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 ... angle AEI = BFK , HEI = GFK , and HEA = GFB . Of these six angles the first three form the solid angle E , the last three ...
... solid angle A , and the same edges AB , AD , AE . PROPOSITION VIII . THEOREM . If two parallelopipedons have a ... angle AEI = BFK , HEI = GFK , and HEA = GFB . Of these six angles the first three form the solid angle E , the last three ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex