Abstract
THE usual profession of “rigour” is followed here by the usual inaccuracies. On page vii. we are told that = means “equal”; on p. 69 it is stated without proof that if r is a proper fraction the limit of r n is zero when n increases indefinitely; the discussion of the exponential theorem in art. 129 is thoroughly unsound, and the proof that every equation has a root (pp. 211-12) is marred by serious defects. On the other hand, the chapters on logarithms, mathematical induction and theory of equations are good. Probably this book has been written rather hastily; otherwise it is difficult to understand how such a competent mathematician as the author is known to be should have overlooked so many deficiencies. Even in the chapter on the binomial theorem for any index, he calmly applies the rule for multiplying two power-series without discussing its validity either there or in any other passage of the book ! Finally, Mr. Charles Smith is made responsible for the assertion that the binomial expansion of (1 + x) n converges for x = 1 if n < -1. Very likely this is an uncorrected misprint for n > -1; but why refer to Mr. Smith instead of to Abel's classical memoir?
College Algebra.
By L. E. Dickson Pp. viii + 214. (New York: Wiley and Sons. London: Chapman and Hall, Ltd., 1902.)
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M. College Algebra . Nature 66, 4 (1902). https://doi.org/10.1038/066004b0
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DOI: https://doi.org/10.1038/066004b0