“At the latter end of the last century Dr Wood, the present learned and venerable Master of St John's College, Cambridge, in conjunction with the late Professor Vince, undertook the publication of a series of elementary works on analysis, and on the application of mathematics to different branches of natural philosophy, principally with a view to the benefit of students at the Universities. The works of the latter of these two writers have already fallen into very general neglect, in consequence partly of their want of elegance, and partly in consequence of their total unfitness to teach the more modern and improved forms of thosedifferent branches of science. But the works of his colleague in this undertaking have continued to increase in circulation, and are likely to exercise for many years a considerable influence upon our national system of education; for they possess in a very eminent degree the great requisites of simplicity and elegance, both in their composition and in their design. The propositions are clearly stated and demonstrated, and are not incumbered with unnecessary explanations and illustrations. There is no attempt to bring prominently forward the peculiar views and researches of the author, and the different parts of the subjects discussed are made to bear a proper subordination to each other. It is the union of all these qualities which has given to his works, and particularly to his Algebra, so great a degree of popularity, and which has secured, and is likely to continue to secure, their adoption as text books for lectures and instruction, notwithstanding the absence of very profound and philosophical views of the first principles, and their want of adaptation, in many important particulars, to the methods which have been followed by the great continental writers. “ In later times a great number of elementary works on Algebra, possessing various degrees of merit, have been published. Those, however, which have been written for purposes of instruction only, without any reference to the advancement of new views, either of the principles of the science, or to the extension of its applications, have generally failed in those great and essential requisites of simplicity, and of adequate, but not excessive, illustration, for which the work of Dr Wood is so remarkably distinguished; whilst other works, which have possessed a more ambitious character, have been generally devoted too exclusively to the developement of some peculiar views of their authors, and have consequently not been entitled to be generally adopted as text-books in a system of academical or national education.”—Professor Peacock's Report to the British Association “ On Certain Branches of Analysis.” CONTENTS Definitions and Signs used in Algebra Addition of Algebraical Quantities Addition and Subtraction of Fractions.. Involution and Evolution...... Problems which produce Simple Equations Problems producing Quadratic Equations. Permutations and Combinations. Limits of the Roots of Equations Solution of Cubic Equation by Cardan's Rule Des Cartes' Solution of a Biquadratic Waring's Solution of a Biquadratic xii xiv xvi xvii APPENDIX II. ........ Solution of Equations by the Application of peculiar Artifices Problems XX--XLix xlix-LX APPENDIX III. Proof of Rules for Multiplication and Division of Decimal Fractions...... Inequalities.......... Application of Algebra to Geometry Maxima and Minima Single and Double Position General Properties of the Quadratic Equation Indeterminate Coefficients Summation of Series .... Interpretation of Anomalous Results Dr Halley's Table from the Bills of Mortality Dr Price's Northampton Table..... De Morgan's Table Lxi Lxiii Lxvi LXX Lxxii Lxxiv LXXV Lxxvii Lxxxi Lxxxiv LXXXV Lxxxvii EXAMPLES........... Lxxxix CORRECTIONS. ERROR CORRECTION ]..... erase ]. pc =90 pc =qd. (Art. 239) (Art. 238). ] wanting ... insert ] at the end of the line. a in the denominator a(4 - 3a). 2 {&c. }...... . {&c.}. a (4 – 3a) - 1 는. 2 a {2a – 1+1}3. q2 9. Ans. X= V1 + 4 (a – 1). 1..... a a cxix 4 cxxi ......... 11... 0:1. V2ab + b 2 cxxy......... 6 cxxxvii 4 cxxxviii 21....... 118.. 26s. V2ab + a2. 58. 28s. (op" -aq") got+ (aq" - bp) pro Ans. p" 9" – p"q" cxliii 10. |