## The Essentials of Geometry (solid) |

### From inside the book

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**altitude**is the perpendicular distance between the planes of the bases . 467. The following is given for convenience of reference : The bases of a prism are equal . 468. It follows from the definition of § 466 that the lat- eral edges ... Page 276

... have equal bases and equal

... have equal bases and equal

**altitudes**; for by inverting one of the prisms if necessary , the equal faces will be similarly placed . 479. Sch . The demonstration of § 477 applies without 276 SOLID GEOMETRY . - BOOK VII . Page 277

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**altitude**a lateral edge of the oblique prism . Ľ G E ' H ' B C ' L F G K E H B C Given FK ' a right prism , having for its base FK a right section of oblique prism AD ' , and its**altitude**FF " equal to AA ' , a lateral edge of AD ... Page 279

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**altitude**AA ' , and ACD - A ' is a right prism whose base is EGH and**altitude**AA ' . ( § 480 ) But these right prisms are equal , for they have equal bases and the same**altitude**. ( § 478 ) .. ABC - A ' ≈ ACD - A ' . PROP . VI ... Page 280

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**altitude**. PROP . VII . THEOREM . 486. Two rectangular parallelopipeds having equal bases are to each other as their**altitudes**. Note . The phrase " rectangular parallelopiped " in the above statement signifies the volume of the ...### 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