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Chapters on the Modern Geometry of the Point, Line, and Circle (Volume 1-2); Being the Substance of Lectures Delivered in the University of Dublin to the Candidates for Honors of the First Year in Arts

Chapters on the Modern Geometry of the Point, Line, and Circle (Volume 1-2); Being the Substance of Lectures Delivered in the University of Dublin to the Candidates for Honors of the First Year in Arts


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About the Book

This historic book may have numerous typos, missing text or index. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. 1863. Not illustrated. Excerpt: ... 376. The general property of Art. 370 supplies obvious and rapid solutions of the two following pairs of reciprocal problems, viz.-- a. Through a given point to draw a line intersecting two given angles, or circles, so that the point shall be a double point of the involution determined by the two pairs of intersections. a. On a given line to find a point subtending two given segments, or circles, so that the line shall be a double line of the involution determined by the two pairs of subtenders. For, since, by the property of that article (370), the two double points (or lines) of the involution in question are harmonic conjugates with respect to the two pairs of intersections (or subtenders), and therefore conjugate points (or lines) with respect to the two angles (or segments) (217), or to the two circles (259, a or a); therefore, the two polars of the given point (or poles of the given line) with respect to the two given angles (or segments) (217), or to the two given circles (174), determine, by their point of intersection (or line of connexion), the second double point (or line) of that involution; and the two double points (or lines) being thus known, their line of connexion (or point of intersection) is of course the required line (or point). N.B. When, in the former case, the given point has the same polar with respect to the two given angles or circles, and when, in the latter case, the given line has the same pole with respect to the two given segments or circles, the above reciprocal constructions become, as they ought, indeterminate; every line through the given point in the former case, and every point on the given line in the latter case, then evidently satisfying the conditions of the problem. 377. The equianharmonic relations of Art. 364, combine...


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Product Details
  • ISBN-13: 9781154214536
  • Publisher: General Books
  • Publisher Imprint: General Books
  • Height: 246 mm
  • No of Pages: 234
  • Spine Width: 12 mm
  • Width: 189 mm
  • ISBN-10: 1154214532
  • Publisher Date: 01 Jan 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 426 gr


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Chapters on the Modern Geometry of the Point, Line, and Circle (Volume 1-2); Being the Substance of Lectures Delivered in the University of Dublin to the Candidates for Honors of the First Year in Arts
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