## Elements of Geometry and Trigonometry |

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Page 117

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**polygon**, and p the in- scribed**polygon**: then , since the triangles aOb , AOB , are like parts of P and p , we ...**inscribed**poly- gons may always be made less than a given surface . Cor . 1. A circumscribed regular**polygon**, having a ...Page 118

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**inscribed polygon**, and since the two polygons are regular , they will be similar ( Prop . I. ) ; and therefore when they become equal , they will exactly coin- cide , and have a common perimeter . But as the sides of the circumscribed ...Page 123

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**inscribed polygon**, and that of a simi- lar polygon circumscribed , being given ; to find the surfaces of the regular inscribed and circumscribed polygons having double the number of sides . Let AB be a side of the given inscribed ...### 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