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Elements of Geometry and Mensuration

Elements of Geometry and Mensuration


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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. 1858 edition. Excerpt: ...diagonals of the parallelogram ACKG, and therefore bisect each other in 0 (76). In like manner, if the diagonals DI and FB be drawn, it may be shown that each of them will be bisected by AK or GC, in the point 0. Therefore, the four diagonals of a parallelopipedon, &c.. (380.) Cor. Any two opposite edges of a parallelopipedon, or of any prism, are parallel to each other, and a plane may therefore pass through them. (381.) ScJw. The point O in which the diagonals of a parallelopipedon mutually bisect each other, may be regarded as the centre of the parallelopipedon. THEOREM VI. (382.) The two triangular prisms into which a parallelopipedon is divided by a plane passing through two opposite edges, arf equivalent. Let ABCD--I be a parallelopipedon divided into the two triangular prisms ABD--I and BCD--I by the plane BI (380); these triangular prisms are equivalent. Through the vertices B and G lej two planes be drawn perpendicular to the edge BG, and forming, by their intersections with the planes of the lateral faces, the parallelograms BKLM and GHOP (377; 345). The planes of these parallelograms, being both perpendicular to BG, are parallel (339); hence their intersections BM and GP with the plane BP are parallel, and the figure MBGP is a parallelogram; for like reasons, BKHG, HL, and LP are parallelograms; moreover, the sections BKLM and GHOP being equal (372), it follows that the solid BKLM--P, with its edge BG perpendicular to its base, is a right parallelopipedon. This parallelopipedon is divided by the plane BLOG into the two right prisms MBL--O and BKL--O, and these two prisms are equal, since they have equal bases MBL and BKL, and the same altitude BG (376). In the parallelograms ABGF and MBGP, the sides AF and MP are equal, because...


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Product Details
  • ISBN-13: 9781236471680
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 82
  • Spine Width: 4 mm
  • Width: 189 mm
  • ISBN-10: 1236471687
  • Publisher Date: 01 Jun 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 163 gr

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