Essai sur les fondements de la géométrie Euclidienne


    M. MALENGREAU conceives the object of a geometrical treatise to be that of investigating the point-aggregates of a space which has been generated by the help of appropriate postulates. In the present essay, he has set himself the task of generating the most elementary space which can be the object of Euclidean geometry, where Euclidean space is understood as that space which corresponds to the conditions of our environment according to such immediate verifications as we possess. The method whereby M. Malengreau obtains this elementary Euclidean space is based upon the generation of aggregates containing an indefinite number of points, from those containing only a definite number. Such a process necessitates the consideration of all those intermediary aggregates which are of use in classifying the new points as they are obtained. But M. Malengreau is careful to introduce as few new definitions as possible ; although he invents several new terms to apply to aggregates which are termed differently in classical geometry, and in some cases, uses the familiar terms in a different sense from that of classical geometry.

    Essai sur les fondements de la géométrie Euclidienne

    Par Julien Malengreau. Pp. 311. (Lausanne et Genène: Payot et Cie., 1938.) 8 francs.

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    Essai sur les fondements de la géométrie Euclidienne. Nature 142, 376 (1938).

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