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V 11 K FACE. "We have endeavoured in the present work to combine some of the modern developments of Higher Algebra with the subjects usually included in works on the Theory of Equations. The first ten Chapters contain all the propositions ordinarily found in elementary treatises on the subject. In these Chapters Ave have not hesitated to employ the more modern notation wherever it appeared that greater simplicity or comprehensiveness could he thereby obtained. Regarding the algebraical and the numerical solution of equations as essentially distinct problems, we have purposely omitted in Chap. "VI. numerical examples in illustration of the modes of solution there given of the cubio and biquadratic equations. Such examples do not render clearer the conception of an algebraical solution ; and, for practical purposes, the algebraical formula may be regarded as almost useless in the case of equations of a degree higher than the second. In the treatment of Elimination and Linear Transfo
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