Elements of Synthetic Solid Geometry |
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Common terms and phrases
ABē altitude axis base bisect bisector centroid chord circle circular cone common line complanar congruent conic cosē cube cuboid curve cylinder cylindroid denote diagonals diameter dihedral angles draw ellipse equal face angles form a sheaf four frustum given line given point Hence hyperbola infinity intersection isoclinal line join line-segment locus mean centre median meet middle point mon line non-complanar lines normal number of faces octahedron opposite parabola parallel lines parallelepiped parallelogram pass perpendicular planar line plane figure plane geometry point equidistant polygon polyhedra polyhedron prism prismatoid projection Proof pyramid radius rectangle right angle right section right-bisector plane ruled surfaces segment sheaf of lines sides skew quadrilateral spatial figure sphere spheric geometry spheric line spheric triangle squares surface tangent line Theorem three-faced corner vertex vertices volume
Popular passages
Page v - I have been induced to present the work to the public, partly by receiving from a number of Educationists inquiries as to what work on Solid Geometry I would recommend as a sequel to my Plane Geometry, and partly from the high estimate that I have formed of the value of the study of synthetic solid geometry as a means of mental discipline. ... " In this work the subject is carried somewhat farther than is customary in those works in which the subject of solid geometry is appended to that of plane...
Page 77 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 11 - The projection of a point on a plane is the foot of the perpendicular from the point to the plane.
Page 107 - S'-A'B'C' be two triangular pyramids having equivalent bases situated in the same plane, and equal altitudes. To prove that S-ABC =c= S'-A'B'C'. Proof. Divide the altitude into n equal parts, and through the points of division pass planes parallel to the plane of the bases, forming the sections DEF, GHI, etc., D'E'F', G'H'I', etc. In the pyramids S-ABC and S'-A'B'C' inscribe prisms whose upper bases are the sections DEF, GHI, etc., D'E'F', G'H'I', etc.
Page 78 - The sum of the squares on the sides of any quadrilateral is greater than the sum of the squares on the diagonals by four times the square on the line joining the middle points of the diagonals.
Page 208 - In any spherical triangle, the greater side is opposite the greater angle; and conversely, the greater angle is opposite the greater side.