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 30
... triangle the angles opposite the equal sides are equal . Let BAC be an isosceles triangle , having the side AB equal to the side AC : then the angle C is equal to the ingle B. Join the vertex A and the middle point D of 30 GEOMETRY.
... triangle the angles opposite the equal sides are equal . Let BAC be an isosceles triangle , having the side AB equal to the side AC : then the angle C is equal to the ingle B. Join the vertex A and the middle point D of 30 GEOMETRY.
Page 31
... middle point D of the base BC . Then , AB is equal to AC , by hypothesis , AD com- mon , and BD equal to DC , by con- struction : hence , the triangles BAD , and DAC , have the three sides of the one equal to those of the other , each ...
... middle point D of the base BC . Then , AB is equal to AC , by hypothesis , AD com- mon , and BD equal to DC , by con- struction : hence , the triangles BAD , and DAC , have the three sides of the one equal to those of the other , each ...
Page 35
... middle point : 1o . Any point of the perpendicular is equally distant from the extremities of the line : 2 ° . Any point , without the perpendicular , is unequally dis- tant from the extremities . Let AB be a given straight line , C its ...
... middle point : 1o . Any point of the perpendicular is equally distant from the extremities of the line : 2 ° . Any point , without the perpendicular , is unequally dis- tant from the extremities . Let AB be a given straight line , C its ...
Page 36
... middle point . PROPOSITION XVII . THEOREM . If two right - angled triangles have the hypothenuse and a side of the one equal to the hypothenuse and a side of the other , each to each , the triangles are equal in all respects . Let the ...
... middle point . PROPOSITION XVII . THEOREM . If two right - angled triangles have the hypothenuse and a side of the one equal to the hypothenuse and a side of the other , each to each , the triangles are equal in all respects . Let the ...
Page 38
... KC and HD are parallel . Through G , the middle point of AB , draw GF perpendicular to KC , and prolong it to E. The sum of the angles GBE and GBD is equal to two right K- E B H- C A F angles ( P. I. ) ; the sum of the 38 GEOMETRY .
... KC and HD are parallel . Through G , the middle point of AB , draw GF perpendicular to KC , and prolong it to E. The sum of the angles GBE and GBD is equal to two right K- E B H- C A F angles ( P. I. ) ; the sum of the 38 GEOMETRY .
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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