The Elements of Solid Geometry |
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Page 51
... ABCD ... : then the sum of the angles in the n triangles , whose common vertex is O , is 2n right angles . ... The same would be true , if the point O were in the plane ABC ... , in which case the vertical angles at O would be to ...
... ABCD ... : then the sum of the angles in the n triangles , whose common vertex is O , is 2n right angles . ... The same would be true , if the point O were in the plane ABC ... , in which case the vertical angles at O would be to ...
Page 72
... ABCD ... and abcd ... are two plane polygons , so situated that AB and ab , BC and bc , & c . , meet in the same straight line , the lines , Aa , Bb , Cc ... all meet in a point , the vertex of a pyramid of which the polygons are plane ...
... ABCD ... and abcd ... are two plane polygons , so situated that AB and ab , BC and bc , & c . , meet in the same straight line , the lines , Aa , Bb , Cc ... all meet in a point , the vertex of a pyramid of which the polygons are plane ...
Page 82
... of a cuboid whose base and height are equal respectively to those of the parallelepiped . t 6 A B Α ' C " Let Aa be any parallelepiped and ABCD its base . 82 [ SECT . V. ELEMENTS OF SOLID GEOMETRY . 57, 58 DIHEDRAL AND SOLID ANGLES.
... of a cuboid whose base and height are equal respectively to those of the parallelepiped . t 6 A B Α ' C " Let Aa be any parallelepiped and ABCD its base . 82 [ SECT . V. ELEMENTS OF SOLID GEOMETRY . 57, 58 DIHEDRAL AND SOLID ANGLES.
Page 95
... abcd has its edges and faces parallel each to a corresponding edge or face of ABCD , and consequently corresponding angles in corresponding faces equal , corresponding dihedral angles equal , and the ratios of corresponding edges all ...
... abcd has its edges and faces parallel each to a corresponding edge or face of ABCD , and consequently corresponding angles in corresponding faces equal , corresponding dihedral angles equal , and the ratios of corresponding edges all ...
Page 97
Robert Baldwin Hayward. the plane abcd in k , OK , Ok will be the heights of the two pyramids , and will be in the ratio of OA : Oa and therefore of AB : ab . A B 2 D A a B But the volumes of the two pyramids are in the ratio compounded ...
Robert Baldwin Hayward. the plane abcd in k , OK , Ok will be the heights of the two pyramids , and will be in the ratio of OA : Oa and therefore of AB : ab . A B 2 D A a B But the volumes of the two pyramids are in the ratio compounded ...
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Common terms and phrases
ABCD angle ACB axis bisected central symmetry centre centre of symmetry circle Crown 8vo cuboid diameter dihedral angle direct line distance drawn Elementary equal bases equally inclined Euclid exterior angle finite four right angles frustrum given line given point Globe 8vo greater Hence less lines joining lines of intersection lune meets the plane middle point number of faces number of sides pair parallel planes perpendicular plane BOC plane faces plane geometry plane parallel plane triangle planes are parallel polar triangle polygon polyhedra polyhedron position prism projection Q. E. D. COR Q. E. D. THEOREM quadrant ratio regular regular polyhedron six right solid angles solid figure Solid Geometry space sphere spherical excess spherical surface spherical triangle Spherical Trigonometry straight line superposable supplementary symmetrical with respect termed tetrahedron three planes triangle ABC vertex volume
Popular passages
Page 130 - ... equal, then the angles opposite to the other pair of equal sides are either equal or supplementary, and in the former case the triangles are identically equal.
Page 120 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...