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On Plane Curves of Degree n with a Multiple Point of Order n −1 and a Conic of 2n -Point Contact

1922
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Proceedings of the London Mathematical Society
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1. We have considered elsewhere the properties of a plane algebraic curve of degree n (an n-ic) with tangents of n-point contact {Messenger of Mathematics, 1920). The case of an ;i-ic with a conic or conies of 2?tpoint contact at once suggests itself. It will be found immediately that an w-ic meeting y = x 2 in 2?i-points coinciding with the origin (which is not a double point) has an equation of the form (y-x 2 )u n -2 = y 11 , where u n _ 2 = 0 is some {n-2)-ic. Then, by a change of axes, we

doi:10.1112/plms/s2-20.1.93
fatcat:e2kja2meg5helazk5rbpqep2ai