07 Dec




















ment as shown in No. 2, Fig. 192, proceed as follows : At right angles to a c in No. 1 in the figure and through c, draw a line indefinitely. At any convenient point, as c in that line, draw through c' a line parallel to c a in No. 1. Then as all the side edges of the prism are parallel to each other, set off on the line drawn through c in No. 1 from c', the distances measured at right angles that those edges are apart ; arid through the points in c c' produced thus found, draw lines indefi- nitely, parallel to that first drawn from c', or to c a No. 1. Now it is evident that the four side (or inclined) edges of the prism will, when the surface is unfolded, lie in the lines last drawn, for if the prism No. 1 as a solid, is laid with its edge ca coinciding with the line ca in No. 2, and rolled over to the right its edges would fall upon the lines drawn parallel to ca. To complete the development, project over from No. 1 at right angles to ac the points ac ; bd; to cut the corresponding edges in No. 2; in a'c', ac, a"c"; and b'd", bd. Join a'b', ba, a a"; and c'd', dc, c c", by straight lines as shown. For the two ends of the prism which is square in cross-section produce the line b d in No. 1 in both direc- tions, and from b and c?, set off in e and /, a length equal to a b or c d. Project over e,/to e'f in No. 2, and through them draw lines at right angles to b'd", to cut b c?, which completes the development required. The envelope of the prism thus produced will, when folded over on the edges represented in dotted lines, be found to cover without vacuities all the surfaces of the given prism. 83. As the development of the surface of any prism whether right or oblique having any number of sides, may be found as above shown, a pyramid is taken as the next object for its surface development. The

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