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Entered according to Act of Congress, in the year 1848, By ANTHoNY D. STANLEY, In the Clerk's Office of the District Court of Connecticut.

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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.

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