The Elements of Solid Geometry |
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Page 5
... superposable on any other part so as to coincide with it . For take the straight line passing through the points A , B , and let the line be moved and replaced on A , B , in a A B new position so that the point P in it falls on A , and ...
... superposable on any other part so as to coincide with it . For take the straight line passing through the points A , B , and let the line be moved and replaced on A , B , in a A B new position so that the point P in it falls on A , and ...
Page 9
... superposable on any other part so as to concide with it . For if the plane through the points A , B , C be moved and then replaced on A , B , C so that another point P in it falls on A , Q on B , and R on C , the plane being defined ...
... superposable on any other part so as to concide with it . For if the plane through the points A , B , C be moved and then replaced on A , B , C so that another point P in it falls on A , Q on B , and R on C , the plane being defined ...
Page 10
... superposable as wholes . Such a postulate would be this : Figures on a plane ( or other surface ) which are symmetrical with respect to a straight ( or direct ) line in it are equal to one another . ( See Discussion on Symmetry , p . 98 ...
... superposable as wholes . Such a postulate would be this : Figures on a plane ( or other surface ) which are symmetrical with respect to a straight ( or direct ) line in it are equal to one another . ( See Discussion on Symmetry , p . 98 ...
Page 12
... superposable figures ( see Discussion on Symmetry , pp . 98 to 108 ) : POST . 6. Figures which are completely symmetrical with respect either to a point , or to a straight line , or to a plane , are equal to one another . SECTION I ...
... superposable figures ( see Discussion on Symmetry , pp . 98 to 108 ) : POST . 6. Figures which are completely symmetrical with respect either to a point , or to a straight line , or to a plane , are equal to one another . SECTION I ...
Page 58
... superposable or opposable ( v . Sect . V. p . 77 ) . Is the same 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 ...
... superposable or opposable ( v . Sect . V. p . 77 ) . Is the same 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 ...
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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...