The most broad-minded of the great mathematicians who have recently given attention to secondary problems is Professor Klein of Goettingen. He has had the good sense to look at something besides the mere question of good mathematics.[34] Thus he insists upon the psychologic point of view, to the end that the geometry shall be adapted to the mental development of the pupil,--a thing that is apparently ignored by Meray (at least for the average pupil), and, it is to be feared, by the other recent French writers. He then demands a careful selection of the subject matter, which in our American schools would mean the elimination of propositions that are not basal, that is, that are not used for most of the exercises that one naturally meets in elementary geometry and in applied work. He further insists upon a reasonable correlation with practical work to which every teacher will agree so long as the work is really or even potentially practical. And finally he asks that we look with favor upon the union of plane and solid geometry, and of algebra and geometry. He does not make any plea for extreme fusion, but presumably he asks that to which every one of open mind would agree, namely, that whenever the opportunity offers in teaching plane geometry, to open the vision to a generalization in space, or to the measurement of well-known solids, or to the use of the algebra that the pupil has learned, the opportunity should be seized. FOOTNOTES: [32] The author is a member of a committee that has for more than a year been considering a syllabus in geometry. This committee will probably report sometime during the year 1911. At the present writing it seems disposed to recommend about the usual list of basal propositions. [33] "Elementi di Geometria," Milan, 1884. [34] See his "Elementarmathematik vom hoeheren Standpunkt aus," Part II, Leipzig, 1909. CHAPTER VII THE TEXTBOOK IN GEOMETRY