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

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Page 174

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**cone**is a solid , which may be pro- duced or generated by the revolution of a right - angled triangle SAB , conceived to re- volve about the side SA . In this rotation , the side AB describes a circular plane BDCE , named the base of the ... Page 175

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**cone**SCDB , the**cone**SFKII be cut off by a section parallel to the base , the remaining solid CBHF is called a truncated**cone**, or the frustum of a**cone**. We may conceive it to be described by the revolution of a trapezium ABHG , whose ... Page 176

... , which is named a spherical sector . NOTE . - The cylinder , the

... , which is named a spherical sector . NOTE . - The cylinder , the

**cone**, and the sphere , are the three round bodies treated of in the elements of geometry . THEOREM I. The lateral or convex surface of a cylinder 176 GEOMETRY . Page 178

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**cone**, S its vertex , and SA its slant height . Then will the convex surface of the**cone**have for its measure circ . OA SA . A E 8 C 30 For , conceive a regular polygon in- scribed in the circle OA ; and on this polygon , as a base ... Page 179

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**cone**is equal to its side multiplied by half the sum of the circumferences of its two bases . In the plane SAB which ...**cone**SAB , which is measured by circ . AO × SA . For a like reason , the triangle SDH is equal to the surface ...### Other editions - View all

### Common terms and phrases

a+b+c AC² 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