. The New York coach-maker's magazine. urface and its new jorojection be-come incorporated upon that plan. In the two cases, theoperation always consists in the transfer of the inclinedsurface into a position either horizontal or vertical, as itmust coincide or be parallel to one of the plans of pro-jection that has such direction. It is not merely in order to determine the size of aninclined surface that it is brought either to a vertical or ahorizontal position, but for the purpose of exactly repre-senting all the lines of construction connected with it, onthat surface and in the new positio
. The New York coach-maker's magazine. urface and its new jorojection be-come incorporated upon that plan. In the two cases, theoperation always consists in the transfer of the inclinedsurface into a position either horizontal or vertical, as itmust coincide or be parallel to one of the plans of pro-jection that has such direction. It is not merely in order to determine the size of aninclined surface that it is brought either to a vertical or ahorizontal position, but for the purpose of exactly repre-senting all the lines of construction connected with it, onthat surface and in the new position it occupies. It alsodetermines all the intersections of surfaces, all the levelsof component parts of the frame composing it, in factall lines that only can rigorously be determined on thedeployed surface or projected in full size. In order to fix the mind on the use of rotation, de-ploying, and varying the plan of projections, we will firstmake the application on a triangle that we will suppose inall its possible positions. r - Q T. LXXII. Suppose ABC (fig. 49) to be the triangle inquestion, formed in such a manner that one of its sidesA C is directed in a perpendicular sense to the verticalplane Q. The triangle ABC, being actually given onthe horizontal plane P, confuses itself on that plane withits projection, and the vertical projection is carried outalong the ground line a B. Now suppose the triangle tobe turned around its side A C, which is the same as thepivot of a hinge, and from whatever position it may oc-cupy in space, determine its new projection on the planesP and In its movement of rotation around the axis A C,which latter remains fixed, each point of the triangle,being always at the same distance from the axis, describesthe circumference of a circle, the plane of which is per-pendicular to the axis, the centre of which is found atpoint of intersection of that plane and the axis (art. 82.) The circumference of the circle of each point, istherefore projected
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