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XXVI.—On the Eliminant of a Set of General Ternary Quadrics
Published online by Cambridge University Press: 06 July 2012
Extract
(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.
- Type
- Research Article
- Information
- Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 39 , Issue 3 , 1900 , pp. 667 - 684
- Copyright
- Copyright © Royal Society of Edinburgh 1900
References
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