Elements of Geometry, Plane and Solid

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American Book Company, 1895 - Geometry - 374 pages
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Page 125 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 310 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...
Page 300 - Sphere is a body bounded by a uniformly curved surface, all the points of which are equally distant from a point within called the center.
Page 285 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 115 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.
Page 180 - ... the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall on it from the opposite angle, and the acute angle.
Page 120 - If the product of two numbers is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means.
Page 32 - Two triangles are equal if two sides and the included angle of the one are equal, respectively, to two sides and the included angle of the other...
Page 181 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle.

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