## Elements of Geometry and Trigonometry |

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Page 44

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**chord**EG . For , since the diameters AB , EF , are equal , the semi- circle AMDB may be applied M D N BE K exactly ...**chord**AD is equal to the**chord**EG . Conversely , supposing again the radii AC , EO , to be equal , if the**chord**AD is ...Page 45

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**chord**AD , of the first , is less than the**chord**AH of the second . PROPOSITION VI . THEOREM . The radius which is perpendicular to a**chord**, bisects the**chord**, and bisects also the subtended arc of the**chord**. Let AB be a**chord**, and ...Page 47

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**chords**, the less is at the greater distance from the centre . First . Suppose the**chord**AB = DE . Bisect these**chords**by the per- pendiculars CF , CG , and draw the radii CA , CD . D A In the right angled triangles CAF , DCG , the ...### 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