Abstract
IN her note on “the binomial equation xp - I = O,” Miss Scott gives a somewhat simpler form of the equation for quartisection than that given by Prof. Cayley (L.Math. S.Proc., vol. xi. pp. 11–14), and works out the equation for quinquisection on apparently different lines from Mr. F. S. Carey's solution (cf. Prof. Cayley, L.Math.S.Proc., vol. xii. and vol. xvi.). Mr. F. N. Cole furnishes “A Contribution to the Theory of the General Equation of the Sixth Degree,” which is interesting from the historical details which he gives. He acknowledges his great indebtedness to Klein, but there is a good deal of original work in the note. Mr. J. C. Fields gives a neat “proof of the elliptic-function addition-theorem.” The pièce de résistance of the number is, however, the long-looked-for notes of “Lectures on the Theory of Reciprocants,” by Prof. Sylvester. These are designed as “a practical introduction to an enlarged theory of algebraical forms, and, as such, are not constructed with the rigorous adhesion to logical order which might be properly expected in a systematic treatise. The object of the lecturer was to rouse an interest in the subject, and in pursuit of this end he has not hesitated to state many results, by way of anticipation, which might, with stricter regard to method, have followed at a later point in the course.” The lectures, which are ten in number, have been reported by Mr. J. Hammond. The subject, which, it will be remembered, was fully brought before our readers by Prof. Sylvester's inaugural lecture, printed in extenso in NATURE (vol. xxxiii. pp. 222–231), has already attracted many of our younger mathematicians, so that there is hope of the Professor's closing aspiration of creating “such a school of mathematics as might go some way at least to revive the old scientific renown of Oxford” being soon an accomplished fact.
American Journal of Mathematics,
vol. viii. No. 3. (Baltimore, July 1886.)
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Our Book Shelf . Nature 34, 521 (1886). https://doi.org/10.1038/034521a0
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DOI: https://doi.org/10.1038/034521a0