The Elements of Solid Geometry |
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Page xiv
... TETRAHEDRON 71 , 72 73 NY 70 74 SECTION V. VOLUMES OF SOLIDS . STEREOMETRY . SYMMETRY 76 to 108 THEOREMS XXVI . TO XXXIV . . 78 to 97 APPENDIX ON SYMMETRY 98 to 108 SECTION VI . SPHERICAL SURFACE GEOMETRY , 109 to 130 THE ELEMENTS OF ...
... TETRAHEDRON 71 , 72 73 NY 70 74 SECTION V. VOLUMES OF SOLIDS . STEREOMETRY . SYMMETRY 76 to 108 THEOREMS XXVI . TO XXXIV . . 78 to 97 APPENDIX ON SYMMETRY 98 to 108 SECTION VI . SPHERICAL SURFACE GEOMETRY , 109 to 130 THE ELEMENTS OF ...
Page xiv
... TETRAHEDRON 74 SECTION V. VOLUMES OF SOLIDS . STEREOMETRY . SYMMETRY 76 to 108 THEOREMS XXVI . TO XXXIV . . 78 to 97 APPENDIX ON SYMMETRY . 98 to 108 SECTION VI . SPHERICAL SURFACE GEOMETRY . 109 to 130 THE ELEMENTS OF SOLID GEOMETRY ...
... TETRAHEDRON 74 SECTION V. VOLUMES OF SOLIDS . STEREOMETRY . SYMMETRY 76 to 108 THEOREMS XXVI . TO XXXIV . . 78 to 97 APPENDIX ON SYMMETRY . 98 to 108 SECTION VI . SPHERICAL SURFACE GEOMETRY . 109 to 130 THE ELEMENTS OF SOLID GEOMETRY ...
Page 58
... tetrahedral or polyhedral ? 13. The locus of a point equidistant from two intersect- ing planes is the pair of planes which bisect the dihedral angles between them . 14. The locus of a point equidistant from three planes which meet in ...
... tetrahedral or polyhedral ? 13. The locus of a point equidistant from two intersect- ing planes is the pair of planes which bisect the dihedral angles between them . 14. The locus of a point equidistant from three planes which meet in ...
Page 65
Robert Baldwin Hayward. This is the regular tetrahedron . It has four faces , four corners , and six edges . 2. Let three equal lines AOA ' , BOB ' , COC ' be at right angles , each to the other two , and each bisected at their point of ...
Robert Baldwin Hayward. This is the regular tetrahedron . It has four faces , four corners , and six edges . 2. Let three equal lines AOA ' , BOB ' , COC ' be at right angles , each to the other two , and each bisected at their point of ...
Page 66
... tetrahedral angles , and twelve edges , which would be inscribed in , and conjugate to , the cube de- scribed above . This is the regular octahedron . 3. On each side of a regular pentagon let another regular pentagon be described , and ...
... tetrahedral angles , and twelve edges , which would be inscribed in , and conjugate to , the cube de- scribed above . This is the regular octahedron . 3. On each side of a regular pentagon let another regular pentagon be described , and ...
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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...