CONTAINING THE 4TH, 5TH, 6тн, 11тн, & 12TH BOOKS. London: JOHN WEALE, 59, HIGH HOLBORN. 1855. 183.c.6. PREFACE. IN presenting to the public the Second Volume of Euclid's Elements, the Author feels that some explanation is required. for the interval which has elapsed since the publication of the former volume. He feels that it will be only necessary for him to state that the work has been written in the intervals snatched from his professional duties, which have occupied so considerable a share of his time as to leave him no choice between delaying the publication, or hurrying it forward in an imperfect form; and he felt that he would best promote the interests of the public, as well as his own reputation, by the adoption of the former alternative. 15, ESSEX STREET, STRAND. 15th May, 1855. H. L. THE ELEMENTS OF EUCLID. BOOK IV. DEFINITIONS. 1. A rectilineal figure is said to be inscribed in another rectilineal figure, when all the angles of the inscribed figure are upon the sides of the figure in which it is inscribed each upon each. 2. In like manner, a figure is said to be circumscribed about another figure, when all the sides of the circumscribed figure pass through the angular points of the figure about which it is circumscribed, each through each. 3. A Rectilineal figure is said to be inscribed in a circle, when all the angles of the inscribed figure are upon the circumference of the circle. 4. A Rectilineal figure is said to be circumscribed 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 rectilinear figure, when the circumference of the circle touches each side of the figure. 6. A circle is said to be circumscribed about a rectilineal figure, when the circumference of the circle passes through all the angular points of the figure about which it is circumscribed. 7. A straight line is said to be placed in a circle, when its extremities are in the circumference of the circle. оо B |