Elements of Geometry and Trigonometry |
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Page 141
... solid angles , these angles will be equal , and they will coincide when applied the one to the other . We have ... angle , formed by the plane angles A , B , C , D , E , and another solid angle , formed by the same angles in an inverse ...
... solid angles , these angles will be equal , and they will coincide when applied the one to the other . We have ... angle , formed by the plane angles A , B , C , D , E , and another solid angle , formed by the same angles in an inverse ...
Page 147
... solid angle of a prism , are equal to the three planes which form the solid angle of another prism , each to each , and are like situated , the two prisms will be equal to each other . Let the base ABCDE be equal to the base abcde , the ...
... solid angle of a prism , are equal to the three planes which form the solid angle of another prism , each to each , and are like situated , the two prisms will be equal to each other . Let the base ABCDE be equal to the base abcde , the ...
Page 148
... solid angle b , namely , ABC = abc , ABG abg , and GBC = gbc ; they are also similarly situated . hence the solid angles B and bare equal ( Book VI . Prop . XXI , Sch . ) ; and therefore the side BG will fall on its equal bg . It is ...
... solid angle b , namely , ABC = abc , ABG abg , and GBC = gbc ; they are also similarly situated . hence the solid angles B and bare equal ( Book VI . Prop . XXI , Sch . ) ; and therefore the side BG will fall on its equal bg . It is ...
Page 149
... angle DAE is equal to the angle CBF , and the planes DAE , CBF , are ... solid bounded by six planes , whereof those lying opposite to each other are ... angles with each other , are known , a parallelopipedon may be formed on those lines ...
... angle DAE is equal to the angle CBF , and the planes DAE , CBF , are ... solid bounded by six planes , whereof those lying opposite to each other are ... angles with each other , are known , a parallelopipedon may be formed on those lines ...
Page 151
... solid angle A , and the same edges AB , AD , AE . PROPOSITION VIII . THEOREM . If two parallelopipedons have a common base , and their upper bases in the same plane and between the same parallels , they will be equivalent . Let the ...
... solid angle A , and the same edges AB , AD , AE . PROPOSITION VIII . THEOREM . If two parallelopipedons have a common base , and their upper bases in the same plane and between the same parallels , they will be equivalent . Let the ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex