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LIU. Notices respecting New Books. 



A Treatise on Algebra. By Profs. Outer, Wait, and Jones. 

 (Ithaca, N. Y. : Dudley Finch, 1887 ; pp. viii + 412.) 



HPHIS is not an Elementary Textbook, and so is not a work for 

 -*- ordinary school-use. It is a work very much of the same 

 high character as that by Prof. Chrystal which we had occasion 

 lately to notice in these columns, and, like it, this also is only a first 

 volume. With points of similarity there are numerous points of 

 dissimilarity. The motto of both is " Thorough." Our present 

 Authors — an unusual combination, a triple chord — "assume no 

 previous knowledge of Algebra, but lay clown the primary definitions 

 and axioms, and, building on these, develop the elementary principles 

 in logical order ; add such simple illustrations as shall make 

 familiar these principles and their uses." Then as to form : 

 " Make clear and precise definition of every word and symbol used 

 in a technical sense ; make formal statement of every general 

 principle, and, if not an axiom, prove it rigorously ; make formal 

 statement of every general problem, and give a rule for its solution, 

 with reasons, examples, and checks ; add such notes as shall 

 indicate motives, point out best arrangements, make clear special 

 cases, and suggest extensions and new uses." It will be gathered 

 from this outline, and our Authors, we think, have kept close to 

 this chart, that here is about the same departure from ordinary 

 textbooks as in the case we have referred to above. Indeed, to 

 our mind we have almost too much logic and careful detail, but for 

 college students and mathematical teachers this elaboration is of 

 great service. Indeed the book has been written for the classes 

 which have been and are under the authors' training. They them- 

 selves admit that the Work has so grown under their hands as to 

 embrace many topics quite beyond the range of ordinary college 

 instruction. The book fulfils their desire that it should be a 

 stepping-stone to the higher analysis. Having indicated the 

 nature of the work we give now some of the matters discussed in 

 the twelve chapters. The first is on primary definitions and signs ; 

 the second is on primary operations (a valuable chapter) ; the third 

 on Measures, Multiples, and Factors ; the fourth on Permutations 

 and Combinations ; the fifth on Powers and Boots of Polynomials ; 

 the sixth on Continued Fractions ; the seventh on Incom- 

 mensurables, Limits, Infinitesimals, and Derivatives ; the eighth 

 on Powers and Hoots ; the ninth on Logarithms ; the tenth on 

 Imaginaries (with graphic representation and preparation for 

 Quaternions) ; the eleventh on Equations (Bezout's method, 

 graphic representation of quadratic equations, application of 

 continued fractions to the same class of equations, maxima and 

 minima) ; and the last on Series (the elementary ones, convergence 

 and divergence, indeterminate coefficients, finite differences, inter- 

 polation, Taylor's theorem, and the computation of logarithms). 

 We have come across much that is new to us and much of interest. 

 Phil. Mag. S. 5. Vol. 23, No. 144. May 1887. 2 I 



