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  • Proceedings of the Edinburgh Mathematical Society, Volume 14
  • February 1895, pp. 31-34

Some Properties of Parabolic Curves


If the tangent at a point P on the parabolic curve cy=xn meet the axis of x at M, it is a well-known property that the area between the radius vector OP and the are OP is n times that between the arc OP and the two tangents OM, MP, O being the origin and n > 1. The converse is also true; for taking any point O on a curve as origin and the tangent at O as axis of x, let us seek for the locus of P if the area between OP and the arc OP be n times the area between the arc OP and the tangents OM, MP.

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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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