Articoli correlati a A treatise on practical plane and solid geometry; containing...
A treatise on practical plane and solid geometry; containing solutions to the honours questions set at the examinations of the science and art department (1887-1896) inclusive - Brossura
Sinossi
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. 1897 Excerpt: ... centre, radius 2 in., describe an arc cutting the perpendicular in a point whose height added to 8 (the index of a) will be the height of the point b. Now with this true length a'b' as base construct an equilateral triangle a'b'c', and imagine this to revolve about its base, when vertex c will have described a circle. And the intersection of this circle with ac will be the required length of the edge ac, which is readily seen in plan, as it must be the crossing-point of the elliptic plan of the circle with the line ac. This method will more readily determine the length of ac than that shown in the last question. Further, the solution will be precisely similar, and need no further description. The method here shown is simpler, as the elliptic base of the cone is dispensed with. Thus, with p" as centre and any radius, draw a circular arc cutting the generators p"q', p"q in points 11, and p"r', p"r, in points 2, 2; join 1,1,2, 2: their crossing-points t' will be points in the required generator p"t'a. The plan of point t' will evidently lie on the circumference of the horizontal circular section 11. With p as centre, describe the circle which is the plan of the horizontal section 11, and project t' to tt. Join pt, pt, and produce it to meet the circular base of the cone in points a and b. Now project a to a' and b to V on XY, and join p'a,' p'b'. Then p'a'p'b' is the elevation, and papb is the plan, of two lines satisfying the given conditions. S7, Draw a cone, base 15 units diameter, height 17-5 units, its base in plane ft, its vertex in plane P, and the centre of its base at 10 units above the horizontal plane of projection (unit = 01 in.). Take xy, a new ground-lino parallel to the scale of slope Q, and erect the end view cu o...
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