## Elements of Geometry and Trigonometry |

### From inside the book

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Page 166

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**cone**; the hypothenuse SB describes the convex surface of the**cone**. The point S is named the vertex of the**cone**, SA the axis or the altitude , and SB the side or the apothem . Every section HKFI , at right angles to the axis , is a ... Page 167

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**cone**, any polygon ABCDE be inscribed , and from the vertices A , B , C , D , E , lines be drawn to S , the vertex of the**cone**, these lines may be regarded as the sides of a pyramid whose base is the polygon ABCDE and vertex S. The ... Page 168

... form the bases of the zone or segment . Note . The Cylinder , the

... form the bases of the zone or segment . Note . The Cylinder , the

**Cone**, and the Sphere , are the three round bodies treated of in the Elements of Geometry . PROPOSITION I. THEOREM . The convex surface of a cylinder 168 GEOMETRY . Page 171

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**cone**, S the vertex , SO the altitude , and SA the side : then will its convex sur- face be equal to circ . OA SA . For , inscribe in the base of A the**cone**any regular polygon ABCD , and on this polygon as a base conceive a pyramid to ... Page 172

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**cone**. The con- vex surface of the frustum of the pyramid is equal to half the sum of the perimeters of its bases multiplied by the slant height fh ( Book VII . Prop . IV . Cor . ) . A di I Let now the number of sides of the inscribed ...### Other editions - View all

### Common terms and phrases

adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex