Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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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 . In the triangles 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 . In the triangles 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 ( Post ...
... 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 ( Post ...
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 C 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 They in all ...
... angle B is equal to the angle C ; which was to be proved . B4 C 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 They in all ...
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Common terms and phrases
ABĀ² ABCD adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed cone consequently convex surface cosec Cosine Cosine D Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area following RULE Formula frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC log cot log sin lower base mantissa measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle principle demonstrated prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar slant height solution sphere spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prism triedral angle upper base vertex volume whence write the following