## Elements of Geometry and Trigonometry |

### From inside the book

Page 223

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**tang**? A = R2 + R2 sin2 A cos2 A R2 ( sin A + cos ? A ) hence R2 +**tang**? A sec2 A , a COS A cos A formula which might be immediately deduced from the right- angled triangle CAT . By these formulas , or by the right - an- gled triangle ...Page 228

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**tang**b Ꭱ : substitute these values , dividing all the terms by cos a cos b ; we shall have**tang**( a + b ) = R2 (**tang**a +**tang**b ) R2 -**tang**a**tang**b ; which is the value of the tangent of the sum of two arcs , ex- pressed by the ...Page 258

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**tang**( A + B ) = cot C. cos ( a + b ) sin ( a — b )**tang**( A — B ) = cot C. ' sin ( a + b ) * Hence , two sides a and b with the included angle C being given , the two other angles A and B may be found by the analogies , C :**tang**( A + ...### 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