## Elements of Geometry and Trigonometry |

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Page 186

... triangle is a portion of the surface of a sphere , bounded by three arcs of great circles . These arcs are named the sides of the triangle , and are always supposed to be each less than a ...

... triangle is a portion of the surface of a sphere , bounded by three arcs of great circles . These arcs are named the sides of the triangle , and are always supposed to be each less than a ...

**Spherical Triangles**and Spherical Polygons, -Page 198

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**spherical triangle**is less than six right angles , and greater than two . For , in the first place , every angle of a**spherical triangle**is less than two right angles : hence the sum of all the three is less than six right angles ...Page 203

... triangle will be equal to two tri - rectangular triangles , or to the fourth part of the whole surface of the sphere . Scholium . While the

... triangle will be equal to two tri - rectangular triangles , or to the fourth part of the whole surface of the sphere . Scholium . While the

**spherical triangle**ABC is compared with the tri - rectangular triangle , the spherical pyramid ...### 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