The Elements of Solid Geometry |
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Page 49
... trihedral , tetra- hedral , ... or polyhedral angles . THEOREM XVIII . ( Euc . XI . 20 ) . Any two of the angles between the edges of a trihedral angle are together greater than the third . This is evident , if the three plane angles ...
... trihedral , tetra- hedral , ... or polyhedral angles . THEOREM XVIII . ( Euc . XI . 20 ) . Any two of the angles between the edges of a trihedral angle are together greater than the third . This is evident , if the three plane angles ...
Page 51
... trihedral angles at each of the points A , B , C , D ... and at A the two angles OAB , OAE , which are two of the base angles of the triangles , are greater than EAB , one of the angles of the polygon ; and similarly at B , C , D ...
... trihedral angles at each of the points A , B , C , D ... and at A the two angles OAB , OAE , which are two of the base angles of the triangles , are greater than EAB , one of the angles of the polygon ; and similarly at B , C , D ...
Page 52
... trihedral angle is greater than two right angles . H A B From any point G , within the trihedral angle O ( ABC ) , let GH , GK , GL be drawn normal to the planes BOC , COA , AOB respectively . Then the angle HGK is supplementary to the ...
... trihedral angle is greater than two right angles . H A B From any point G , within the trihedral angle O ( ABC ) , let GH , GK , GL be drawn normal to the planes BOC , COA , AOB respectively . Then the angle HGK is supplementary to the ...
Page 53
... trihedral angle since they are not in the same plane , therefore the sum of the angles HGK , KGL , LGH is less than ... trihedral angle are equal , the dihedral angles which these planes make with the third are equal . Let O ( ABC ) be a ...
... trihedral angle since they are not in the same plane , therefore the sum of the angles HGK , KGL , LGH is less than ... trihedral angle are equal , the dihedral angles which these planes make with the third are equal . Let O ( ABC ) be a ...
Page 54
... normal to the planes MPQ , NPQ , are both perpendicular to PQ , and therefore PQ is normal to their plane , that is , the plane BOC . THEOREM XXII . A trihedral angle is proportional to the 54 ELEMENTS OF SOLID GEOMETRY . [ SECT . III .
... normal to the planes MPQ , NPQ , are both perpendicular to PQ , and therefore PQ is normal to their plane , that is , the plane BOC . THEOREM XXII . A trihedral angle is proportional to the 54 ELEMENTS OF SOLID GEOMETRY . [ SECT . III .
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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...