Elements of Geometry

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Harper & brothers, 1897 - Geometry - 354 pages
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Page 170 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or as the squares of their apothems.
Page 204 - If a line is perpendicular to one of two parallel lines, it is perpendicular to the other also.
Page 106 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.
Page 5 - If the first of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third.
Page 82 - An angle formed by a tangent and a chord is measured by one-half its intercepted arc.
Page 73 - A line perpendicular to a radius at its extremity is tangent to the circle.
Page 177 - C and area S. To PROVE S — ^RxC. Circumscribe a regular polygon and call its perimeter C' and area S'. Then S
Page 285 - Two triangles are congruent if (a) two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other...
Page 45 - If, from a point within a triangle, two straight lines are drawn to the extremities of either side, their sum will be less than the sum of the other two sides of the triangle.
Page 83 - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

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