Pascal's Triangle

(Playground)

2nd Consequence

In every arithmetical triangle each cell is equal to the sum of all the cells of the preceding parallel row from its own perpendicular row to the first, inclusive.

Let any cell, T, be taken. I say that it is equal to J + K + L + M, which are the cells of the next higher parallel row from the perpendicular row of ω to the first perpendicular row.

This is evident if we simply consider a cell as the sum of its component cells.

Next :: (3rd Consequence)
1
2
3
4
5
6
7
8
1
G
1
B
1
C
1
D
1
E
1
F
1
H
1
I
1
2
J
1
K
2
L
3
M
4
N
5
O
6
P
7
3
Q
1
R
3
S
6
T
10
U
15
V
21
4
W
1
X
4
Y
10
Z
20
AA
35
5
AB
1
AC
5
AD
15
AE
35
6
AF
1
AG
6
AH
21
7
AI
1
AJ
7
8
AK
1