A Course of Mathematics Volume 3; Composed for the Use of the Royal Military Academy
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A Course of Mathematics Volume 3; Composed for the Use of the Royal Military Academy

A Course of Mathematics Volume 3; Composed for the Use of the Royal Military Academy


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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. 1811 Excerpt: ...we multiply them one by another, there will result a complex equation which at once comprizes all the lines assumed. For example, if from the centre c, with a radius CA=fl, a circle be described; and further, if a right line Ln be drawn through the centre c; then we may, for any assumed axis, find an equation which will at once include the circle and the right line, as though these two lines formed only one. Suppose there be taken for an axis the diameter AB, that forms with the right line Ln an angle equal to half a right angle: having placed the origin of the abscissas in A, make the abscissa Ap = x, and the applicate or ordinate Pm = y; we shall have for the right line, Pm = CP = a--x; and since the point M of the right line falls on the side of those ordinates which are reckoned negative, we have.y =--a + x, or y--x + a = 0: but, for the circle, we have Pm = Ap.pb, and Bp = 2a--x, which gives yz = 2ax--x, or yx + x--2ax = 0. Multiplying these two equations together we obtain the complex equation of the third order, y--yv + yx-x3 + ay-2axy + 3ax2-2ar = 0, which represents, at once, the circle and the right line. Hence, we shall find that to the abscissa Ap = x, corresponds three ordinates, namely, two for the circle, and one for the right line. Let, for example, x = the equation will become y + iayx--$aly-a? = 0; whence we first find y + a = 0, and by dividing by this root, we obtainy1--= 0, the two roots of which being taken and ranked with the former, give the three following values ofy: Vol. Hi. O 1. y = t y =-la. U. y = + III. y-ia/3. We see, therefore, that the whole is represented by one equation, as if the circle together with the right line formed only one continued curve. 10. This difference between simple and complex curves being once establish...


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Product Details
  • ISBN-13: 9781236404480
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 112
  • Spine Width: 6 mm
  • Width: 189 mm
  • ISBN-10: 1236404483
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 213 gr


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