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Descriptive Geometry

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    Available in PDF - DJVU Format | Descriptive Geometry.pdf | Language: ENGLISH
    Linus Faunce (Author)

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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. 1888 edition. Excerpt: ...To draw a plane tangent to the cone at the point (a', a).--Here, as in the case of the cylinder, HP, drawn tangent to the base of the cone at c, will be the horizontal trace of the tangent plane (Art. 80), and the trace of the horizontal Y determines one point s' in VP. VP could have been determined by finding the vertical trace d' of the element of contact B. VQ and HQ, found in the same way, are the traces of a plane tangent to the cone at the point (a, a,). 88. Fig. 49 shows the construction when the axis of the cone is parallel to both V and H. Let n' be the vertical projection of a point on its surface. Pass the profile plane X through the base of the cone, and revolve it about VX into V. Gy is the vertical projection of the elements through n. In revolution d' moves to df and d,,', and in counter revolution they are found in plan at d and df: Gh and G,h drawn through d and d and the vertex o, are the horizontal projections of the two elements vertically projected in GT, and n' and n, are the horizontal projections required. In finding the traces of the tangent plane through the point (n', n), we find one point in each trace,--that is, c' and m, just the same as in Fig. 47: another point in each trace is obtained, of course, by finding the two traces of the element of contact G: joining the horizontal and vertical traces, respectively, we have VP and HP. The plane Q is found in the same way. If the cone had been so situated that the traces of the element of contact did not fall within easy reach, we would have made use of another profile plane, getting two more points, as we did c' and m. 89. Problem 28.--To pass a plane tangent to a cone, through a given point without the surface....
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Book details

  • PDF | 18 pages
  • Linus Faunce (Author)
  • RareBooksClub.com (12 Oct. 2012)
  • English
  • 7
  • Science Nature

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