No. LXXXIX.—CUT OFF THE CORNERS

A very simple rule of thumb method for striking the points in the sides of a square, which will be at the angles of an octagon formed by cutting off equal corners of the square, is to place another square of equal size upon the original one, so that the centre is common to both, and the diagonal of the new square lies upon a diameter of the other parallel to its side.

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No. XCIII.—MAKING MANY SQUARES

The subjoined diagram shows how the two oblongs, applied to the two concentric squares, produce 31 perfect squares, namely, 17 small ones, one equal to 25 of these, 5 equal to 9, and 8 equal to 4.

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No. XCIV.—CUT ACROSS

The Greek Cross can be divided by two straight cuts, so that the resulting pieces will form a perfect square when re-set, as is shown in these figures:—