A Text-book of Geometry

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Ginn, 1888 - Geometry - 437 pages
 

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Page 46 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle 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 69 - The exterior angles of a polygon, made by producing each of its sides in succession, are together equal to four right angles.
Page 187 - Two triangles having 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.
Page 64 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Page 148 - If two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, they are similar. In the triangles ABC and A'B'C', let ZA = Z A', and let AB : A'B' = AC : A'C'. To prove that the A ABC and A'B'C' are similar. In this case we prove the A similar by proving them mutually equiangular. Proof. Place the A A'B'C...
Page 134 - If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.
Page 331 - The volume of a frustum of a cone is equivalent to the sum of the volumes of three cones whose common altitude is the altitude of the frustum and whose bases are the lower base, the upper base, and a mean proportional between the bases of the frustum.
Page 350 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...
Page 401 - Show that the locus of a point which moves so that the sum of its distances from two h'xed straight lines is constant is a straight line.
Page 132 - If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion in which the other two are made the means.

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