 | George Salmon, Arthur Cayley - Curves, Algebraic - 1873 - 379 pages
...anharmonic ratio of the four tangents from any point on the curve will be the same (Art. 229). When Z>=1, the coordinates of any point on the curve can be expressed as rational functions of a parameter 0, and of V(®) where 0 is a quartic function of 0. It is sufficient to shew... | |
 | George Salmon - Curves, Algebraic - 1879 - 426 pages
...short of the maximum ; this number playing a very important part in the theory of curves. If D = 0, that is, if a curve have its maximum number of double...other assumed points on the curve, making together \ (n+ 1) (n— 2) — 1 points, or one less than enough to determine a curve of degree n — 2, we... | |
 | Great Britain. Education Department. Department of Science and Art - 1886 - 640 pages
...can possess, when it does not resolve into curves of lower dimensions; and show that, if a curve has its maximum number of double points, the coordinates...any point on the curve can be expressed as rational algebraical functions of a variable parameter. (65.) 48. Find the general form of the equation to a... | |
 | Great Britain. Education Department. Department of Science and Art - 1894 - 894 pages
...(60-) 45. Find the maximum number of double points possible on a carve of the nth degree. Show that if a curve have its maximum number of double points,...any point on the curve can be expressed as rational algebraical functions of a variable parameter. (60. ) 46. Having given the axis, and one of the generating... | |
 | Mathematics - 1899 - 522 pages
...By WA Houston, St. John's College. IT is proved in Salmon's Higher Plane Curves* that " If a plane curve have its maximum number of double points, the...rational algebraic functions of a variable parameter," the algebraic functions being of the same degree as the curve. It is there stated that the converse... | |
 | University of Calcutta - 1911 - 760 pages
...1. What do you understand by " the deficiency of a curve " ? If there is no deficiency, prove that the co-ordinates of any point on the curve can be expressed as rational algebraical functions of a variable parameter, that is, the curve is unicursal. Prove that if a curve... | |
 | Great Britain. Board of Education - Education - 1912 - 1044 pages
...sum of vectors is — OA.OB.OC {cos4 BOC + cos'- CO A + cos5 AOB -f 6 cos BOC cos CO A cos AOB}*. 8. If a curve have its maximum number of double points, the coordinates of any point on it can be expressed as rational algebraic functions of a variable parameter. How many double points... | |
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Q, that is, if a curve have its maximum number of double points, the coordinates of any point on the curve can be expressed as rational algebraic functions of a variable parameter. 