Elements of Geometry |
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Page 126
... parallelopiped . A parallelopiped is rectangular when all its faces are rect- angles . 374. Among rectangular parallelopipeds is distinguished the cube or regular hexaedron comprehended under six equal squares . 375. A pyramid is a ...
... parallelopiped . A parallelopiped is rectangular when all its faces are rect- angles . 374. Among rectangular parallelopipeds is distinguished the cube or regular hexaedron comprehended under six equal squares . 375. A pyramid is a ...
Page 131
... parallelopiped is a solid compre- hended under six planes , of which the opposite ones are equal and parallel , it follows that either of the faces and its opposite may be taken for the bases of the parallelopiped . 392. Scholium ...
... parallelopiped is a solid compre- hended under six planes , of which the opposite ones are equal and parallel , it follows that either of the faces and its opposite may be taken for the bases of the parallelopiped . 392. Scholium ...
Page 132
... parallelopiped re- quired . THEOREM . 393. In every parallelopiped the opposite solid angles are sym metrical , and the diagonals drawn through the vertices of these angles bisect each other . = Demonstration . Let us compare , for ...
... parallelopiped re- quired . THEOREM . 393. In every parallelopiped the opposite solid angles are sym metrical , and the diagonals drawn through the vertices of these angles bisect each other . = Demonstration . Let us compare , for ...
Page 133
... parallelopiped AG , are Fig . 208 . equivalent . Demonstration . Through the vertices B , F , perpendicular to the side BF , suppose the planes Bad c , Fehg to pass , meeting the three other sides , AE , DH , CG Of Polyedrons . 133.
... parallelopiped AG , are Fig . 208 . equivalent . Demonstration . Through the vertices B , F , perpendicular to the side BF , suppose the planes Bad c , Fehg to pass , meeting the three other sides , AE , DH , CG Of Polyedrons . 133.
Page 134
... parallelopiped , the one in a , d , c , the other in e , h , g ; the sections Bad c , Fehg , will be equal parallelograms . They are equal , because they are made by planes , which are perpendicular to the same straight line , and ...
... parallelopiped , the one in a , d , c , the other in e , h , g ; the sections Bad c , Fehg , will be equal parallelograms . They are equal , because they are made by planes , which are perpendicular to the same straight line , and ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence