Page:The Elements of Euclid for the Use of Schools and Colleges - 1872.djvu/245
|BOOK XI. DEFINITIONS||221|
9. A solid angle is that which is made by more than two plane angles, which are not in the same plane, meeting at one point.
10. Equal and similar solid figures are such as are contained by similar planes equal in number and magni- tude. [See the Notes.]
11. 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.
12. A pyramid is a solid figure contained by planes which are constructed between one plane and one point above it at which they meet.
13. A prism is a solid figure contained by plane figures, of which two that are opposite are equal, similar, and par- allel to one another ; and the others are parallelograms.
14. A sphere is a solid figure described by the revolu- tion of a semicircle about its diameter, which remains fixed.
15. The axis of a sphere is the fixed straight line about which the semicircle revolves.
16. The centre of a sphere is the same with that of the semicircle.
17. The diameter of a sphere is any straight line which passes through the centre, and is terminated both ways by the superficies of the sphere.
18. A 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 cone ; and if greater, an acute-angled cone.
19. The axis of a cone is the fixed straight line about which the triangle revolves.