The Mathematician Volume 1

The Mathematician Volume 1

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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. 1856 edition. Excerpt: ...corresponding to the successive changes of value of the variables of which it is composed; and, conversely, by the same fertile method may be exhibited a faithful analytical representation of a given geometrical figure. Among the numerous systems of co-ordinates which may be employed in the performance of these operations, it is important to distinguish, on the one hand, those which offer the greatest facilities for depicting equations geometrically; and on the other, those which produce the analytical representation of the given figure in its simplest form, or in that form from which its properties may be most conveniently evolved, as may be required. Since the determination of geometrical magnitude may generally be effected by finding its projections on certain planes, it will sulfite to consider here plane curves and their equations. Continuous plane curves may either be traced by joining a considerable number of approximate points, or described mechanically by continued motion. The first process will be most easily executed when the co-ordinateB to be measured in order to determine each point have b.en selected from the first elements of figure, as straight lines, angles, etc.; and the proposed object will be best accomplished in the second instance when the variation of the position of the co-ordinates is produced by the simplest motions, viz. those of translation or rotation. Of the various possible combinations of the elements of figure and motion, a little consideration will shew that the system best adapted for graphical purposes, both on account of the simplicity of the co-ordinates themselves, as of their mode of variation, is that by which the curve is generated by the intersection of two right lines having motions of translation...
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Product details

  • Paperback | 88 pages
  • 189 x 246 x 5mm | 172g
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236491270
  • 9781236491275