Practical engineering drawing and third angle projection, for students in scientific, technical and manual training schools and for ..draughtsmen .. . osses the extremeelement, draw an in-definite line, OS, par-allel to c d, and cut it at m by aline a m that is perpendicular to a 6at its intersection with the frontelement cf of the cylinder; then0 m = p = r For we haA-eoa = 0 7) sec 9 = r sec 0; and o a (= )•) : oa :: o a : o m; whence o m = r sec 6 = p. The circumference of circle p equals 2 ir r sec 0, the actual length of the helix, as may he seenby developing the cylinder on which
Practical engineering drawing and third angle projection, for students in scientific, technical and manual training schools and for ..draughtsmen .. . osses the extremeelement, draw an in-definite line, OS, par-allel to c d, and cut it at m by aline a m that is perpendicular to a 6at its intersection with the frontelement cf of the cylinder; then0 m = p = r For we haA-eoa = 0 7) sec 9 = r sec 0; and o a (= )•) : oa :: o a : o m; whence o m = r sec 6 = p. The circumference of circle p equals 2 ir r sec 0, the actual length of the helix, as may he seenby developing the cylinder on which the latter lies. The elements which were tangent to the hehxmaintain the same relation to the developed hehx, and appear in their tme length on the student can make a model of one nappe of this surface by wrapping a sheet of Bristolboard, shaped like Fig. 273, upon a. cylinder of radius r in the equation r sece = p; or a two-napped hehcoid by superposing two equal circular rings of paper, binding them on their inner edgesTvith gummed paper, making one radial cut through both rings, and then twisting the inner edgeinto a THE INTERSECTION OF SURFACES. 421. When plane-sided surfaces intersect, their outhne of interpenetration is necessarily composed ofstraight hnes; but these not being, in general, in one plane, form what is called a tioisted or toarpedpolygon; also called a gauche polygon. 422. If either of two intersecting surfaces is curved their common line will also be curved,except under special conditions. 423. AMien one of the surfaces is of uniform cross section —as a cylinder or a prism —its end\iew will show whether the surfaces intersect in a continuous line or in two separate ones. In Casesa, b, c, d and (/ of Fig. 275, ^\heve the end ^-iew of one surface either cuts but one limiting line ofthe other surface or is tangent to one or both of the outhnes, the intersection will be a continuousline. Two separate curves of intersection will occ
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Keywords: ., bookcentury1800, bookdecade1890, booksubjec, booksubjectlettering
