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Conic Sections Treated Geometrically, by S.H. Haslam and J. Edwards

Conic Sections Treated Geometrically, by S.H. Haslam and J. Edwards


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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. 1881 Excerpt: ...of AB in the same ratio. Fig. 88. For from our last proposition we have AT' AP:: P'B' PB and.-. A'P' P'B' AP: PB Q.E.D. 191. Cor. 2.--If P be the middle point of AS, then P' will be the middle point of A'B'. 192. Cor. 3.--It is evident that by properly choosing the plane of projection a line AB can be shortened in any ratio; for if we have only to describe a semicircle on AB and place in it a line AE of the length required, then if we take the plane of projection parallel to AE the projection A'B' will be equal to AE. 193. Cor. 4.--If the plane of projection be taken parallel to any line AB, then the projection A'B' is equal to AB. tion. PROP. 3. 194. The projection of an ellipse is an ellipse. Let ABA' be the given ellipse, aba' its orthogonal projec Fig. 90. The centre c projects into the middle point of aa' by Prop. 2, Cor. 2. The middle points N and C of an ordinate PP' and of the axis BB' project into the middle points of two parallel lines pp' and bb' by Props. 1 and 2. 195. Cor.--An ellipse can be projected into a circle by properly choosing the plane of projection. For describe a semicircle on AC in a plane perpendicular to the plane of the ellipse, and place in it a line CE equal to CB; then if we take a plane parallel to BEB' as plane of projection, the line AC will project into a line equal to CE or CB, while the length of CB remains unchanged. Conversely, in the same manner as in Prop. 3, the projection of a circle is an ellipse. PROP. 4. 196. The projection of a parabola is a parabola. For all the ordinates (being parallel lines) project in the same ratio, so also do all the abscissae. But in the original curve the square of the ordinate varies as the abscissa, whence this relation holds also in the projected curve, which is therefore a parab..


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Product Details
  • ISBN-13: 9781130793000
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 28
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1130793001
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 68 gr


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