## Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry and Mensuration. Accompanied with All the Necessary Logarithmic and Trigonometric Tables |

### From inside the book

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**altitude**or height is the common perpendicular to these bases , of which one is called the inferior or lower base , and the other the superior or upper base . In the rectangle , two consecutive sides form the base Definitions. Page 88

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**altitude**, are equivalent . We will suppose the one L F / D I E ' CF figure placed upon the other , so that their inferior bases , which are equal , may coin- cide . Let ABCD be the L B E L ' first parallelogram , and ABEF or ABE'F ... Page 89

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**altitude**. Two rectangles of the same base and the same**altitude**are equal , and consequently equivalent . THEOREM XIX . A triangle is equivalent to half of a parallelogram having the same base and the same**altitude**. For , through B ... Page 90

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**altitude**, will be to each other as their bases AB , AF . THEOREM XXI . Any two rectangles are to each other as the product of their bases multiplied by their**altitudes**. Let ABCD , AFGH be two rectangles , then will ABCD : AFGH :: AB ... Page 91

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**altitude**AD , are to each other as their bases AB , AF . In like manner , the two rectangles AFKD , AFGH , having the same**altitude**AF , are to each other as their bases , AD , AF . Hence we have these two pro- portions : ABCD AFKD ...### Other editions - View all

### Common terms and phrases

a+b+c ACē altitude angles equal apothem bisect centre chord circ circumference cone consequently corresponding cosec Cosine Cotang cylinder decimal denote described diameter dicular distance divided draw drawn equation equivalent exterior angles feet figure formed frustum give given line greater half hence homologous sides hypotenuse inscribed circle intersection logarithm measure middle point multiplied number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedral angle polyedron prism PROBLEM proportion pyramid quadrant radii radius ratio rectangle regular inscribed regular polygon respectively equal right angles right-angled triangle Scholium secant sector similar similar triangles Sine slant height solid sphere spherical triangle square straight line subtract suppose surface Tang tangent THEOREM three sides triangle ABC triangular prism vertex volume