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apex auxiliary plane axis base circle cone director conical surface Construction coordinate plane counter-revolution curve of intersection curvilinear directrices Determine the prs Determine the traces distance double-curved surface Draw the projections Draw the prs drawn F"and given line ground line heavy type helicoid helix hori horizontal projection horizontal trace hyperbola hyperbolic paraboloid hyperboloid intersecting lines line of intersection line parallel lines Arts Method multiples of 16 oblique projection obtain parallel to H pass a plane perpendicular plane containing plane director plane N plane of lines plane perpendicular plane tangent point draw point of tangency Principle Problems profile projection profile trace projecting plane purlin pyramid rectilinear generatrix required plane required tangent plane revolved position right line right-hand division line ruled surfaces shadow single-curved surface sphere surface of revolution tion traces of plane triangle true length V-pr V-tr vertical projection vertical trace warped surface
Page 46 - Fig. 1. 5. >Shadow: When a surface is in light and an object is placed between it and the source of light, intercepting thereby some of the rays, that portion of the surface from which light is thus excluded is said to be in shadow. 6. In actual practice distinction is seldom made between these terms "shade" and " shadow," and "shadow" is generally used for that part of an object from which light is excluded.
Page 46 - That portion of space from which light is excluded is called the umbra or invisible shadow. (a) The umbra of a point in space is evidently a line. (b) The umbra of a line is in general a plane. (c) The umbra of a plane is in general a solid. (d) It is also evident, from Fig.
Page 118 - We have now shown that the surface generated by the revolution of a right line about an axis which it does not intersect, may also be generated by a right line touching constantly three rectilinear directrices.
Page 46 - Fig. 1, that the shadow of an object upon another object is the intersection of the umbra of the first object with the surface of the second object. For example, in Fig. 1, the shadow of the given sphere on the surface in light is the intersection of its umbra (in this case a cylinder) with the given surface producing an ellipse as the shadow of the sphere. 8. Ray of light: The sun is the supposed source of light in
Page 80 - Pass a plane through the center of the sphere and perpendicular to the given line.
Page 45 - The distance from a point to a plane is the perpendicular distance from the point to the plane.
Page 80 - Fig. 59, be the centre of the sphere ; prq its horizontal, and p's'q' its vertical projection. Let M be the point assumed, as in Art. (107). Analysis. Since the radius of the sphere, drawn to the point of contact, is perpendicular to the tangent to any great circle at this point, and since these...
Page 46 - ... graphically by a straight line. Since the sun is at an infinite distance, it can be safely assumed that the rays of light are all parallel. 9. Plane of light: A plane of light is any plane containing a ray of light, that is, in the sense of the ray lying in the plane. 10. Shade line: The line of separation between the portion of an object in light and the portion in shade is called the shade line. • 11. It is