64 SQUARE NUMBEBS.
anihmetical stadies, he must take for granted that they are of some use. The very Table about which he has been rea- soning poesesses a special name — it is called a Table of Tri- angular Numbers. Almost every general collection of Tables hitherto published contains portions of it of more or less extent
Above a century ago, a volume in small quarto, containing the first 20,000 triangular numbers, was published at the Hague by E. De Joncourt, A.11L, and Professor of Philosophy * I cannot resist quoting the author's enthusiastic expression of the happiness he enjoyed in composing his celebrated work :
« The Trigonals here to be found, and nowhere else, are
- exactly elaborate. Let the candid reader make the best
- ' of these numbers, and feel (if possible) in pemnng my work
- the pleasure I had in composing it"
- That sweet joy may arise from such contemplations
- cannot be denied. Numbers and lines have many charmsy
- unseen by vulgar eyes, and only discovered to the unwearied
- and respectful sons of Art In features the serpentine line
- (who starts not at the name) produces beauty and love ; and
- ' in numbers, high powers, and humble roots, give soft delight
Lo! the raptured arithmetician! Easily satisfied, he ^ asks no Brussels lace, nor a coach and six. To calculate,
- ' contents his liveliest desires, and obedient numbers are
'< within his reach."
I hope my young friend is acquainted with the &ct — ^that the product of any number multiplied by itself is called the square of that number. Thus 36 is the product of 6 multi- plied by 6, and 36 is called the square of 6. I would now recommend him to examine the series of square numbers
1, 4, 9, 16, 25, 36, 49, 64, &c.,
- ' Oii tbe Nature and Notable Use of tho most Simple Trigonal NUm-
ben.' By E. De JoAoourt, at the Ha^ie. 1762.