Pascal's Triangle

In every arithmetical triangle each cell exceeds by unity the sum of all the cells within its parallel and perpendicular rows, exclusive.

Let any cell, U, be taken. I say that U − G = G + B + C + D + J + K + L + M, which are all the numbers between row QRSTU and row ENU exclusive.

N.B. I have written in the enunciation each cell exceeds by unity because the generator is unity. If it were some other number, the enunciation should read: each cell exceeds by the generating number.