## Elements of Geometry and Trigonometry |

### From inside the book

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**radii**AC , EO , to be equal , if the chord AD is equal to the chord EG , the arcs AMD , ENG will also be equal . For , if the**radii**CD , OG , be drawn , the triangles ACD , EOG , will have all their sides equal , each to each , namely ...Page 119

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**radii**of the circumscribed circles , and also , as the**radii**of the inscribed circles ; and their areas are to each other as the squares of those**radii**. d Let AB be the side of the one polygon , O the centre , and consequently a OA the ...Page 182

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**radii**; and since their solidities are as their surfaces multiplied by their**radii**, it follows that the solidities of spheres are to each other as the cubes of their**radii**, or as the cubes of their diameters . Scholium 3. Let R be the ...### 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