## 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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Page 180

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**cone**having AO and DC for the radii of its bases , the vertex of the whole**cone**being S. Hence this surface will be measured as above . This measure will always hold good , even when the point D falls on S , and thus forms a whole**cone**... Page 181

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**cone**has for its measure the product of its base into one third of its altitude . Let the**cone**have OA for the radius of its base , and SO for its altitude ; then will ...**cone**is equivalent to three**cones**having the SEVENTH BOOK . 181. Page 182

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**cone**is equivalent to three**cones**having the common altitude of the frustum , and for bases the lower base of the frustum , the upper base , and a mean proportional between them . If the radii of the two bases of a frustum of a**cone**be ... Page 185

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**cone**described by the triangle ADC is the third part of the cylinder described by the rectangle ADCE : hence the sum of the two**cones**, or the solid described by ABC , is the third part of the two cylinders taken together , or of the ... Page 187

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**cone**described by ACM is equal to AM2 . CM , and the**cone**described by BCN to .AM2 . CN . Add the first two solids , and take away the third : we shall have the measure of the solid de- scribed by ABC equal to . AM2 . ( MN + CM - CN ) ...### 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