## Elements of Geometry and Trigonometry |

### From inside the book

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**sphere**; any circular sector , as DCF or FCH , describes a solid , which is named a**spherical**sector . 10. The radius of a**sphere**is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line ...Page 183

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**sphere**; its surface will be expressed by 47R2 , and its solidity by 4¬R2 × † R , or R3 . If the diameter is called D , we shall have RD , and R3 - D3 : hence the solidity of the**sphere**may likewise be expressed by π × D3 = πD3 ...Page 186

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**spherical**segment has but one base , the other being nothing , its solidity will be PH + дπН3 . OH BOOK IX . OF**SPHERICAL**TRIANGLES AND**SPHERICAL**POLYGONS . Definitions . 1. A**spherical**triangle is a portion of the surface of a**sphere**...### Contents

Ratios and Proportions | 34 |

The Circle and the Measurement of Angles | 41 |

Problems relating to the First and Third Books | 57 |

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### 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 consequently convex surface Cosine Cotang 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 M.
M. Sine number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant segment similar slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM triangle ABC triangular prism vertex