Elements of Geometry: Including Plane, Solid, and Spherical Geometry

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E.H. Butler & Company, 1807 - 398 sider
 

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Side 327 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Side 88 - A circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the center.
Side 207 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Side 99 - In the same circle or in equal circles, equal chords are equally distant from the center; and conversely.
Side 152 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Side 10 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.
Side 392 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Side 176 - If from, a point without a circle a secant and a tangent are drawn, the tangent is a mean proportional between the whole secant and the external segment.
Side 258 - If two planes are perpendicular to each other, a straight line drawn in one of them, perpendicular to their intersection, is perpendicular to the other.
Side 39 - If two parallel lines are cut by a transversal, the sum of the two interior angles on the same side of the transversal is two right angles.

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