The Complete Works in Philosophy, Politics and Morals of the late Dr. Benjamin Franklin, Vol. 2 [of 3]

By Benjamin Franklin

Page 254

bent row of 8 numbers, ascending and descending
diagonally, viz. from 16 ascending to 10, and from 23 descending
to 17; and every one of its parallel bent rows of 8 numbers make
260.--Also the bent row from 52 descending to 54, and from 43
ascending to 45; and every one of its parallel bent rows of 8 numbers
make 260.--Also the bent row from 45 to 43, descending to the left,
and from 23 to 17, descending to the right, and every one of its
parallel bent rows of 8 numbers, make 260.--Also the bent row from
52 to 54, descending to the right, and from 10 to 16, descending to
the left, and every one of its parallel bent rows of 8 numbers make
260.--Also the parallel bent rows next to the above-mentioned, which
are shortened to 3 numbers ascending, and 3 descending, &c. as from
53 to 4 ascending, and from 29 to 44 descending, make, with the two
corner numbers, 260.--Also the 2 numbers 14, 61 ascending, and 36,
19 descending, with the lower 4 numbers situated like them, viz. 50,
1, descending, and 32, 47, ascending, make 260.--And, lastly, the 4
corner numbers, with the 4 middle numbers, make 260.

[Illustration:

_Plate XI._ _Vol. II. page 327._

_A Magic Square of Squares._

_Published as the Act directs, April 1, 1806, by Longman, Hurst, Rees
& Orme, Paternoster Row._]

So this magical square seems perfect in its kind. But these are not
all its properties; there are 5 other curious ones, which, at some
other time, I will explain to you.

Mr. Logan then shewed me an old arithmetical book, in quarto, wrote,
I think, by one Stifelius, which contained a square of 16, that he
said he should imagine must have been a work of great labour; but if
I forget not, it had only the common properties of making the same
sum, viz. 2056, in every row, horizontal, vertical, and diagonal.
Not willing to be out-done by Mr. Stifelius, even in the size of my
square, I went home, and made, that evening, the following magical
square of 16, which, besides having all the properties of the
foregoing square of 8, _i. e._ it would make the 2056 in all the same
rows and diagonals, had this added, that a four-square hole being cut
in a piece of paper of such a size as to take in and show through it
just 16 of the little squares, when laid on the greater square, the
sum of the 16 numbers so appearing through the hole,

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