TRIANGULAR NUMBERS, are a kind of polygonal numbers; being the sums of arithmetical progressions, which have 1 for the common difference of their terms.
Thus, from these arithmeticals 1 2 3 4 5 6, are formed the triangular numbers 1 3 6 10 15 21, or the third column of the arithmetical triangle above-mentioned.
The sum of any number of the terms of the triangular numbers, 1, 3, 6, 10, &c. is =
which is also equal to the number of shot in a triangular pile of balls, the number of rows, or the number in each side of the base, being .
The sum of the reciprocals of the triangular series, infinitely continued, is equal to 2; viz.
trionee
Tristan.
that of Ireland, where it had 52; besides a great number of monasteries in Saxony, Hungary, Bohemia, and other countries. The convent of Ceryro in France was head of the order. It is impossible for us to say what is now the state of the order, which can have no visible existence in France, and is probably suppressed even in Italy.