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 20
... proved . Cor . 1. If one of the angles DCA , DCB , is a right angle , the other must also be a right angle . Cor . 2. The sum of the an- gles BAC , CAD , DAE , EAF , formed about a given point on the same side of a straight line BF , is ...
... proved . Cor . 1. If one of the angles DCA , DCB , is a right angle , the other must also be a right angle . Cor . 2. The sum of the an- gles BAC , CAD , DAE , EAF , formed about a given point on the same side of a straight line BF , is ...
Page 22
... proved . Cor . 1. If one of the angles about C is a right angle , all of the others are right angles also . For , ( P. I. , C. 1 ) , each of its adjacent angles is a right angle ; and from the proposition just demonstrated , its ...
... proved . Cor . 1. If one of the angles about C is a right angle , all of the others are right angles also . For , ( P. I. , C. 1 ) , each of its adjacent angles is a right angle ; and from the proposition just demonstrated , its ...
Page 23
... proved , and then continuing the reasoning until the assumed hypothesis is shown to be false . Its contradictory is thus proved to be true . This method of demonstration is often used in Geometry . PROPOSITION IV . THEOREM . If a ...
... proved , and then continuing the reasoning until the assumed hypothesis is shown to be false . Its contradictory is thus proved to be true . This method of demonstration is often used in Geometry . PROPOSITION IV . THEOREM . If a ...
Page 24
... proved . PROPOSITION V. THEOREM . If two triangles have two sides and the 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 ...
... proved . PROPOSITION V. THEOREM . If two triangles have two sides and the 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 ...
Page 25
... proved . PROPOSITION VI . THEOREM . If two triangles have two angles and the inciuded side of the one equal to two angles and the included side of the other , each to each , the triangles are equal in all respects .. In the triangles ...
... proved . PROPOSITION VI . THEOREM . If two triangles have two angles and the inciuded side of the one equal to two angles and the included side of the other , each to each , the triangles are equal in all respects .. In the triangles ...
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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