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Home > History and Archaeology > History > A Paper on the Foundations of Projective Geometry; (Read Before the Aristotelian Society, Dec. 13, 1897)
A Paper on the Foundations of Projective Geometry; (Read Before the Aristotelian Society, Dec. 13, 1897)

A Paper on the Foundations of Projective Geometry; (Read Before the Aristotelian Society, Dec. 13, 1897)


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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: ...origin and the U0 in the equator. It will obviously be simplest to collate together the U0 in each ray which constitutes at once the origin and the dividing boundary of each half ray. As the unit in the section of the pencil belonging to each half ray is used to collate the half rays, these units must all be collated together, and therefore we must revert tfte units in each ray with respect to the origin as pivot and the section as equator by an unique reversion, which will completely collate the units of the two halves of any one ray. If (0, 0, '), (02 02'), (0,03') be the first three arbitrarily selected U08 out of the (-+1) which determine the system of pencils used to collate the whole group, (0, 0/) will be the first origin and (02 0,02' 0/) the first section; (02 02') will be the second origin, and (0a 0, ') the U0 with one of whose units the whole pencil of U, s will be collated in the next stage of the process. Hence, to collate the two halves of the section with each other we similarly revert it uniquely with respect to (02 02') as pivot and (03 03') as equator. To collate together the section and the rays of the pencil, if we wish to do so, we may collate together the pivots of reversion and the equators in each case; thus O, in the ray is collated with 02 in the section, and 02 in the ray with Oa in the section. Or we may catalogue the rays and the sections independently. To determine the collation completely, we have, however, to collate together some third unit in each ray and in each section. I will show how these third units may be determined for all the rays of a pencil of the first order by choosing arbitrarily units in two of them, or an unit in one and an unit in the section. Select any two units, P1 between Ov 02, and P2 between 0V 0S, ...


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Product Details
  • ISBN-13: 9781151343710
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 30
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1151343714
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 73 gr


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A Paper on the Foundations of Projective Geometry; (Read Before the Aristotelian Society, Dec. 13, 1897)
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A Paper on the Foundations of Projective Geometry; (Read Before the Aristotelian Society, Dec. 13, 1897)
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