An Elementary Treatise on Plane and Solid Geometry

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William H. Dennet, 1873 - Geometry - 150 pages

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Page 133 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180 and less than 540. (gr). If A'B'C' is the polar triangle of ABC...
Page 126 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 80 - Problem. To construct a polygon similar to a given polygon, and having a given ratio to it.
Page 31 - In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.
Page 87 - To construct a parallelogram equivalent to a given square, and having the difference of its base and altitude equal to a given line.
Page 141 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Page 6 - Your geometry states it as an axiom that a straight line is the shortest way from one point to another; and astronomy shows you that God has given motion only in curves.
Page 31 - In the same circle or in equal circles, equal chords subtend equal arcs; and of two unequal chords the greater subtends the greater arc. In the equal circles whose centres are 0 and 0', let the chords AB and A'B' be equal, and the chord AF greater than A'B'. To prove that 1. arc AB = arc A'B'; 2.
Page 40 - The three sides of a triangle being given, to construct the triangle. Draw the straight line...
Page 78 - Now, since the areas of similar polygons are to each other as the squares of their homologous sides...

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