## The Essentials of Geometry (solid) |

### From inside the book

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**cube**( § 474 ) whose edge is some linear unit ; for example , a cubic inch or a cubic foot . 465. Two solids are said to be equivalent when their vol- umes are equal . PRISMS AND PARALLELOPIPEDS . DEFINITIONS . 466. A prism is 273 ... Page 275

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**cube**is a rectangular parallelopiped whose six faces are all squares . PROP . I. THEOREM . 475. The sections of a prism made by two parallel planes which cut all the lateral edges , are equal polygons . D F E C F E of prism AB . Given ... Page 284

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**cube**whose edge is the linear unit , and the unit of surface the square whose side is the linear unit . ( Compare § 306. ) 494. Cor . I. The volume of a**cube**is equal to the**cube**of its edge . 495. Cor . II . The volume of a rectangular ... Page 285

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**cubes**, each equal to the unit of volume . Thus , if the dimensions of rectangular parallelopiped P are 5 ...**cube**whose edge is 34 in . 7. Find the area of the entire surface of a rectangular parallelo- piped , the dimensions ... Page 289

... . 4 15. Find the length of the diagonal of a rectangular parallelopiped whose dimensions are 8 , 9 , and 12 . 16. The diagonal of a

... . 4 15. Find the length of the diagonal of a rectangular parallelopiped whose dimensions are 8 , 9 , and 12 . 16. The diagonal of a

**cube**is equal to its edge multiplied by √3 . PROP . XIV . THEOREM . 507. In a regular PYRAMIDS . 289.### Other editions - View all

### Common terms and phrases

ABCD Algebra altitude approaches the limit area ABC axis bisecting centre cents circle circular cone circular cylinder circumference circumscribed cone of revolution conical surface convex polyedron cube cylinder of revolution diameter diedral angle distance Draw lines entire surface equal parts occur equal spheres equally distant Find the area Find the volume frustum Geometry Given line given point homologous inscribed intersection lateral area lateral edges lateral faces lateral surface line drawn lune O-ABC parallel planes perimeter perpendicular plane determined Plane Geometry plane MN pole polyedral angle proof is left PROP Prove pupil radii radius rectangular parallelopiped regular polygon respectively sector sides slant height solid Solid Geometry spherical angle spherical polygon spherical pyramid spherical triangle straight line tangent tetraedron THEOREM total surface tri-rectangular triangular prism triedral vertex vertices Wells's Whence