This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1913 Excerpt: ... xy. These are the projections of a horizontal line passing through P, lying in the tangent plane, and terminated at C by the vertical plane. Hence lm drawn through c and m is the required vertical trace. Examples.--1. Draw the plan and elevation of a cone with its base on the ground, diameter of base height 2." Draw ...
Read More
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1913 Excerpt: ... xy. These are the projections of a horizontal line passing through P, lying in the tangent plane, and terminated at C by the vertical plane. Hence lm drawn through c and m is the required vertical trace. Examples.--1. Draw the plan and elevation of a cone with its base on the ground, diameter of base height 2." Draw the traces of a plane which touches the cone along a generator whose plan makes 45 with xy. 2. Draw the plan and elevation of a line inclined at 45 to touch the cone in Ex. I at the middle point of the given generator. 3. Determine the traces of a tangent plane as in Ex. 1, but with the cone inverted so that its vertex rests on the ground. 287. Problem.--A given cone, vertex V, rests with its base on the horizontal plane, determine the traces of a plane which shall pass through a given external point P and be tangential to the cone. The required plane must contain the line VP. Therefore obtain h, the plan of the horizontal trace of VP. Draw nhm tangential to the plan of the base of the cone. Then nm is the horizontal trace of the required plane. Determine / the elevation of the vertical trace of VP. Then r'lm is the required vertical trace. Note.--Since two tangents may be drawn from h to the plan of the base of the cone, there are two tangent planes satisfying the given conditions. 288. Problem.--To determine the traces of the plane which shall be tangential to a given sphere, centre S, at a point on its upper surface, the plan p of the point being given. First Method.--With centre J describe a circle to pass through p, and obtain a'b' the elevation of this circle; a projector from p to meet a'b' will determine p'. At a and V draw tangents to the circle, meeting each other in v and xy in ef; then v'e'f is the elevation of a cone which tou...
Read Less
