School: a monthly record of educational thought and progress . To take a simple case. Having found the area of thetriangle ABC (Fig. i) by the trapezoidal method, thestudent may be shown—or, better still, may be led todeduce for himself—that it should be half that of therectangle HKML, whose length and breadth may beread off and thus check the result obtained by thetrapezoidal Or, having been introduced to the useful conceptionof a step, he may be shown how to obtain AD parallelto BC by taking the steps AK, KD equal to the stepsBH, HC, and hence how to obtain the triangle BLCequal to
School: a monthly record of educational thought and progress . To take a simple case. Having found the area of thetriangle ABC (Fig. i) by the trapezoidal method, thestudent may be shown—or, better still, may be led todeduce for himself—that it should be half that of therectangle HKML, whose length and breadth may beread off and thus check the result obtained by thetrapezoidal Or, having been introduced to the useful conceptionof a step, he may be shown how to obtain AD parallelto BC by taking the steps AK, KD equal to the stepsBH, HC, and hence how to obtain the triangle BLCequal to the triangle BAG and read off its base andheight (LB, HC). (Fig. 2.) It would not be advisable forhim to do much further graphic arithmetic with squaredpaper until he had mastered the theorems on equaUtyof area and learned to apply them to such problemsin practical geometry as : To describe a triangle equal to a given quadri-lateral. To draw a triangle equal in area to a given trianglehaving one angle in common with it and having one ofthe sides containing this angle of given length. On a given base to describe a rectangle equal in areato a given rectangle. To make a square equal to two given squares. ^ Having, independently of the use of squared paper,become famihar with the solution of these problemsand their application, to find, by means of drawing toscale, approximate nume
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