The Elements of Solid Geometry |
From inside the book
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Page 9
... true of no other surface , might have been taken as the definition of a plane , analogous to that given above for the straight line . B All the parts of a plane are identically like , or any one part is superposable on any other part so ...
... true of no other surface , might have been taken as the definition of a plane , analogous to that given above for the straight line . B All the parts of a plane are identically like , or any one part is superposable on any other part so ...
Page 51
... true , if the point O were in the plane ABC ... , in which case the vertical angles at O would be to- gether equal to four right angles , and the base angles together equal to the angles of the polygon . But , O not being in the plane ...
... true , if the point O were in the plane ABC ... , in which case the vertical angles at O would be to- gether equal to four right angles , and the base angles together equal to the angles of the polygon . But , O not being in the plane ...
Page 58
... true if the angles are 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 ...
... true if the angles are 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 ...
Page 60
... true that F + C E + I. = The same is true for each addition of a face with one side only coinciding with a previously existing edge . When a face is added with two or more consecutive sides coinciding with existing edges , it is easily ...
... true that F + C E + I. = The same is true for each addition of a face with one side only coinciding with a previously existing edge . When a face is added with two or more consecutive sides coinciding with existing edges , it is easily ...
Page 61
... true , since , if points be taken in a plane opposite each corner , one point in each of the faces that meet in that corner , the plane faces formed by joining these points will include another polyhedron in- scribed in the former with ...
... true , since , if points be taken in a plane opposite each corner , one point in each of the faces that meet in that corner , the plane faces formed by joining these points will include another polyhedron in- scribed in the former with ...
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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...