## Elements of Geometry and Trigonometry |

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**half**of BE . For a like reason , the angle CAD will be measured by the**half**of ED ; hence BAC + CAD , or BAD will be measured by**half**of BE + ED , or of BED . Suppose , in the second place , that the centre C lies without the angle BAD ...Page 55

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**half**of the same arc BOC . B Cor . 2. Every angle BAD , inscribed in a semicircle is a right angle ; because it is mea- sured by**half**the semicircumference BOD , that is , by the fourth part of the whole cir- cumference . Cor . 3. Every ...Page 56

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**half**the arc FDB ( Prop . XVIII . ) ; therefore , DEB E C D B is measured by**half**of FDB ; that is , by**half**of DB + DF , or**half**of DB + AC . In the same manner it might be proved that the angle AED is measured by**half**of AFD + BC ...### 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