quaelibet quantitas ex istis trebus, XX, _, xx se habet eodem modo, hinc pars rationalis
posp