Elements of Plane and Solid Geometry; And of Plane and Spherical Trigonometry; To Which Is Added Mensuration, Surveying, and Navigation - Softcover

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1867 edition. Excerpt: ...same point (Dem. 1), and the first two not parallel, which is contrary to the supposition. Again, as every two of these lines of intersection are lines of the same plane, and can not meet, therefore they must all be parallel to each other. SOLID GEOMETRY. BOOK VII. DEFINITIONS. 1. Similar solid figures are such as have all their solid angles equal, each to each, and are contained by the same number of similar planes. 2. A pyramid isra solid figure contained by planes that are constituted between one plane and one point above it, in which they meet. 3. A prism is a solid figure contained by plane figures, of which two that are opposite are equal, similar, and parallel to each other, and the others are parallelograms. 4. A sphere is a solid figure described by the revolution of a semicircle about its diameter, which remains unmoved. Thus the inner side of the semicircle revolving round the diameter, which remains fixed, generates a sphere. 5. The axis of a sphere is the fixed right line about which the semicircle revolves. 6. The centre of a sphere is the same with that of the semicircle. 7. The diameter of a sphere is any right line which passes through the centre, and is terminated both ways by the superficies of the sphere. 8. A right cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which side remains fixed. If the fixed side be equal to the other side containing the right angle, the cone is called a right-angled cone; if it be less than the other side, an obtuse-angled; and if greater, an acute-angled cone. Thus the side AC, revolving round AB, one of the sides which contains the right angle and remains fixed, generates a cone. 9. The axis of a cone is the...