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 78
... similar manner , it may be shown that the fourth term can not be less than AD : hence , it must be equal to AD ; therefore , we have , angle ACB : angle ACD :: arc AB which was to be proved . : arc AD ; Cor . 1. The intercepted arcs are ...
... similar manner , it may be shown that the fourth term can not be less than AD : hence , it must be equal to AD ; therefore , we have , angle ACB : angle ACD :: arc AB which was to be proved . : arc AD ; Cor . 1. The intercepted arcs are ...
Page 97
... SIMILAR POLYGONS are polygons which are mutually equiangular , and which have the sides about the equal angles , taken in the same order , proportional . 2. In similar polygons , the parts which are similarly placed in each , are called ...
... SIMILAR POLYGONS are polygons which are mutually equiangular , and which have the sides about the equal angles , taken in the same order , proportional . 2. In similar polygons , the parts which are similarly placed in each , are called ...
Page 117
... similar . Let the triangles ABC and DEF have the angle A equal to the angle D , the angle B to the angle E , and the angle C to the angle F : then they are similar . For , place the triangle DEF upon the triangle ABC , so that the angle ...
... similar . Let the triangles ABC and DEF have the angle A equal to the angle D , the angle B to the angle E , and the angle C to the angle F : then they are similar . For , place the triangle DEF upon the triangle ABC , so that the angle ...
Page 118
... 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 are similar ( B. I. , P. XXV . , C. 2 ) . PROPOSITION XIX . THEOREM . Triangles which ...
... 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 are similar ( B. I. , P. XXV . , C. 2 ) . PROPOSITION XIX . THEOREM . Triangles which ...
Page 119
... similar . For , on BA lay off BG equal to ED ; on BC lay off BH equal to EF , and draw GH . Then , because BG is equal to ED , and BH to EF , we have , B BA : BG :: BC BH ; : F 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 , because BG is equal to ED , and BH to EF , we have , B BA : BG :: BC BH ; : F hence , GH is parallel to AC ( P. XVI . ) ; and ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence