BY WEBSTER WELLS, S.B., PROFESSOR OF MATHEMATICS IN THE MASSACHUSETTS BOSTON, U.S.A. D. C. HEATH & CO., PUBLISHERS 1906 ICT -5 199 —— ***USTRIAL CONFERENCE FUN2 PREFACE. THIS work is designed as a text-book for the use of colleges and scientific schools. The first eighteen chapters have been arranged with reference to the needs of those who wish to make a review of that portion of Algebra preceding Quadratics. While complete as regards the theoretical parts of the subject, only just enough examples are given to furnish a rapid review in the class-room. Attention is respectfully invited to the following: The proofs of the five fundamental laws of Algebra — the Commutative and Associative Laws for Addition and Multiplication, and the Distributive Law for Multiplication -for positive or negative integers, and positive or negative fractions, Chapter II.; Arts. 114 and 115; Arts. 208 to 215; Arts. 230 and 232; Chapter XVI.; the proofs of the fundamental laws of Algebra for irrational numbers, Chapter XVII.; Arts. 350 and 351; Arts. 355 to 357; Chapters XXIV. and XXVI.; the proof of the Binomial Theorem for positive integral exponents, Arts. 443 and 444; Chapter XXXI.; the Note to Art. 469; the proof of the Binomial Theorem for fractional and negative exponents, Art. 483; Arts. 532 to 538; Art. 542; Chapters XXXVII., XXXVIII., and XL.; Art. 650; the proof of Descartes' Rule of Signs for Positive Roots, for incomplete as well as complete equations, Art. 653; Arts. 657 to 663; Arts. 673 and 674; iii |