Descriptive geometry . es with H and V, andslopes downward, backward, to the right. Hence si determinesone side of the base of the prism. Revolve si about IIQ intoH to the position sHr (Prob. 21, Corollary, § 138). With shlr(produced) as one side, draw the square lr2r3r4r, making eachside 1 long ; this square is the revolved position of the baseof the prism. Note that, since point 1 is to be the lowest corner,no position of the square, other than that shown, is possible. XVII, § 149] COUNTER-REVOLUTION OF PLANES 173 Assume CrjL, perpendicular to HQ; locate VXQ by means ofsome point, as e, and
Descriptive geometry . es with H and V, andslopes downward, backward, to the right. Hence si determinesone side of the base of the prism. Revolve si about IIQ intoH to the position sHr (Prob. 21, Corollary, § 138). With shlr(produced) as one side, draw the square lr2r3r4r, making eachside 1 long ; this square is the revolved position of the baseof the prism. Note that, since point 1 is to be the lowest corner,no position of the square, other than that shown, is possible. XVII, § 149] COUNTER-REVOLUTION OF PLANES 173 Assume CrjL, perpendicular to HQ; locate VXQ by means ofsome point, as e, and counter-revolve the square (Prob. 29,Corollary, § 147). As a check, note that the point 2 must fallon the line si, produced, already determined. The long edges of the prism are lines If long and perpen-dicular to Q. Draw these lines, lxv 5^, 21r61, etc., in thesecondary projection ; from this projection find the projectionson H and V (Prob. 30, Second Analysis, § 148). Complete theprojections of the prism as An alternative method for finding the long edges of theprism is also given in Fig. 254. From point 1 draw the line(lhfh, L/j perpendicular to Qand of unknown length. Findthe true length Make 1*5!the required length, L§; from5t find the projections 5and 5* (Prob. 30, First Analysis, > 1 18).The remaining long edges, 2-6, 3-7, and 4-8, may now bedrawn equal and parallel to 1-5. CHAPTER XVIII TANGENT LINES AND PLANES — GENERAL PRINCIPLES 150. Curves. A curve may be defined as a line, no portion ofwhich is straight. A plane curve is one which lies wholly in a plane. If nopart of the curve is plane, the curve is a space curve, or curve ofthree dimensions. Familiar examples of plane curves are circlesand ellipses. An example of a space curve is the helix, asshown by a screw thread or a spiral spring. Space curvesresult usually, though not necessarily, when two curved sur-faces of any kind intersect each other. 151. Projections of Curves. The projection of a
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