ARITHMETICAL

The name given by Pascal to a table of certain numbers disposed in the form of a triangle. The first vertical column of the table contains units only; the second contains the series of natural numbers; the third the series of triangular numbers; the fourth the series of pyramidal numbers; and soon. (See FiGURATE Numbers.) Thus — 1 2 3 1 3 4 6 4 1 5 10 10.") I 6 15 20 15 6 1 . . . . . . Any number in the table is obtained by adding the number next above it, in the same column, to the number in the same line in the next preceding column; and it will be observed that the oblique diagonal rows, beginning at the left and descending towards the right, are the same as the vertical columns. One of the properties of the table is, that numbers taken on the horizontal lines are the coefficients of the different powers of a binomial. For the description and uses of the table, see the Introduction to Hutton's Mathematical Tables. [s. 1270]