The Elements of Solid Geometry |
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Page 60
... corners are equal , being the sides and angles of that face , so that F , C , E denoting the number of faces , corners , and edges respectively , FCE + I. Now if a second face be added with one side coinciding with one of the existing ...
... corners are equal , being the sides and angles of that face , so that F , C , E denoting the number of faces , corners , and edges respectively , FCE + I. Now if a second face be added with one side coinciding with one of the existing ...
Page 61
... corners and as many corners as the first has faces . This may readily be seen to be 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 ...
... corners and as many corners as the first has faces . This may readily be seen to be 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 ...
Page 65
... 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 intersection 0 ; then , if planes normal to AOA ' be taken through A , A ' , and ...
... 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 intersection 0 ; then , if planes normal to AOA ' be taken through A , A ' , and ...
Page 66
... corners with two faces meeting in each , and five corners with a single face : then an exactly similar and equal basket may be placed on the former so that each single - faced corner in the one fits into a double faced corner of the ...
... corners with two faces meeting in each , and five corners with a single face : then an exactly similar and equal basket may be placed on the former so that each single - faced corner in the one fits into a double faced corner of the ...
Page 69
... corners , and twelve edges , and its angles are trihedral . The following properties being easily proved , may be left as exercises for the student : 1. The opposite faces of a parallelepiped are identically equal parallelograms . 2 ...
... corners , and twelve edges , and its angles are trihedral . The following properties being easily proved , may be left as exercises for the student : 1. The opposite faces of a parallelepiped are identically equal parallelograms . 2 ...
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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...