Plane and Solid Geometry |
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Page vii
... an excellent means to overcome this difficulty . Draw equal lines or equal angles in the same color , or if this is impracticable , mark them by equal viii SUGGESTIONS TO TEACHERS crossmarks ; denote parallel lines by vii.
... an excellent means to overcome this difficulty . Draw equal lines or equal angles in the same color , or if this is impracticable , mark them by equal viii SUGGESTIONS TO TEACHERS crossmarks ; denote parallel lines by vii.
Page viii
Arthur Schultze, Frank Louis Sevenoak. viii SUGGESTIONS TO TEACHERS crossmarks ; denote parallel lines by arrows ; draw a greater line in some color , e.g. green , a smaller line in another color , e.g. yellow , etc. The following ...
Arthur Schultze, Frank Louis Sevenoak. viii SUGGESTIONS TO TEACHERS crossmarks ; denote parallel lines by arrows ; draw a greater line in some color , e.g. green , a smaller line in another color , e.g. yellow , etc. The following ...
Page xii
... parallel to . parallels . cor . corr . def . alternate . axiom . circumference . complement . construction . corollary . corresponding . definition . · ex . exercise . ext . exterior . hom .. homologous . is similar to , or similar . hy ...
... parallel to . parallels . cor . corr . def . alternate . axiom . circumference . complement . construction . corollary . corresponding . definition . · ex . exercise . ext . exterior . hom .. homologous . is similar to , or similar . hy ...
Page 17
... PARALLEL LINES 77. DEF . Parallel lines are lines which lie in the same plane and do not meet if produced indefinitely . parallel . 78. AXIOM 11. Two intersect- ing lines cannot be both parallel to a third straight line . AB and CD are ...
... PARALLEL LINES 77. DEF . Parallel lines are lines which lie in the same plane and do not meet if produced indefinitely . parallel . 78. AXIOM 11. Two intersect- ing lines cannot be both parallel to a third straight line . AB and CD are ...
Page 18
... parallel . Suppose they meet in G. Then BEG is a triangle whose exterior ABE is equal to a remote interior / BEG , which is impossible . Hence AC and DF are parallel . Q.E.D. 81. SCHOLIUM . That the lines AC and DF cannot meet on the ...
... parallel . Suppose they meet in G. Then BEG is a triangle whose exterior ABE is equal to a remote interior / BEG , which is impossible . Hence AC and DF are parallel . Q.E.D. 81. SCHOLIUM . That the lines AC and DF cannot meet on the ...
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Common terms and phrases
ABCD altitude angles are equal bisect bisector chord circumference circumscribed cone construct a triangle cylinder diagonals diagram for Prop diameter diedral angles divide draw drawn equiangular equiangular polygon equilateral triangle equivalent exterior angle face angles find a point Find the area Find the radius Find the volume frustum given circle given line given point given triangle Hence HINT homologous hypotenuse inches inscribed intersecting isosceles triangle joining the midpoints lateral area lateral edges line joining mean proportional median opposite sides parallel lines parallelogram parallelopiped perimeter perpendicular plane MN point equidistant polyedral angle polyedron PROPOSITION prove Proof quadrilateral radii ratio rectangle regular polygon respectively equal rhombus right angles right triangle SCHOLIUM segments sphere spherical polygon spherical triangle square straight angle straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal triedral vertex
Popular passages
Page 148 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Page 150 - If, from a point without a circle, a tangent and a secant be drawn, the tangent is the mean proportional between the secant and its external segment.
Page 180 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 45 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Page 337 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...
Page 305 - A cylinder is a solid bounded by a cylindrical surface and two parallel planes ; the bases of a cylinder are the parallel planes; and the lateral surface is the cylindrical surface.
Page 312 - The lateral areas, or the total areas, of similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of their radii ; and their volumes are to each other as the cubes of their altitudes, or as the cubes of their radii. Let S, S' denote the lateral areas, T, T...
Page 149 - If, from a point without a circle, two secants are drawn, the product of one secant and its external segment is equal to the product of the other and its external segment.
Page 328 - Every section of a sphere made by a plane is a circle.
Page 257 - If two intersecting planes are each perpendicular to a third plane, their intersection is perpendicular to that plane.