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Elements of Geometry and Conic Sections

Elements of Geometry and Conic Sections


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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 Excerpt: ...the piane MN in AC. The two lines AC, BD will be parallel (Prop. XII.). But the line AB, being perpendicular to the plane MN, is perpendicular to the straight line AC which it meets in that plane; it must, therefore, be perpendicular to its parallel BD (Prop. XXIII., Cor. 1, B. I.). But BD is any line drawn through B in the plane PQ; and since AB is perpendicular to any line drawn through its foot in the plane PQ, it must be perpendicular to the plane PQ (Def. 1). ThereCore, if two planes, &c. PROPOSITION XIV. THEOREM. Parallel straight lines included between two parallel planes ire equal. Let AB, CD be the two parallel straight lines included between two arallel planes MN, PQ; then will AB e equal to CD. Through the two parallel lines AB, CD suppose a plane ABDC to pass, intersecting the parallel planes in AC and BD. The lines AC, BD will be parallel to each other (Prop. XII.). But AB is, by supposition, parallel to CD; therefore the figure ABDC is a parallelogram; and, consequently, AB is equal to CD (Prop. XXIX., B. I.). Therefore, parallel straight lines, &c. Cor. Hence two parallel planes are every where equidistant; for if AB, CD are perpendicular to the plane MN, they will be perpendicular to the parallel plane PQ (Prop. XIII.); and being both perpendicular to the same plane, they will be parallel to each other (Prop IX.), and, consequently, equal. PROPOSITION XV. THEOREM. If two angles, not in th.'. same plane, have their sides parallel and similarly situated, these angles will be equal, and their planes will be parallel. Let the two angles ABC, DEF, lying in different planes MN, PQ, have their M sides parallel each to each and similarly situated; then will the angle ABC be equal to the angle DEF, and the plane MN be parallel to the plane PQ...


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Product Details
  • ISBN-13: 9781152519770
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 66
  • Spine Width: 4 mm
  • Width: 189 mm
  • ISBN-10: 1152519778
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 136 gr

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