Sentence Examples


  • These curves are instances of unicursal bicircular quartics.
  • Hence it is unicursal (see CURVE).
  • When D = o, the curve is said to be unicursal, when = i, bicursal, and so on.
  • [In particular a curve and its reciprocal have this rational or (I, r) correspond ence, and it has been already seen that a curve and its reciprocal have the same deficiency.] A curve of a given order can in general be rationally transformed into a curve of a lower order; thus a curve of any order for which D=o, that is, a unicursal curve, can be transformed into a line; a curve of any order having the deficiency r or 2 can be rationally transformed into a curve of the order D+2, deficiency D; and a curve of any order deficience = or> 3 can be rationally transformed into a curve of the order D+3, deficiency D.
  • In particular if D =o, that is, if the given curve be unicursal, the transformed curve is a line, 4 is a mere linear function of 0, and the theorem is that the co-ordinates x, y, z of a point of the unicursal curve can be expressed as proportional to rational and integral functions of 0; it is easy to see that for a given curve of the order m, these functions of 0 must be of the same order m.

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