Lectures on the Geometry of Position Volume 1 - Bookswagon
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Lectures on the Geometry of Position Volume 1

Lectures on the Geometry of Position 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. 1898 Excerpt: ...will rotate about the same point in the opposite sense, the two sheaves described by the diameters thus being equal. The sheaves of rays by which an equilateral hyperbola is projected from the extremities of any diameter are also equal to each other; for any two corresponding rays are parallel to two conjugate diameters (Art. 155), since they intersect in a point of the hyperbola. 165. The straight line joining the middle point D of a chord AB of a parabola (Fig. 51) to the point of intersection C of the tangents constructed at A and B is a diameter of the parabola, since it is the polar of the infinitely distant point of AB (Art. 134). But C and D are harmonically separated by the two points of intersection of CD with the parabola, and one of these intersections is infinitely distant; the other, therefore, bisects the segment CD, or, "The straight line, which joins the pole of any chord of a "parabola with the middle point of the chord, is bisected by the "parabola." It may be shown, in a similar manner, that each of the two straight lines which can be drawn from any point of the plane to its polar, parallel to the asymptotes of a hyperbola, is bisected by the hyperbola. 166. These are some of the most important of the metric relations which are derived from the polar theory of curves of the second Fig. 51. order. But from the theorems upon inscribed and circumscribed quadrangles and triangles there may be deduced other relations not wholly unimportant--in particular from the theorem of Art. 116, which may be stated as follows: "The two diagonals of a quadrangle BBDD circumscribed "to a curve of the second order intersect in a point S, which lies in "a straight line with the points of contact of either pair of opposite &q...


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Product Details
  • ISBN-13: 9781130234503
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 84
  • Spine Width: 4 mm
  • Width: 189 mm
  • ISBN-10: 1130234509
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 168 gr


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