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 25
... side BC will coincide with the side EF ( A. 11 ) . The two triangles , therefore , coincide through- out , and are consequently equal in all respects ( I. , D. 15 ) ; which was to be proved . PROPOSITION VI . THEOREM . If two triangles ...
... side BC will coincide with the side EF ( A. 11 ) . The two triangles , therefore , coincide through- out , and are consequently equal in all respects ( I. , D. 15 ) ; which was to be proved . PROPOSITION VI . THEOREM . If two triangles ...
Page 26
... 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 than the third side AC . be For , the distance from A to C , measured on any broken line AB , BC ...
... 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 than the third side AC . be For , the distance from A to C , measured on any broken line AB , BC ...
Page 27
... side , their , sum is less than that of the two remaining sides of the triangle . Let O be any point within the triangle BAC , and let the lines OB , OC , be drawn to the extremities of any side , as BC : then the sum of BO BO and OC is ...
... side , their , sum is less than that of the two remaining sides of the triangle . Let O be any point within the triangle BAC , and let the lines OB , OC , be drawn to the extremities of any side , as BC : then the sum of BO BO and OC is ...
Page 28
... sides and the included angle of the one equal to two sides and the included angle of the other , each to each ; consequently , GC is equal to EF ( P. V. ) . Now , the point G may be without the triangle ABC , it may be on the side BC ...
... sides and the included angle of the one equal to two sides and the included angle of the other , each to each ; consequently , GC is equal to EF ( P. V. ) . Now , the point G may be without the triangle ABC , it may be on the side BC ...
Page 29
... BC > AB + EF . Taking away the common part AB , there remains ( A. 5 ) , 2 ° . When G is on BC . BC > EF . In this ... side AB is equal to the side DE , the side AC to DF , and BC greater than EF , then is the angle BAC greater than the ...
... BC > AB + EF . Taking away the common part AB , there remains ( A. 5 ) , 2 ° . When G is on BC . BC > EF . In this ... side AB is equal to the side DE , the side AC to DF , and BC greater than EF , then is the angle BAC greater than the ...
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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