## Elements of Geometry and Trigonometry |

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Page 96

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**multiplying**these numbers together . Scholium . It may also be demonstrated , that the area of a triangle is equal to its perimeter**multiplied**by half the radius of the inscribed circle . For , the triangles AOB , BOC , AOC , which have ...Page 171

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**multiplied**by half its side . Let the circle ABCD be the base of a 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 ...Page 182

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**multiplied**by a third of its radius . Scholium 1. The solidity of every spherical sector is equal to the zone which forms its base ,**multiplied**by a third of the radius . For , the solid described by any portion of the regular poly- gon ...### Contents

BOOK | 7 |

Problems relating to the First and Third Books 57 | 57 |

BOOK IV | 68 |

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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 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 sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line TABLE OF LOGARITHMIC tang tangent THEOREM triangle ABC triangular prism vertex