Euclid's Elements of Geometry. By H. M. Taylor, M.A. (Cam-
bridge University Press.)—Mr. Taylor has made various changes in the preliminaries of Euclid, omitting some definitions (as trapezium, &sc.), and changing others (a figure is "a combination of points, lines, and surfaces "). The postulates are increased in number to eight, including now the geometrical axioms, the " axioms " being only general axioms. The propositions are sup- plemented by a number of exercises. Book I. has more than two hundred of these appended to the several propositions, and a general supplement of a hundred and five more. Every teacher knows that the real test of the pupil's aptitude for geometrical studies is to be found in these. Additional proofs are furnished for some of the propositions. The same method is followed in dealing with the other books. A specially large number of ad- ditional propositions has been given in Book XL—In Elements of Geometry, by George C. Edwards, M.A. (Macmillan), we have a treatise by a Professor of the Californian University, which is in- tended for a text-book of the new geometry.---Practical Trigo- nometry, by Henry Adams (Whittaker), is intended for the use of "Engineers, Architects, and Surveyors)."
Three School-books that have had a considerable success may be mentioned together ; they are intended to teach language on the "conversational method," a method the merits of which obviously depend upon the purpose with which the language is learnt. These are Otto's Conversation Grammar, revised by Franz Lange, Ph.D. (D. Nutt), and, the editors and publishers being the same, Otto's .First German Book, and Materials for Turning English into German. The method goes by the name of " Goupey-Otto-Satter."
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