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6. Cut off a square, (fig. 2.)
If the great square and one of the small ones be given, it is easy to find the size of the other.
First draw the great side, then the semicircle, then draw from either end of the great side, (which you will notice is the diameter of the semicircle) a cord of the semicircle, which is equal to a side of the given small square. The other cord which will finish the right angled triangle, is the side of the square required.
7. Take the half of a square. (fig. 3.)
A perpendicular to the middle of the long side, will strike the semi-circle, and a cord from this point of intersection to either end of the diameter or long side, will give the side of the square, half as large as the great square.
8. Make a graduated semicircle, usually called a Protracter. (fig. 4.)
By general consent a circle is divided into 360 equal parts, called degrees. A semicircle of course contains 180 degrees, that is, half of 360.
After having drawn a semicircle and its diameter, draw a perpendicular radius. This radius forms a right angle with the diameter, and cutting the semicircle in two equal parts or quarters of circles, leaves 90 degrees for each of them. If 90 degrees of a circle make a right angle, 45 degrees will make half a right angle, &c.
