A Course in Descriptive Geometry and Photogrammetry for the Mathematical Laboratory Volume 1

A Course in Descriptive Geometry and Photogrammetry for the Mathematical Laboratory Volume 1

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1915 edition. Excerpt: ...is the surface of revolution generated by the rotation of a circle about one of its diameters. Evidently any section of a surface of revolution made by a plane at right angles to the axis of revolution is a circle, which is known as a parallel. The sections made by planes passing through the axis of revolution are all equal to each other, no matter what be the position of the plane, and these curves are known as meridians, and the corresponding planes as meridian planes. The advantage of this method of definition, from the point of view of descriptive geometry, now becomes clear, for instead of representing the surface by the projections of a certain number of selected points on it, it is now possible to represent it by the projections of a certain number of generating curves. If a point on the surface has to be dealt with, then the projections of the generator passing through that point are considered, a more elegant process than that of considering the projections of adjacent points chosen at random on the surface. A surface may often be generated in either of several distinct ways, and the problem under consideration will determine, in such cases, the choice of a method. The first few problems in this chapter will be devoted to the consideration of tangent planes to curved surfaces. The tangent plane at any point of a curved surface may be defined as the plane containing the tangent lines at that point to all curves traced on the surface and passing through the point. It is thus determined if the tangent lines to any two such curves are known. The following lemmas will be required, viz.: --a. The projection of the tangent to a curve at any point on it is the tangent to the projected curve at the corresponding point. /3. The tangent..show more

Product details

  • Paperback | 24 pages
  • 189 x 246 x 1mm | 64g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236571444
  • 9781236571441