A Course of Mathematics; For the Use of Academies, as Well as Private Tuition Volume 2
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A Course of Mathematics; For the Use of Academies, as Well as Private Tuition Volume 2

A Course of Mathematics; For the Use of Academies, as Well as Private Tuition Volume 2


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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1812 edition. Excerpt: ... lines which this equation expresses, x and;/ denoting the rectangular co-ordinates. These curve lines are therefore the most simple of all, since there arc no curves in the first order of lines; it is for this reason that some writers call them curves of the first order. But the curves included in this equation are better known under the name of Conic Sections, because they all result from sections of the cone. The different kinds f these lines are the ellipse, the circle, or ellipse with equal axes, the parabola, and the hyperbola; the properties of all which may be deduced with facility from the preceding general equation. Or this equation may be transformed into the subjoined one: n + Y $x?v + y H =0 and and this again may be reduced to the still more simple form Here, when the first term/a'3 is affirmative, the curve expressed by the equation is a hyperbola; when/jr is negative the curve is an ellipse; when that term is absent, the curve is a parabola. When x is taken upon a diameter, the equations reduce to those already given in sect. 4 ch. i. The mode of effecting these transformations is omitted for the sake of brevity. This section contains a lummary, not an investigation of properties: the latter would require many volumes, instead of a section. 4. Under lines of the third order, or curves of the second, are classed all those which may be expressed by the equation o = +j3;r+yy + $3 + q-i/+ y2 + 13? + xy + ixy+y. And in like manner we regard as lines of the fourth order, those curves which are furnished by the general equation o = + Px + vy + 9x + ixy + y2 + ix3 + xy + txy + y3-f-Aar4 + txy + xy + fxy3 + y; taking always x and y for rectangular co-ordinates. In the most general equation of the...


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Product Details
  • ISBN-13: 9781155047157
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 162
  • Spine Width: 9 mm
  • Width: 189 mm
  • ISBN-10: 115504715X
  • Publisher Date: 01 Oct 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 299 gr


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