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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 10r, page id 00068195:0019
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X
Tabula Binomialis
sit X = a + b. Erit
X - a- b = 0
XX - aa - bb = 2ab
X - a - b3 = 3 ab7
N - at - b = 4 ab XX - 2aa bb
X - a = b = 5abX = SaabbX
X = a - b =6 ab X  - 9 aabb. XX + 2a13
X = a - b = 7ab X - 14 aabbX + 7 a b X 
28 - a - b = 8abx - 20 aabex + 16a b xx - 2 a 
X = a) - b7 = gab X - 27 aabbX +30ab x - 9ab
Xo - a - bo = 10 abX - 35 aabbx + 50ab x - 25 a6 x + 2 ab
X = a = b = 1abX -Aa abbX +77abX - 55abX +mabx
 - a - b2 = 12 abX - 54aabbX +I2abX -105 ab X +36abXX = 2ab
Et ita
porto
quaecungue
Esto jam proposita atequatio quae Tritermina gradus imparis
Tritermina, carens termino  secundo 
exempli gratia X +  hqur
sit sequatio X 
sit aqualio X a  r XX  t sumanti
Ponatur X = arbre et sit ab+ ac + bc = 0 fiet c = -ab:, atb
fiet a+ be  XS + sabc XX = a - V+ C = 0 fiat abc= r
et a + b + C L +5, sit at
Z et ab =hv, per
d 1et 6 fiet Hlivo = (13Z
Curjus per 3 et 2 est a + b + r (. k N) = 1
a a + 65 = Z - 5 Z hV + 5Ztlivo = - Y (. k v) + +5
(.  -(o: pes) p1o + 5(K: 19) V h  5 (hk: B3) vellivB = - r (:R v ) + F
seu X. k y
HB) V 5h
a v5 p2 V7
= v + V
ab + ac + bE quaerantur et his, quia ab 20 + atbr cx
fiet = (sabC  aabbec set ab + a c + b = - 5a b’ c X
ab cct
sit jam a+ b+c = t, fiit a a
si esset abc = r, fieret ab ac + b  = r X
et C5 = r X - a b:, a + b = r: ab
+V XX = + t5 Xx = l - a u b5)
tu
= 5 abc
=abrC
r- sabe
arsabe
Hanc aequationem ita divellamus: sit
sit aequalio data X + Y XX = f. faciamus
X = a +b+C sd ab tact be =0 fiet X + Sabc XX = a +b +C
et proinde sollendo es fiet 4hXX + - pex = a = sabeXX
seu XX = t - N, :, r - sabe Aursus est x = ab: 10 abc
ergo xx = qu’ a = t a haec aquatio divellenda in
100 a b r - 5abc
tres, ita ut s habeantur a ab, et abc et ita
solutio propositae q aequationis est in potestate. idem
eris in cquatione tritermina quacunque
ab + ac + b = ab + E (a rb)
3b (V, ab) abs  = ab
ssarb Pessanb)
atbu v
ab + ac + bc = 0 c = - ab:, a +b,
abc = ab a b: (5) (a +b) - Alb datue, 95
a + b = dato S B et ab: qu () (a + b) -9
qu 1d a +b) = ars Av ab - gabo = v
a 4 a  b
a: (rb)
ab = v = 9
Si + sab 2 4idos
de B
3
118 a vi9s ib- absiem
ser (1 - 99) ab = ab f + 59
 abtactbe = 0 -  V
abeZ. ab
Erpo ab = D - 5 a a saitut sitp
Ey. si P =0. fit
Gab. de aabe - 5. ab 
BE. al t abe
a b = - 10 ab8X seu p - à b, : 10 ibc
qusà b) r = Sabe qu (a 6) = 10a bE 1 - 1ooabé a
Squ (a. 13 = 19 abet qu (aebJ: abc =- 2 +5
qu. (a b) : abc = = 100 abc. a: r3
igitur 100 abc a = 2 l
a c = - ab :, a +b
qu (ae b + (a + b5) al
() Cat 6)
(r= 3 ab ) 100a V ab, t3
Q sarb))
a1b
F larb)
(at b)
 ab ap
atb = V atb - Z ab = W01o
1+ 3, r -  5u= 100 Wu, 1 - v - v
si arbre. e 10 X +V, YZ. si B 109 10, l5- Y 10
erit arb = t’4
sd
e Fiaib
~ B t B
beo v = 2- 5101Z +5
12 rZC mq 
pee
d 
int
eee
tou