F. H. Richardson's bluebook of projection (1935)

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704 RICHARDSON'S BLUEBOOK OF PROJECTION The area of a circle is equal to the square of its radius (half its diameter) multiplied by 3.1416, or to the square of its diameter multiplied by 0.7854. ^ Regardless of its size every circle is divided into 360 degrees, hence the width or length of .one degree of any circle is equal to its circumference divided by 360. The diagonal of any square is equal to one of its sides divided by 1.4142. Fractions It very often is necessary to add/subtract, multiply or divide common fractions. Rare necessity for them makes one frequently unfamiliar in an emergency. The operations are as follows : _ To add two fractions, as 1/2 plus 1/3, it is first necessary to reduce them to a "common denominator/ which is done by multiplying both the numerator and denominator of each fraction by the denominator of the other fraction, thus: / 1X3 \ = 3/6 V2X3 / and 1/3 multiplied in the same manner by 2, the denominator of the other fraction equals 2/6 #1X2 m V3X2 6 / and 2/6 + 3/6 = 5/6 . Any two fractions may be added in this way. To subtract one common fraction from another, proceed in exactly the same way as in addition, except that you subtract the smaller numerator from the larger, after having reduced them to a common denominator of course. To multiply two common fractions, you merely multiply one numerator by the other and one denominator by the other, thus: 11 IX 1 i — X — equals = — • 2 4 2X4 8