Sentence Examples

  • He next gives by aid of these projective rows and pencils a new generation of conics and ruled quadric surfaces, "which leads quicker and more directly than former methods into the inner nature of conics and reveals to us the organic connexion of their innumerable properties and mysteries."
  • A curve is of the first order, second order, third order, &c., according as it is represented by an equation of the first order, ax+by+c = o, or say (1 x, y, 1) = o; or by an equation of the second order, ax 2 +2hxy+by e +2fy+2gx+c=o, say (*I x, y, 1) 2 =o; or by an equation of the third order, &c.; or what is the same thing, according as the equation is linear, quadric, cubic, &c.
  • A curve of the second order is a conic, and is also called a quadric curve; and conversely every conic is a curve of the second order or quadric curve.
  • It is to be remarked that an equation may break up; thus a quadric equation may be (ax+by+c) (a'x.+b'y+c') = o, breaking up into the two equations ax+by+c = o, a'x+b'y+c' = o, viz.
  • The pair of lines is considered as a quadric curve.

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