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Proceedings of the Section of Sciences Volume 10, No. 2

Proceedings of the Section of Sciences Volume 10, No. 2


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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. 1908 Excerpt: ...diagram on the top leftside, represents an eightcell which indicates besides the diameters normal to the different series of parallel intersecting spaces a few other lines appearing in the solution; for our case (1, 1, 1, 1) to which the four following diagrams refer the axis EE' is this diameter. To characterize this case the mark (1,1,1,1) is noted down to the right at the 4 3 2 1 bottom in the rectangle; moreover the fractions--, -, -, -placed to 8 8 8 8 the left at the top of each diagram indicate the part of the axis EE' lying with E on the same side of the intersecting space. It is easy to follow in these diagrams the changes in form which each face of the regular octahedron forming the central section undergoes, when the point of intersection of the intersecting space with the axis OE moves from 0 to E. Thus the face lying in the upper cube of the eightcell, which is at the same time the visible upper plane of the octahedron regarded by itself, transforms itself first into a regular.hexagon, then into an equilateral triangle of opposite orientation, etc.; if the eightcell is a C then the sides of the triangles of the first and third diagrams are 2/2, those of the hexagons and the triangles of the second and fourth diagrams are VI, whilst the series closes with the transition form consisting of the single vertex E to which the fraction-answers. 8 We now arrive at the question how the remaining eightcells that are likewise cut by the intersecting space are intersected in each of the considered cases. To this end we suppose the above intersected eightcell to be the central one of the net and so we assume the centre of this cell to be the origin of the system of coordinates with respect to which we have determined in the tirst communication the coordi.


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Product Details
  • ISBN-13: 9781130295900
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 160
  • Spine Width: 9 mm
  • Width: 189 mm
  • ISBN-10: 1130295907
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 299 gr


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