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Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: BOOK IV. DEFINITIONS. 1. A RECTiLnfEAL figure is said to be inscribed in another rectilineal figure, when all the angles of the inscribed figure are on the sides of tlio figure in which it is inscribed, each on each. 2. In like manner, a figure is said to be described about another figure, when all the sides of the circumscribed figure pass through the angular points of the figure about which it is described, each through each. 3. A rectilineal figure is said to be inscribed in a circle, when all the f angles of the inscribed figure are on the circumference of the circle. 4. A rectilineal figure is said to be described about a circle, when each side of the circumscribed figure touches the circumference of the circle. 5. In like manner, a circle is said to be inscribed in a rectilineal figure, when the circumference of the circle touches each side of the figure. 6. A circle is said to be described about a rectilineal figure, when the circumference of the circle passes through all the angular points of the figure about which it is described. 7. A straight line is said to be placed in a circle, when the extremities of it aro in the circumference of the circle. PROPOSITION 1. PROBLEM. In a given circle, to place a straight line, equal to a given straight line, which is not greater than the diameter of the circle. Let ABC be the given circle, and D the given straight line, not greater than the diameter of the circle: it is required to place in the circle ABC, a straight line equal to2. Draw BC, a diameter of the circle ABC. Then, if BC is equal to D, the thing required is done; for in the circle ABC, a straight line is placed equal to D. But, if it is not, BC is greater than D. [Hypothesis. Make CE equal to D, [I. 3. and from the centr...