Descriptive Geometry |
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Common terms and phrases
auxiliary planes base circle cone of revolution corresponding traces Descriptive Geometry determined diameter Draw the projections edge elements ellipse Find shades Find the angle Find the distance Find the traces gear given angle given line given point H Fig H projection H trace helicoidal helix hip rafter horizontal hyperboloids inclined at 30 line of intersection line of shade oblique parallel to H pass a plane pendicular perpendicular to H plane 2 Fig plane containing plane parallel plane perpendicular plane tangent planes of projection point of intersection prism projecting lines projections and true pulley purlin pyramid required line Revolve the plane revolved into H revolved position right triangle ruled surfaces shades and shadows shadows Fig Show projections Show the projections Show the traces shown in Fig side slant height solid of revolution sphere straight line surfaces of revolution tion true form true length vertex angle
Popular passages
Page 68 - Therefore, to make the construction for the tangent plane, pass a plane through the center of the sphere and perpendicular to the line MN.
Page 24 - The angle between a line and a plane is the angle between the line and its projection on the plane; therefore, project the given line on the given plane, pass a plane m FIG.
Page 83 - SECTIONS OF A CONE The circle, parabola, ellipse, and hyperbola are known as conic sections because each may be obtained by cutting a cone by a plane. If the cutting plane is perpendicular to the axis of the cone, the section is a circle.
Page 66 - Fig. 55, and let P be the given point. Analysis. Since the required plane must contain a rectilinear element, it will pass through the vertex; hence, if we join the given point with the vertex by a right line, it will be a line of the required plane, and pierce the horizontal...
Page 95 - This surface may be generated (1) by the rotation of a straight line about an axis not in the same plane...
Page 38 - If a line lies in a plane, the traces of the line lie in the traces of the plane; and conversely.
Page 87 - ... in the simplest manner, that is, in straight lines or circles, we have the following principles. To cut right lines, at once, from two cylinders, as in Fig. 5, a plane must be parallel to both their axes. To cut a cylinder and cone, at once, in the same manner, as in Fig. 7, each plane must contain the vertex of the cone, and be parallel to the axis of the cylinder. To cut elements at once from two cones, a plane must simply contain both vertices.
Page 54 - Hence, if a right line is perpendicular to a plane, its projections are perpendicular to the traces of the plane, respectively.
Page 55 - Through a given point to draw a line perpendicular to a given plane: (1) the point being without the plane, (2) the point being in the plane.