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    The Mathematical Gazette, No. 1, April 1893, 8 pp. (London: Macmillan.)—It is now maiter of ancient history that a correspondence in the columns of NATURE resulted in the formation, in January 1871, of the Association for the Improvement of Geometrical Teaching. The original objects of the association were threefold: to collect and distribute information as to the prevailing methods of instruction in geometry practised in this and other countries, to use its influence to induce examining bodies to frame their questions in geometry without reference to any particular text-book, and to stamp with its approval some text-book already submitted, or to bring out a new one under its own auspices. Ten years later, viz. in January 1881, the association widened its basis, though after some discussion it retained its name. The objects it had in view were now sought to be carried out by the reading of papers and raising discussions, and by the appointment of committees to report on existing defects in the usual methods, order, range, &c, in teaching special subjects—all branches of elementary mathematics and mathematical physics being included in the widened basis. Now that the association has passed its majority, it is thought that it owes its continued existence to a “widespread desire on the part of teachers of mathematics to become acquainted with the methods of other teachers.” The editor of the Gazette, Mr. E. M. Langley, to whose long-continued and enthusiastic advocacy of its aims the Association for the Improvement of Geometrical Teaching owes so much as late secretary, hopes, through the agency of its columns, to extract from experienced teachers MSS. which have long been lurking in desk or pigeonhole for want of a suitable organ for making them known. This new venture, which has been started in consequence of a resolution passed at the association's annual meeting in January last, is proposed to be “a terminal journal for students and teachers.” The editor has to feel his way: words of encouragement have come from the far East and West, as well as from many teachers in this country. The number before us opens with a short paper, by the editor, on the eccentric circle of Boscovich. We borrow from Dr. C. Taylor's classical book on Conies the following verdict on Bosovich's work:—It is “a clear and compact treatise, which for simplicity, depth, and suggestiveness will not readily be surpassed.” Dr. j. S. Mackay abstracts the first book of Gino Loria's treatise on “the exact sciences in ancient Greece,” viz. that on the Greek geometers before Euclid. In addition to the works cited by Dr. Mackay, we may call attention to three notes on the history of mathematics by the Danish mathematician, H. G. Zeuthen (which have recently been published in the Bulletin de l'Acadénie Royale des Sciences de Danemark (1893). Prof. A. Lodge gives some useful approximations and reductions. Then follow some elegant solutions of examination questions, and a select number of questions for solution. A commendation of the new French journal, l'Intermédiare des Mathematiciens closes this No. 1. The size of the page, the clear type, and the excellent paper, should secure for the Gazette far more than a mere succés d'estime. The figures are lithographed on a separate sheet. We note one little slip—Adam's property for Adams' (p. S.)

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