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 are equal in all respects . In the triangles ABC and DEF , let AB be equal to DE , AC to DF , and the angle A to the 24 ...
... included angle of the one equal to two sides and the included angle of the other , each to each , the triangles are equal in all respects . In the triangles ABC and DEF , let AB be equal to DE , AC to DF , and the angle A to the 24 ...
Page 25
... included side of the other , each to each , the triangles are equal in all respects .. In the triangles ABC and DEF , let the angle B be equal to the angle E , the angle C to the angle F , and the side BC to the side EF : then are the ...
... included side of the other , each to each , the triangles are equal in all respects .. In the triangles ABC and DEF , let the angle B be equal to the angle E , the angle C to the angle F , and the side BC to the side EF : then are the ...
Page 28
... 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 , or it may be ...
... 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 , or it may be ...
Page 30
... included angle of the one equal to two sides and the included angle of the other , each to each ; and , conse- quently , they are equal in all respects ( P. V. ) ; which was to be proved . Scholium . In triangles , equal in all respects ...
... included angle of the one equal to two sides and the included angle of the other , each to each ; and , conse- quently , they are equal in all respects ( P. V. ) ; which was to be proved . Scholium . In triangles , equal in all respects ...
Page 31
... included angle ACB equal to the included angle DBC , by hypothesis : hence , the two triangles are equal in all respects ( P. V. ) . But this BOOK I. 31.
... included angle ACB equal to the included angle DBC , by hypothesis : hence , the two triangles are equal in all respects ( P. V. ) . But this BOOK I. 31.
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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