A Treatise on Special Or Elementary Geometry: Including an Elementary, and Also, in Part III, a Higher Course, in Plane, Solid, and Spherical Geometry; and Plane and Spherical Trigonometry, with the Necessary Tables

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Sheldon, 1879 - 440 Seiten

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Seite 226 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Seite 39 - The homologous sides of similar triangles are to each other as the square roots of their areas. This theorem is involved in the theorem that the areas of similar triangles are to each other as the squares of their homologous sides.
Seite 197 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Seite 129 - Theorem. — The area of a trapezoid is equal to the product of its altitude...
Seite 211 - If two semicircumferences of great circles intersect on the surface of a hemisphere, the sum of the two opposite triangles thus formed is equivalent to a lune whose angle is that included by the semicircumferences. DEM. — Let the semicircumferences CEB and DEA intersect at E on the surface of the...
Seite 26 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Seite 126 - Theorem — Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other.
Seite 270 - Find the locus of a point the sum of whose distances from two fixed intersecting lines is constant, ie, is equal to a given line.
Seite 94 - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Seite 200 - 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 will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.

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