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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 52r, page id 00068197:0103
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11Y +21 _ + 1ady + 2dZ + 120a = 0
dg 9 + decc
319 +41Z + 31dy+ 41d3+ 340 a =a
d31y + d41 d7
X+ a, X+b, X + C invicem ducenda, fiat X = 10y+ 11: yrs de quaeretur am
formula secund y possit recipere duas radices aequales
2t
a
una radix + 10y + 11a allae seu y +. natat
V
a y +af
11+5
1ota
nam y  
1a +
a et
sit 77 20XX + 20_X + 22, fiat X
= X + aac sit
X = ayy-aac
alia
d
Cy +
11 + F
ab + bF sed haec duo
10+ b non possunt
10 esse aequalur
10 +1 unde  et  forent aequales
et X = V (ayy = aac)
fiet X = 3C 10, 10a vV + 2. 101aa V + 1 11. ad .. v v + 25V + ff)
0v + ia
= aac VV = 2. aac f V = aac ffd
ante omnia tollatur vV, sit 10 = sac et quod si etiam tolli posset V, foret f = Ha= E 11 : ac
p+
5
y =
OV + 2
1+a H sac: C, Ita. Hac et ita in valorers destrueretur v
tam namqus no fieret duca ergo sufficit estiui sumia
is
ostat +2. 40. 1 aas +. 11. a malliplicand per v +f
aa c f  = aacff
(Z.. VV +. v +..
)
10. 11 = cF
Coc pC
fiet . vo +.. v+.. . = co +3 cc01o + 3 aecd tC
a V + 11. 1aa = ac55 si posset esse o
10. 10-aC
vel
10-
8
10. 10 - ac
10. 10. 11. 11) 2. 10. 11 Cf (+ cC55, 
an
10.1 ef2
qu (10.10 -ac) a
+ 21Vac V +. H. 11 a
10. 10 - ac
= II. 1Ia = c ff, 10. 10 = aC = (10. 10. 11. 11a,  11. 11ac
ba
-10. 10 cff accff)
firiet 10. 10ff = 11. Maa = 2. 10. 11a5 = 0 seu 107-1 a
U. Ha - c Quod nonlliet
-2 cf . = c fF divividi polis per v +f. Ergov +-
et foret 11. 11a - cF 3 :, 2. 11 Yac-2Cf. = f
2. I1 Vac - cf
v45
seu foret Una ( cfF) = 2. 11 lac f( csf) et fieet f= 1a: 2 Vac
seu fsret. Il. 11a ( cff) = 2. ilsVaC - (2Cff, et fiet ff = 211 sac f+ 1 11a
= 11. 11 a = 11. 1. a et C = 1 Hac =0 quod non licet
g =  X + a, x+b, XFC, sublato termino sum fit yy=
7l, ZFm
n
Z+ l, 7+ m
23-0 cub (Z +4)
gu = X + bXF abX + bXX + cx + C fiat 99  + y = v + f x +
Eus
2fX = X + bXX
et si veo t fict n t 2 X seu vvt +
+
n. 11. aa - ac f
et
X
dividi dedit per