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 12
... respects , when they may be so placed as to coincide throughout their whole extent ; they are equal in all their parts when each part of one is equal to the corresponding part of the other , when taken either in the same or in the ...
... respects , when they may be so placed as to coincide throughout their whole extent ; they are equal in all their parts when each part of one is equal to the corresponding part of the other , when taken either in the same or in the ...
Page 21
... respect to each other . 1o . ADJACENT ANGLES are those which lie on the same side of one line , and on opposite sides of the other ; thus , ACE and ECB , or ACE and ACD , ACD , are are adjacent angles . E 2o . OPPOSITE , or VERTICAL ...
... respect to each other . 1o . ADJACENT ANGLES are those which lie on the same side of one line , and on opposite sides of the other ; thus , ACE and ECB , or ACE and ACD , ACD , are are adjacent angles . E 2o . OPPOSITE , or VERTICAL ...
Page 24
... of the one equal to two sides and the included angle of the other , each to each , the triangles are equal in all respects . In the triangles ABC and DEF , let AB be equal to DE , AC to DF , and the angle A to the 24 GEOMETRY .
... of the one equal to two sides and the included angle of the other , each to each , the triangles are equal in all respects . In the triangles ABC and DEF , let AB be equal to DE , AC to DF , and the angle A to the 24 GEOMETRY .
Page 25
... respects . For , let ABC be ap- plied to DEF , in such a manner that the angle A shall coincide with the angle D , the side AB taking the direction DE , and the side AC the direction DF . Then , because AB is equal to DE , the ver- tex ...
... respects . For , let ABC be ap- plied to DEF , in such a manner that the angle A shall coincide with the angle D , the side AB taking the direction DE , and the side AC the direction DF . Then , because AB is equal to DE , the ver- tex ...
Page 26
... respects ( I. , D. 15 ) ; which was to be proved . PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is greater than the third side . Let ABC be a triangle : then will the 4 sum of any two sides , as AB , BC , greater ...
... respects ( I. , D. 15 ) ; which was to be proved . PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is greater than the third side . Let ABC be a triangle : then will the 4 sum of any two sides , as AB , BC , greater ...
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Common terms and phrases
ABē ABCD ACē 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