=1743.= If we consider the beauty of the theorem [Sylvester’s Theorem on Newton’s Rule for the Discovery of Imaginary Roots] which has now been expounded, the interest which belongs to the rule associated with the great name of Newton, and the long lapse of years during which the reason and extent of that rule remained undiscovered by mathematicians, among whom Maclaurin, Waring and Euler are explicitly included, we must regard Professor Sylvester’s investigations made to the Theory of Equations in modern times, justly to be ranked with those of Fourier, Sturm and Cauchy.--TODHUNTER, I. _Theory of Equations (London, 1904), p. 250._ =1744.= Considering the remarkable elegance, generality, and simplicity of the method [Homer’s Method of finding the numerical values of the roots of an equation], it is not a little surprising that it has not taken a more prominent place in current mathematical textbooks.... As a matter of fact, its spirit is purely arithmetical; and its beauty, which can only be appreciated after one has used it in particular cases, is of that indescribably simple kind, which distinguishes the use of position in the decimal notation and the arrangement of the simple rules of arithmetic. It is, in short, one of those things whose invention was the creation of a commonplace. --CHRYSTAL, GEORGE. _Algebra (London and Edinburgh, 1893), Vol. 1, chap. 15, sect. 25._ =1745.= _To a missing member of a family group of terms in an algebraical formula._ Lone and discarded one! divorced by fate, Far from thy wished-for fellows--whither art flown? Where lingerest thou in thy bereaved estate, Like some lost star, or buried meteor stone? Thou mindst me much of that presumptuous one Who loth, aught less than greatest, to be great, From Heaven’s immensity fell headlong down To live forlorn, self-centred, desolate: Or who, like Heraclid, hard exile bore, Now buoyed by hope, now stretched on rack of fear, Till throned Astæa, wafting to his ear Words of dim portent through the Atlantic roar, Bade him “the sanctuary of the Muse revere And strew with flame the dust of Isis’ shore.” --SYLVESTER, J. J. _Inaugural Lecture, Oxford, 1885; Nature, Vol. 33, p. 228._