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 26
... 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 a triangle ...
... 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 a triangle ...
Page 28
... triangle ABC , it may be on the side BC , or it may be within the triangle ABC . Each case will be considered separately . 1o . When G is without the triangle ABC . In the triangles GIC and AIB , we have , B A F ( P. VII . ) , G E GI + ...
... triangle ABC , it may be on the side BC , or it may be within the triangle ABC . Each case will be considered separately . 1o . When G is without the triangle ABC . In the triangles GIC and AIB , we have , B A F ( P. VII . ) , G E GI + ...
Page 29
... triangle ABC . From Proposition VIII . , we have , BA + BC > GA + GC ; Α D or , since GA BA , and GC = EF , we B G have , BABC BA + EF . Taking away the common part AB , there remains , BC > EF . ......... ليا E Hence , in each case ...
... triangle ABC . From Proposition VIII . , we have , BA + BC > GA + GC ; Α D or , since GA BA , and GC = EF , we B G have , BABC BA + EF . Taking away the common part AB , there remains , BC > EF . ......... ليا E Hence , in each case ...
Page 30
... ABC and DEF , let AB be equal to DE , AC to DF , and BC to EF : then are the triangles equal in all respects . For ... triangle the angles opposite the equal sides are equal . Let BAC be an isosceles triangle , having the side AB equal ...
... ABC and DEF , let AB be equal to DE , AC to DF , and BC to EF : then are the triangles equal in all respects . For ... triangle the angles opposite the equal sides are equal . Let BAC be an isosceles triangle , having the side AB equal ...
Page 31
... triangle are equal , the sides opposite to are also equal , and consequently , the triangle is isosceles . In the triangle ABC , let the angle ABC be equal to the angle ACB : then is AC equal to AB , and consequently , the triangle is ...
... triangle are equal , the sides opposite to are also equal , and consequently , the triangle is isosceles . In the triangle ABC , let the angle ABC be equal to the angle ACB : then is AC equal to AB , and consequently , the triangle 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