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 20
... hence , But , DCA + DCB ECA + ECD + DCB ; ECD + DCB is equal to ECB ( A. 9 ) ; hence , DCA + DCB = ECA + ECB . The sum of the angles ECA and ECB , is equal to two right angles ; consequently , its equal , that is , the sum of the angles ...
... hence , But , DCA + DCB ECA + ECD + DCB ; ECD + DCB is equal to ECB ( A. 9 ) ; hence , DCA + DCB = ECA + ECB . The sum of the angles ECA and ECB , is equal to two right angles ; consequently , its equal , that is , the sum of the angles ...
Page 22
... Hence , the proposition is proved . Cor . 1. If one of the angles about C is a right angle , all of the others are right angles also . For , ( P. I. , C. 1 ) , each of its adjacent angles is a right angle ; and from the proposition just ...
... Hence , the proposition is proved . Cor . 1. If one of the angles about C is a right angle , all of the others are right angles also . For , ( P. I. , C. 1 ) , each of its adjacent angles is a right angle ; and from the proposition just ...
Page 26
... hence , the triangles coincide throughout , and are therefore equal in all 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 ...
... hence , the triangles coincide throughout , and are therefore equal in all 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 ...
Page 31
... hence , the triangles BAD , and DAC , have the three sides of the one equal to those of the other , each to each ; therefore , by the last Proposition , the angle B is equal to the angle which was to be proved . Cor . 1. An equilateral ...
... hence , the triangles BAD , and DAC , have the three sides of the one equal to those of the other , each to each ; therefore , by the last Proposition , the angle B is equal to the angle which was to be proved . Cor . 1. An equilateral ...
Page 32
... hence , the hypothesis that AB and AC are unequal , is false . They must , therefore , be equal ; which was to be proved . Cor . An equiangular triangle is equilateral . PROPOSITION XIII . THEOREM . In any triangle , the greater side is ...
... hence , the hypothesis that AB and AC are unequal , is false . They must , therefore , be equal ; which was to be proved . Cor . An equiangular triangle is equilateral . PROPOSITION XIII . THEOREM . In any triangle , the greater side is ...
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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