Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 76
... similar manner , it may be shown that the fourth term cannot be less than AD : hence , it must be equal to AD ; therefore , we have , angle ACB : angle ACD :: arc AB arc AD ; which was to be proved . • Cor . 1. The intercepted arcs are ...
... similar manner , it may be shown that the fourth term cannot be less than AD : hence , it must be equal to AD ; therefore , we have , angle ACB : angle ACD :: arc AB arc AD ; which was to be proved . • Cor . 1. The intercepted arcs are ...
Page 93
... similar polygons , the parts which are similarly placed in each , are called homologous . The corresponding angles ... SIMILAR ARCS , SECTORS , or SEGMENTS are those which correspond to equal angles at the centre . Thus , if the angles A ...
... similar polygons , the parts which are similarly placed in each , are called homologous . The corresponding angles ... SIMILAR ARCS , SECTORS , or SEGMENTS are those which correspond to equal angles at the centre . Thus , if the angles A ...
Page 113
... similar . Let the triangles ABC and equal to the angle D , the angle DEF have the angle A B to the angle E , and the angle C to the angle F : then will they be similar . For , place the triangle DEF upon the triangle ABC , so that the ...
... similar . Let the triangles ABC and equal to the angle D , the angle DEF have the angle A B to the angle E , and the angle C to the angle F : then will they be similar . For , place the triangle DEF upon the triangle ABC , so that the ...
Page 114
... similar ( D. 1 ) ; which was to be proved . Cor . If two triangles have two angles in , one , equal to two angles in the other , each to each , they will be similar ( B. L. , P. XXV . , C. 2 ) . PROPOSITION XIX . THEOREM . Triangles ...
... similar ( D. 1 ) ; which was to be proved . Cor . If two triangles have two angles in , one , equal to two angles in the other , each to each , they will be similar ( B. L. , P. XXV . , C. 2 ) . PROPOSITION XIX . THEOREM . Triangles ...
Page 115
... similar . For , on BA lay off BG equal to ED ; on BC lay off BH equal to EF , and draw GH Then , G because BG is equal to DE , and BH to EF , we have , B C E D BA BG :: BC : BH ; hence , GH is parallel to AC ( P. XVI . ) ; and ...
... similar . For , on BA lay off BG equal to ED ; on BC lay off BH equal to EF , and draw GH Then , G because BG is equal to DE , and BH to EF , we have , B C E D BA BG :: BC : BH ; hence , GH is parallel to AC ( P. XVI . ) ; and ...
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence