The Elements of Solid Geometry |
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Page vii
... Regular Solids , with the definitions and a summary of the leading characteristics of the Prism , Cylinder , Pyramid , Cone , and Sphere . In Section V. the Volumes of Solids are considered , and the usual rules or formulæ for the ...
... Regular Solids , with the definitions and a summary of the leading characteristics of the Prism , Cylinder , Pyramid , Cone , and Sphere . In Section V. the Volumes of Solids are considered , and the usual rules or formulæ for the ...
Page xiv
... REGULAR POLYHEDRA EXERCISES POLYHEDRA , NOT REGULAR , AND OTHER SOLIDS PARALLELEPIPED PRISM AND CYLINDER PYRAMID AND CONE 63 to 67 68 69 to 75 69 • SPHERE TETRAHEDRON 71 , 72 73 NY 70 74 SECTION V. VOLUMES OF SOLIDS . STEREOMETRY ...
... REGULAR POLYHEDRA EXERCISES POLYHEDRA , NOT REGULAR , AND OTHER SOLIDS PARALLELEPIPED PRISM AND CYLINDER PYRAMID AND CONE 63 to 67 68 69 to 75 69 • SPHERE TETRAHEDRON 71 , 72 73 NY 70 74 SECTION V. VOLUMES OF SOLIDS . STEREOMETRY ...
Page xiv
... REGULAR POLYHEDRA EXERCISES POLYHEDRA , NOT REGULAR , AND OTHER SOLIDS PARALLELEPIPED PRISM AND CYLINDER 63 to 67 68 69 to 75 69 70 PYRAMID AND CONE 71 , 72 2 SPHERE 73 TETRAHEDRON 74 SECTION V. VOLUMES OF SOLIDS . STEREOMETRY ...
... REGULAR POLYHEDRA EXERCISES POLYHEDRA , NOT REGULAR , AND OTHER SOLIDS PARALLELEPIPED PRISM AND CYLINDER 63 to 67 68 69 to 75 69 70 PYRAMID AND CONE 71 , 72 2 SPHERE 73 TETRAHEDRON 74 SECTION V. VOLUMES OF SOLIDS . STEREOMETRY ...
Page 65
... regular hexahedron , whose faces are squares and angles trihedral . It has obviously six faces , eight corners , and twelve edges . F If the equilateral triangle ABC be taken , and the SECT . IV . ] 65 REGULAR POLYHEDRA .
... regular hexahedron , whose faces are squares and angles trihedral . It has obviously six faces , eight corners , and twelve edges . F If the equilateral triangle ABC be taken , and the SECT . IV . ] 65 REGULAR POLYHEDRA .
Page 66
... regular octahedron . 3. On each side of a regular pentagon let another regular pentagon be described , and let these last be turned about the sides of the first until they meet , then the six pentagons will form an open basket or tray ...
... regular octahedron . 3. On each side of a regular pentagon let another regular pentagon be described , and let these last be turned about the sides of the first until they meet , then the six pentagons will form an open basket or tray ...
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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...