My four Sons and two orphan Grandchildren had retired to their
several apartments; and my wife alone remained with me to see
the old Millennium out and the new one in.
I was rapt in thought, pondering in my mind some words that had
casually issued from the mouth of my youngest Grandson, a most
promising young Hexagon of unusual brilliancy and perfect angularity.
His uncles and I had been giving him his usual practical lesson in
Sight Recognition, turning ourselves upon our centres, now rapidly,
now more slowly, and questioning him as to our positions; and his
answers had been so satisfactory that I had been induced to reward him
by giving him a few hints on Arithmetic, as applied to Geometry.
Taking nine Squares, each an inch every way, I had put them together
so as to make one large Square, with a side of three inches,
and I had hence proved to my little Grandson that--though it
was impossible for us to SEE the inside of the Square--
yet we might ascertain the number of square inches in a Square
by simply squaring the number of inches in the side: "and thus,"
said I, "we know that three-to-the-second, or nine, represents the
number of square inches in a Square whose side is three inches long.
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