No CrossRef data available.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 06 July 2012
(1) The process of dialytic elimination was first applied to a set of general ternary quadrics by Sylvester in 1841, his method being to form from the three quadrics u1u2u3 ten cubics, viz.:—
and then eliminate dialytically the ten quantities
The actual work of obtaining the eliminant as a determinant of the 10th order he did not perform; and, indeed, with the notation which he used the labour would have been very irksome.
page 667 note * Sylvester, J. J., “Examples of the Dialytic Method of Elimination as applied to Ternary Systems of Equations,” Cambridge Math. Journ., ii. pp. 232–236.Google Scholar
page 667 note † Salmon, G., Lessons introductory to the Modern Higher Algebra (1859), p. 38, § 55. [The paragraph appears unaltered in all the subsequent editions.]
page 668 note * The connection between ∂J/∂α and the corresponding quadric used by Sylvester is
page 668 note † Muir, T., “A Problem of Sylvester's in Elimination,” Proc. Boy. Soc. Edin., xx. pp. 300–305Google Scholar; Cayley, A., “Note on Dr Muir's paper, ‘A Problem, etc.,’” ibid., xx. pp. 306–308; Muir, T., “Further Note on ‘A Problem, etc.,’” ibid., xx. pp. 371–382; Muir, T., “ On the Eliminant of a Set of Ternary Quadrics,” ibid., xxi. pp. 220–234.
page 678 note * Sylvester, J. J., “Examples of the Dialytic Method, etc.” Cambridge Math. Journ., ii. p. 233.Google Scholar
page 678 note † Nanson, E. J., “On the Eliminant of a Set of Quadrics, Ternary or Quaternary,” Proc. Roy. Soc. Edin., xxii. p. 354.Google Scholar