Les Nombres positifs Exposé des Théories modernes de l'Arithmétique élementaire

    Abstract

    THIS treatise certainly deserves a trial by school teachers. The author realises that there is a great gulf between arithmetic, as usually taught in schools, and the strict logic of the subject, and, at the same time, that it is impossible to teach it with complete rigour to a school class. He assumes the commutative law of addition, and then proves the elementary rules in a way which is quite sufficient for school purposes, and does not involve any fallacies which afterwards have to be renounced. The treatment of irrationals follows Dedekind; that of fractions is based upon the definition that a/b=c/d if ad=bc. Proportion is treated in the way that is usual in France; the section on this subject would require to be expanded and illustrated by the teacher; the same is true of other articles, notably §. 13, which is unduly condensed, and where the distinction between algebraic and arithmetical divisibility is rather blurred. Many teachers will regret seeing contracted multiplication expounded by Oughtred's rule of reversing the digits of the multiplier. The rule for contracted division, though instructive, is needlessly complicated from a practical point of view; and, alas! the rule for arithmetical subtraction is given in its oldfashioned form. However, these are minor points, and it is woith while to refer to them only because the book is o attractive in other respects. Attention should be. drawn to the author's way of considering fractions, which he sketches out in his preface.

    Les Nombres positifs. Exposé des Théories modernes de l'Arithmétique élementaire.

    By M. Stuyvaert. Pp. xii + 132. (Gand: Van Goethem, 1906.) Price 3 francs.

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    Les Nombres positifs Exposé des Théories modernes de l'Arithmétique élementaire . Nature 75, 246 (1907) doi:10.1038/075246d0

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