Page:Passages from the Life of a Philosopher.djvu/70

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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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