A Course of Mathematics for the Use of Academies, as Well as Private Tuition
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A Course of Mathematics for the Use of Academies, as Well as Private Tuition

A Course of Mathematics for the Use of Academies, as Well as Private Tuition


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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. 1822 Excerpt: ... is so situated, that the ratio of x to z shall be that of 1 to m: then will tnx =z, and m x3--z. These substituted for z and z3 in the equation of the surface, will give, for the equation of the projection of the section on the plane -f the base, r3--2mx+(m2--1) x3 = y3. Now this equation, if m be greater than unity, or if the cutting plane pass between the vertex of the cone and the parabolic section, will be that of an hyperbola: and if, on the contrary, the cutting plane pass between the parabola and the base, i. e. if m be less than unity, the term (m3--l)x3 will be negative, when the equation, will obviously designate any ellipse. Schol. It might here be demonstrated, in a nearly similar manner, that every surface formed by the rotation of any conic section on one of its axes, being cut by any plane whatever, will always give a conic section. For the equation of such surface will not contain any power of x, y, or z, greater than the second; and therefore the substitution of any values of z in terms of x or of y, will never produce any powers of x or of y exceeding the square. The section therefore must be a line of the second order. See on this subject, Hutton's Mensuration, part iii, sect. 4. Ex. 3. Let the equation to the curve surface be xyz=a3. Then will the curve surface bear the same relation to the solid right angle, which the curve line whose equation is xy--a3 bears to the plane right angle. That is, the curve surface will be posited between the three rectangular faces bounding such solid right angle, in the same manner as the equilateral hyperbola is posited between its rectangular asymptotes. And in like manner as there may be 4 equal equilateral teral hyperbolas comprehended between the same rectangular asymptotes, when produced both ...


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Product Details
  • ISBN-13: 9781235918667
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 176
  • Spine Width: 10 mm
  • Width: 189 mm
  • ISBN-10: 1235918661
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 327 gr


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