Euclidean Geometry


    IT is interesting to compare the attitudes of the two most recent writers in English who deal with Euclidean geometry. Sir Thomas Heath, in the second edition of his three-volume translation of the “Elements”(Cambridge, 1926), reiterates his opinion that Euclid “remains the greatest elementary text-book in mathematics that the world is privileged to possess”; Mr. Forder, in the book under review, emphasises the fact that “many flaws have been noticed in his treatment during the two thousand years that have elapsed since his work was written.” The two points of view are, of course, not in the least contradictory. Indeed, Sir Thomas Heath is careful to point out that “much valuable work has been done on the continent in the investigation of the first principles, including the formulation and classification of axioms or postulates which are necessary to make good the deficiencies of Euclid's own explicit postulates and axioms,” and not the least valuable part of his great work consists in his notes and commentaries on research on the axiomatic side. Mr. Forder is mainly concerned with foundations, and his book will go far to remove the reproach implied in the words “on the continent” in the passage quoted. Having laid down his foundations, he goes on to erect his edifice of elementary geometry, remarking that “scarcely one proof in any school-text will survive a critical examination.” Sir Thomas Heath would probably agree (cf. his original preface, loc. cit., vol. 1, pp. v-vi).

    The Foundations of Euclidean Geometry.

    By Henry George Forder. Pp. xii + 349. (Cambridge: At the University Press, 1927.) 25s. net.

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    Euclidean Geometry. Nature 123, 44–45 (1929).

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