The Essentials of Geometry (plane)

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Leach, Shewell & Company, 1898 - Geometry - 242 pages
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Page 222 - The perpendiculars from the vertices of a triangle to the opposite sides are the bisectors of the angles of the triangle formed by joining the feet of the perpendiculars.
Page 41 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Page 47 - ... the three sides of one are equal, respectively, to the three sides of the other. 2. Two right triangles are congruent if...
Page 71 - A chord is a straight line joining the extremities of an arc ; as AB.
Page 149 - If one leg of a right triangle is double the other, the perpendicular from the vertex of the right angle to the hypotenuse divides it into segments which are to each other as 1 to 4.
Page 190 - 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.
Page 140 - In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Page 161 - DB as often as possible. As the lines AD and DB are incommensurable, there must be a remainder, B'B, less than one of the equal parts. Draw B'C
Page 49 - Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.

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