Elements of descriptive geometry; with applications to spherical and isometric projections, shades and shadows, and perspective - Tapa blanda

Sinopsis

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. 1911 Excerpt: ...be revolved about the common axis, each will generate the surface to which it belongs, while the common point will generate the circumference of a circle common to the two surfaces, and therefore their intersection. Should the meridian lines intersect in more than one point, the surfaces will intersect in two or more circumferences. 167. The cylinder of revolution. The simplest curved surface of revolution is that which may be generated by a straight line revolving about another straight line to which it is parallel. This is evidently a cylindrical surface (Art. 79), and if the plane of the base be perpendicular to the axis, it is a right cylinder with a circular base. The cone of revolution. If a straight line be revolved about another straight line which it intersects, it will generate a conical surface (Art. 83), which is evidently a right cone, the axis being the line with which the rectilinear elements make equal angles. These are the only two single-curved surfaces of revolution. The Hyperboloid Op Revolution Of One Nappe 168. If a straight line be revolved about another straight line not in the same plane with it, it will generate a surface of revolution called a hyperboloid of revolution of one nappe. To prove that this is a warped surface, let us take the horizontal plane perpendicular to the axis, and the vertical plane parallel to the generatrix in its first position, and let c, Fig. 74, be the horizontal, and cV the vertical projection of the axis, and MP the generatrix; cm will be the horizontal, and cW the vertical projection of the shortest distance between these two lines (Art. 53). As MP revolves about the axis, CM will remain perpendicular to it, and M will describe a circumference which is horizontally projected in mxy, and vertically in ...

"Sinopsis" puede pertenecer a otra edición de este libro.