## Elements of Geometry and Trigonometry |

### From inside the book

Page 223

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**tang**90 ° == R2 0 ' an expression which designates an infinite quantity ; for the quotient of radius divided by a very small quantity , is very great , and increases as the divisor diminishes ...**tang**B :**tang**PLANE TRIGONOMETRY . 223.Page 228

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**tang**a 9**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 , expressed by the tangents of each of these arcs . For the tangent of their difference , we should in like ...Page 273

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**tang**c :**tang**( a + b ) sin ( A + B ) : sin ( A — B ) : :**tang**c :**tang**( a — b ) . From which a and b are found as in the last case . The remaining angle can then be found by Case I. Ex . 1. In a spherical triangle ABC , there are ...### Contents

Ratios and Proportions | 34 |

The Circle and the Measurement of Angles | 41 |

Problems relating to the First and Third Books | 57 |

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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 logarithm M.
M. Sine 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 slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM triangle ABC triangular prism vertex