The Elements of Solid Geometry |
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Page 7
... diameter of a sphere , but these cases are exceptional and confined to particular surfaces and to points on such surfaces specially related to one another , while for all other pairs of points there is only one direct line passing ...
... diameter of a sphere , but these cases are exceptional and confined to particular surfaces and to points on such surfaces specially related to one another , while for all other pairs of points there is only one direct line passing ...
Page 43
... the same plane pass through a ring of a given diameter ; find the limits between which the ring can play . SECTION III . DIHEDRAL AND SOLID Angles . Def . SECT . II . ] 43 NORMALS AND OBLIQUES . to 39, to NORMALS AND OBLIQUES TO XV.
... the same plane pass through a ring of a given diameter ; find the limits between which the ring can play . SECTION III . DIHEDRAL AND SOLID Angles . Def . SECT . II . ] 43 NORMALS AND OBLIQUES . to 39, to NORMALS AND OBLIQUES TO XV.
Page 73
... diameter normal to the plane the poles of the great circle . 4. A great circle can be drawn through any two points on a spherical surface ; and only one , unless the points are the extremities of a diameter , in which case every great ...
... diameter normal to the plane the poles of the great circle . 4. A great circle can be drawn through any two points on a spherical surface ; and only one , unless the points are the extremities of a diameter , in which case every great ...
Page 74
... diameter , and plane - symmetry with respect to every plane through its centre . 7. The tangent lines drawn at a given point on a spherical surface to all the great circles which pass through that point lie in a plane , which is called ...
... diameter , and plane - symmetry with respect to every plane through its centre . 7. The tangent lines drawn at a given point on a spherical surface to all the great circles which pass through that point lie in a plane , which is called ...
Page 103
... diameter . 6. A regular tetrahedron with respect to the line joining . the middle point of two opposite edges . III . Symmetry with respect to a Plane . Two points on a normal to a plane at equal distances from it on opposite sides are ...
... diameter . 6. A regular tetrahedron with respect to the line joining . the middle point of two opposite edges . III . Symmetry with respect to a Plane . Two points on a normal to a plane at equal distances from it on opposite sides are ...
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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...