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 24
... included angle of the one equal to two sides and the included angle of the other , each to each , the triangles will be equal in all their parts . In the triangles ABC and DEF , let AB be equal to DE , AC to DF , and the angle 24 GEOMETRY .
... included angle of the one equal to two sides and the included angle of the other , each to each , the triangles will be equal in all their parts . In the triangles ABC and DEF , let AB be equal to DE , AC to DF , and the angle 24 GEOMETRY .
Page 25
... angles and the included side of the one equal to two angles and the included side of the other , each to each , the triangles will be equal in all their parts . triangles In the ABC and DEF , let the angle B be equal to the angle E , the ...
... angles and the included side of the one equal to two angles and the included side of the other , each to each , the triangles will be equal in all their parts . triangles In the ABC and DEF , let the angle B be equal to the angle E , the ...
Page 28
... included angle . In the triangles BAC and DEF , let AB be equal to DE , AC to DF , and the angle A greater than the an- gle D : then will BC be greater than EF . Let the line AG be drawn , making the angle CAG equal to the angle D ...
... included angle . In the triangles BAC and DEF , let AB be equal to DE , AC to DF , and the angle A greater than the an- gle D : then will BC be greater than EF . Let the line AG be drawn , making the angle CAG equal to the angle D ...
Page 30
... angle A can neither be greater nor less than D : hence , it must be equal to it . The two triangles have , therefore , two sides and the included angle of the one equal to two sides and the inclu- ded angle of the other , each to each ...
... angle A can neither be greater nor less than D : hence , it must be equal to it . The two triangles have , therefore , two sides and the included angle of the one equal to two sides and the inclu- ded angle of the other , each to each ...
Page 31
... angle B is equal to the angle C ; which was to be proved . B4 D Cor . 1. An equilateral triangle is equiangular ... included angle ACB equal to the included angle DBC , by hypothesis : hence , the two triangles are equal in all their ...
... angle B is equal to the angle C ; which was to be proved . B4 D Cor . 1. An equilateral triangle is equiangular ... included angle ACB equal to the included angle DBC , by hypothesis : hence , the two triangles are equal in all their ...
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Common terms and phrases
ABē ACē adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence