An Elementary Treatise on Plane and Solid Geometry

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W.H.Dennet, 1865 - Geometry - 150 pages
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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 24 - 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 20 - The sum of the three angles of any triangle is equal to two right angles.
Page 16 - Theorem. In an isosceles triangle the angles opposite the equal sides are equal.
Page 87 - To construct a parallelogram equivalent to a given square, and having the sum of its base and altitude equal to a given line.
Page 31 - Theorem. In the same circle, or in equal circles, equal arcs are subtended by equal chords.
Page 17 - Jl will be equal to C. 56. Corollary. An equilateral triangle is also equiangular. 57. Theorem. The line BD (fig. 32), which...
Page 68 - 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 71 - Rectangles of the same altitude are to each other as their bases, and rectangles of the same base are to each other as their altitudes. 245.
Page 135 - ... equal as to the magnitude of those parts. Hence, those two triangles, having all their sides respectively equal in both, must either be absolutely equal, or at least symmetrically so; in both of which cases their corresponding angles must be equal, and lie opposite to equal sides.

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