Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry and Mensuration. Accompanied with All the Necessary Logarithmic and Trigonometric Tables |
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Page 28
... included angle of the one , equal to the two sides and the included angle of the other , the triangles will be identical , or equal in all respects . In the two triangles ABC , DFG , if the side CA be equal to the side DG , and the ...
... included angle of the one , equal to the two sides and the included angle of the other , the triangles will be identical , or equal in all respects . In the two triangles ABC , DFG , if the side CA be equal to the side DG , and the ...
Page 29
... angle ACG ( Post . VI . ) , and meet- ing AB at L , draw GL . The two triangles ACL , GCL , are equal ( T. XX ... included angle of the first will be greater than the included angle of the second . For , if the included angle of ...
... angle ACG ( Post . VI . ) , and meet- ing AB at L , draw GL . The two triangles ACL , GCL , are equal ( T. XX ... included angle of the first will be greater than the included angle of the second . For , if the included angle of ...
Page 31
... included angle ABD of the first triangle equal to BAC , the included angle of the second tri- angle . Hence ( T. XX . ) , the triangle BAD is equal to ABC , that is , a part is equal to the whole , which is impossible ( A. VIII ...
... included angle ABD of the first triangle equal to BAC , the included angle of the second tri- angle . Hence ( T. XX . ) , the triangle BAD is equal to ABC , that is , a part is equal to the whole , which is impossible ( A. VIII ...
Page 34
... included angles ABD , CDB , equal , being alternate angles with reference to the parallels AB , DC . Hence these triangles are equal ( T. XX . ) , and the angle ADB is equal to CBD , but these are alternate angles with reference to AD ...
... included angles ABD , CDB , equal , being alternate angles with reference to the parallels AB , DC . Hence these triangles are equal ( T. XX . ) , and the angle ADB is equal to CBD , but these are alternate angles with reference to AD ...
Page 35
... angle ADB = CBD . Therefore , the two triangles ABD and CDB have a common side BD , and the adjacent angles of the ... included between two other parallels are equal . Cor . III . If one angle of a parallelogram is right , the ...
... angle ADB = CBD . Therefore , the two triangles ABD and CDB have a common side BD , and the adjacent angles of the ... included between two other parallels are equal . Cor . III . If one angle of a parallelogram is right , the ...
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Common terms and phrases
ABē ABCD altitude angles equal apothem base bisecting centre chord circle circumference circumscribed circle circumscribed polygon cone consequently corresponding cosec Cosine Cotang cubic cylinder decimal denote diameter dicular distance divided draw drawn equally distant equation exterior angles feet figure frustum GEOMETRY given angle given line gives greater half hence homologous hypotenuse inches included angle intersection logarithm measure middle point multiplied number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedral angle polyedron prism PROBLEM proportion pyramid quadrant quadrilateral radii radius ratio rectangle regular polygon respectively equal right angles right-angled triangle Scholium secant similar similar triangles Sine slant height solid sphere spherical triangle square straight line subtract suppose surface Tang Tangent THEOREM three sides triangle ABC volume