Abstract
AMONG the 110 papers contained in this volume there are five or six which represent the author at his best. First of all there are three on Newton's rule for the discovery of imaginary roots of equations; here we see Sylvester working his way from a laborious and partly tentative method to the simple and beautiful proof which is reproduced in Tod-hunter's “Theory of Equations.” (It is not impossible, by the bye, that there may be a series of cubic functions of the coefficients which would give information supplementary to that afforded by Newton's series.) Then there are two papers on the motion of a rigid body containing a well-known addition to Poinsot's theory; these show admirably Sylvester's power of combining analytical and geometrical methods. Finally, there are the notes of his King's College lectures on the partition of numbers, which, in spite of their fragmentary form, supply some very interesting reading. They contain, practically, an outline of three distinct methods, that of combining a deficient set of linear equations, that of partial fractions, derived from Euler's generating function, and a barycentric method, or rather a baryccntric way of stating the problem and its solution, especially with regard to its definite or indefinite character.
The Collected Mathematical Papers of James Joseph Sylvester.
Vol. ii. (1854–73). Pp. xvi + 732. (Cambridge: University Press, 1908.) Price 18s. net.
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M., G. The Collected Mathematical Papers of James Joseph Sylvester . Nature 79, 303–304 (1909). https://doi.org/10.1038/079303b0
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DOI: https://doi.org/10.1038/079303b0