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.
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