This section is from the book "Constructive Carpentry", by Charles A. King. Also available from Amazon: .
To Construct A Square. (A.) ½ area of a given square. (Fig. 56*.) Given the square a b c d, lay the framing square upon one side, say ab, with equal figures upon To. and Bl., resting upon a and b. Lines drawn along the two edges of the framing square to e will give two sides of a square ½ the area of the given square. Locate f by turning the square around.
(B.) Twice the area of a given square. - (Fig. 57.) The same solution may be applied, by using the diagonal of the given square a b c d, as one side of the desired square.

Fig. 56. - Construction of a Square of one half of the area of a Given Square.

Fig. 57. - Construction of a Square twice the Area of a Given Square.
 
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