Principles of Plane Geometry

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Allyn and Bacon, 1889 - Geometry - 63 pages

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Page 47 - 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.
Page 44 - The perimeters of two similar polygons have the same ratio as any two corresponding sides.
Page 35 - An angle formed by two tangents is measured by half the difference of the intercepted arcs.
Page 24 - If four quantities are in proportion, they will be in proportion by INVERSION ; that is, the second will be to the first as the fourth to the third.
Page 14 - Any exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Page 28 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.
Page 25 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Page 36 - Given, two sides of a triangle, and the angle opposite one of them, to construct the triangle. Let A and B be the given sides, and G the given angle.
Page 17 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Page 13 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.

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