Elementary Algebra, with Numerous Exercises, for Use in Higher and Middle-class Schools
1876; Nature Portfolio; Volume: 14; Issue: 346 Linguagem: Inglês
10.1038/014147a0
ISSN1476-4687
Tópico(s)Mathematics Education and Teaching Techniques
ResumoTHE chief justification, perhaps, for the production of this work is that the exigencies of a “school series” demanded the publication of an elementary algebra. There is not much more in it than is to be found in a half-dozen similar works, and the explanations of rules seem to us to fall short of those given elsewhere. We do not like the frequent use of evidently in an elementary work; our own extended experience with English schoolboys is that these elementary details are by no means evident to the ordinary schoolboy mind. On p. 70 “the L.C.M. of a3b2c and a2b3c2 will evidently be a3b2c3” is evidently wrong, for it evidently ought to be a3b3c2. Art. 8 on p. 45 (to show that when a certain algebraical polynomial is divided by (x-a), the remainder is what the polynomial becomes when in it x is changed to a) is useful, and we teach it to advanced pupils, but we are disposed to think that few beginners could grasp the truth and apply it. On pp. 173 to 176 we have some interesting Miscellaneous Propositions on the progressions which we do not remember to have seen in previous textbooks. The most important mistakes we have found are on pp. 66, 96, 107, 151, 153. Here we may remark that there is a very plentiful crop of typographical blunders; many of these we are disposed to attribute to a hasty examination of the “proofs;” frequent instances, too, occur in which 2, 3, or 5 have got interchanged. There is a large collection of exercises, but happily no answers are given at the end, or the list of errata would doubtless have been greatly enlarged. From the fact that (am)n = (an)m for positive integers, “it follows that (a(p/q)q = ap.” This, we think, will hardly be admitted; we should prefer to assume that the result holds, and thence derive an interpretation of a(p/q. The book takes in Indeterminate Equations, Permutations, Ratio, Proportion, Variation, and the Binomial Theorem. The only Scoticism we have noticed is one that frequently occurs: it is, “we will find,” &c.
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