Transactions of the Historic Society of Lancashire and Cheshire for the Year Volume 15

Transactions of the Historic Society of Lancashire and Cheshire for the Year Volume 15

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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. 1863 edition. Excerpt: ...circles to touch each other and the given circle, so that the sides of the triangle formed by drawing tangents at the three points of contact of the given circle, and the circle required to be described, may pass through three given points not in the same straight line, This is Castillon's and Malfatti's problems combined. The investigation is very lengthy and includes various eases of several subsidiary problems. Problem II. In a given circle, it is required to describe three other circles to touch each other and the given one, so that two of the sides of the triangles formed by drawing tangents at the points of contact, as before, may be parallel to lines given in position, and the remaining side pass through a given point. This investigation is also lengthy, and he remarks at the close that there are fourteen other cases of this problem yet to be considered. The analyses of the preceding involve considerable difficulty, and evince an amount of reading which reflects great credit upon their author. His power of invention is conspicuous throughout; and this, together with the admitted elegance of his writings, entitles him to rank high amongst our modern geometers. Nor was he less successful in the investigation of Porisms, considered geometrically. Several of these have been contributed to the "Educational Times," but by no means the greater portion. At one time he intended to publish a small work on this difficult subject; but various causes prevented his carrying this intention into effect. The following may be adduced as an example of his mode of procedure. Those who desire to see a complete restoration of the three lost Books of Porisms, may be referred to "Les trois Livres de Porismes d'Euclid, Question VII. A B is a...
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Product details

  • Paperback | 90 pages
  • 189 x 246 x 5mm | 177g
  • United States
  • English
  • black & white illustrations
  • 1236875486
  • 9781236875488