C O N TENTS. SPH ERICAL G E O METRY. Page Straight Line and Sphere - - - - - 9 Plane and Sphere - - - - - - - 11 Poles of Spherical Circles - - - - - - 17 Spherical Angles - - - - - - 20 Spherical Triangles - - - - - - 22 Comparison of Triangles - - - - - 29 Comparison of Right-angled and Quadrantal Triangles - 39 Spherical Surfaces - - - - - - 46 SPHERICAL TRIG ON O METRY. Bi-quadrantal Triangles - - - - - - 55 Right-angled Triangles - - - - - 56 Napier's Rules of the Circular Parts - - - - 62 Oblique-angled Triangles - - - - - 69 Bowditch's Rules for Oblique-angled Triangles - - 88 Subject treated algebraically. (Art. 26) - - - 91 Trigonometrical formulae often used - - - - 92 Fundamental theorem investigated - - - * * Other theorems deduced from this - - - - 97 Formulae prepared for use in Logarithmic Calculations - 101 Napier's Analogies - - - - - - 105 SPHERICAL GEOMETRY. DEFINITIONS. 1. A sphere is a solid such that all points in its surface are equidistant from a certain point within called the center. 2. A radius of a sphere is any straight line drawn from the center to the surface. All radii of a sphere are equal. 3. A sphere may be described by the revolution of a semicircle about its diameter, the middle of the diameter being the center, and half the diameter a radius of the sphere. 4. A diameter of a sphere is any straight line passing through the center and terminating each way in the surface. All diameters of a sphere are equal, each of them consisting of two radii. 5. The awls of a sphere is a diameter about which the sphere is supposed to have been described by the revolution of a semicircle. 6. Every intersection of a plane with a sphere is a circle, as will be seen from the demonstration of Prop. VI. 7. The intersection of a sphere with a plane passing through the center is called a great circle, and its intersection with any other plane, a small circle. |