This section is from the book "The American House Carpenter", by R. G. Hatfield. Also available from Amazon: The American House Carpenter.

Let A B CD

(Fig. 276) be a rectangle of equal sides, or A £ equal A C and each equal one foot. Then A B multiplied by A C will equal the area A B CD, or 1 x 1 = 1 square foot. Let the line E F be parallel with A B, and midway between A B and CD. Then A B x A E equals half the area of AB CD, or 1 x 1/2 = 1/2. Again; let G H be parallel with E C, and midway between E C and F D. Then EGxEC = 1/2x1/2 equals the area E G CH, which is equal to a quarter of the area

Fig. 276.

A B CD; or 1/2 x 1/2 = 1/4; which is a quarter of the superficial area.

The product here obtained is less than either of the factors producing it. It must be remembered, however, that while the factors represent lines, the product represents superficial area. The correctness of the result may be recognized by an inspection of the diagram.

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