WILLIAM SNOW BURNSIDE, M. A., FELLOW OF TRINITY COLLEGE, DUBLIN ; ERASMUS SMITH'S PROFESSOR OF MATHEMATICS IN AND ARTHUR WILLIAM PANTON, M. A., FELLOW AND TUTOR, TRINITY COLLEGE, DUBLIN; DUBLIN: HODGES, FIGGIS, & CO., GRAFTON-STREET. LONDON LONGMANS, GREEN, & CO., PATERNOSTER-ROW. 1886. L PREFACE TO THE FIRST EDITION. 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 we have not hesitated to employ the more modern notation wherever it appeared that greater simplicity or comprehensiveness could be 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 cubic 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 Transformation, as well as in the more advanced treatment of Symmetric Functions, a knowledge of Determinants is indispensable. We have |