Plane Geometry: Experiment, Classification, Discovery, Application ...

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B. Blakiston's Son & Company, 1922 - Geometry, Modern - 301 pages


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Page 149 - 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.
Page 63 - 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.
Page 32 - Things that are equal to the same thing are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are multiplied by equals, the products are equal.
Page 5 - A circle is a portion of a plane bounded by a curved line, all points of which are equally distant from a point within called the centre. The bounding line is called the circumference of the circle.
Page 147 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Page 154 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 75 - If two sides of one triangle are equal respectively to two sides of another triangle, but the included angle of the first is greater than the included angle of the second, then the third side of the first is greater than the third side of the second, and conversely.
Page 67 - If two angles of a triangle are equal, the sides opposite these angles are equal.
Page 215 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 135 - The projection of a point upon a line is the foot of the perpendicular from the point to the line.

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