## 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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**pyramid**. The perpen- dicular distance from the vertex to the base is called its altitude . VII . A**pyramid**is triangular , quadrilateral , pentagonal , etc. , according as the base is a triangle , quadrilateral , pentagon , etc. VIII ... Page 166

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**pyramid**be cut by a plane parallel to its base , the section thus formed will be a polygon similar to the base , and the lateral edges and the altitude will be cut into proportional parts . First , since the planes ABCDEF , abcdef are ... Page 167

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**pyramids**S - ABCDE , T- MNP have equivalent bases situated in the same plane , and equal altitudes , the sections made by a plane parallel to their bases , are also equivalent . S C B m C P M T N For , since the polygons ABCDE , abcde ... Page 168

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**pyramid**, it follows that the lateral surface is equal to the sum of the bases of all these triangles , or the perimeter of the**pyramid's**base , into one half the slant height . E F A B C Cor . I. If two right**pyramids**have the same ... Page 169

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**pyramid**, construct interior prisms , having for edges the corresponding parts of sa . It is plain that the sum of all the exterior prisms of the pyra- mid S- ABC will be greater than this**pyramid**; and , also , that the sum of all ...### 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