of the Binomial Theorem . 
321 
* r -7 -* x r r r +, &c. 
1 1 — r i 2 r 1 — 3 r 
r 2 r 
i+i 3 "+»->• 
X r -~zx r +~x 1 7 fz 2 . 
v + i-r 
— Z X T -f — X — z*x 
n-\-\—zr 
"+1— 3 r 
—— n n — r n 
2 r ~3 - r ■ 
C r X 2 r X - 
3 r * * -+•> occ, 
* + 1 — 2 r 
*+ 1 — 3 r 
T ^ ^ ^ v 
f I z 2 ~ T 1 
X * — — X " X 
2 r -r» • 
K + 1 8 T 
» + 3 ^ 
x T —X — — — ■ X 
r 2 r 
— z 3 # r -f, &c. 
» + i — 3 r 
1 1 — r : 
[ 1—1 2 r ^3 r J- &C 
~ 7 _X T 7 _X ‘ 
3 r 
And' from hence it is evident that these perpendicular lines 
differ from those in the 14th article, in the signs only ; the 
signs in the above being alternately -f and — . It therefore 
may be demonstrated, as in the foregoing articles, that x — zV 
n n n n ** 1 ** 2 
= x T — -ZX‘ 
> x r 3 4-, &c. 
, « — - 1 s ~- 2 
+ 7 x V a ’ 
r X 2 X 
3 
