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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 115ar, page id 00068124:0231
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Binomia cubica
imaginariis
+34 f 2 Cabice aequ c a + s-b cubire aequ. a134d- b- 2
mixta; an ab illis liberanda
vide altera pagina
sub finem
estenor in
calculo
datur. (2 
3a
seu aequ +a + 3a Y- b
3ab
+ N- e
sit C aequ f2 et fet fb
erit: f aequ 3 a - b. et b b aequ C
et
3a- b b aequ C. Hinc
Ars inventendi haec, ut
l et s-e sic tractemus  ut si
Addanturs  a - 6 ab +9 a b n 9a qu +1
a +b
1
a19 ab2 - 6ae b1 + 16
a + 3ab + 3a b + 1.
datur et + a 3- 3ab, l. et 3a p. b  e Eagu
a- ab riag.
ero 4 abn. _ ag. 1
lam
aequ+e
+haet hb a aqu n a 9
m..
tu
oriatuo
1 a + b aequal. dato 9
maedmba aequ n
et ordinando tha F h
+a - 3ab. aequ. -
ql
+ 3a b - b3 y5.... e
a- b aequ +a 211C
+bs
a +b aequ g
Ergo 2a aequ a ve +b (C + 24
a- Site Ergo 2a aequ. 2a stre t 9 
seu a = ea Ite aequ 94 -= 1te
+
equ. l’+e.
te
Y Pte
quod si ergo l+e p 27 l+e + ile func videtur
res proddere
Re sumamus:
64
a + f- b13 aequ. + a + 3a s- b aequ  fa p+ 3aG.
aequ ila
Sit satum binomincus.
in stnte
- 3ab
3ab = b2 S-1 3ab - b35
+3ab7 - Y
+ C u- 1
ab F video nullo modo uliliter componi l et e.
a + b+ ab ad extrahenda radicem: illud tum patet +a - b +3ab - 3 ab divid.
qu l+ e dividiposse per a - b. item a + b = 3ab- 3ab divrdi posse per aut
Ergo tre 1tC d
a +
et pa
abtab
ja
aequ a +b +2ab
Porro etsi in ipsis  eti
ura le
l- C
- 3 ab) aequ a +6 - 4ab 2. Ergo He +  aeqo2 aerib
aqu a +b- ab
et 
a b Vaequ.aerb taab
a- b a +b
ji item alaaLa
uro 1. er9- 1oa b Aba t ( b + be sin ralriber abelia
sei altbe aequ. ~- b+
e compositis es non sicedat succedet Tamem
dni eorum quadratis compositis. nam verum est et maner a4b aequl40
Ergo: al +be aqu. ga - gb. et  ab aqu al +be. Gui 24 ag altbe
qua l e g aequ 9 - 16ab
al+bE SCo YC
a + b aequ. 94 pelmlanu
2b aequ g- al-be. raaqu  al. be distaliibe
baqu.
pasma rersu
b
+a +ab. 7 ab F
a +b + ab
O
ab
et l-e
e ab
tab +ab
ta