School: a monthly record of educational thought and progress . wn that a plane is a magnitude of twodimensions. By observation of the two sections of theplane situated on each side of the given line, he showsspace to have at least three dimensions. Abandoningthe system which considers plane as distinct from sohdgeometry, he has recourse to Euclids postulate onlywhen he comes to study the metric properties of geo-metry ; but the young pupil already comprehendsclearly several important geometrical data. However,in this study of the properties of space, we must avoidgiving to proofs the form of t
School: a monthly record of educational thought and progress . wn that a plane is a magnitude of twodimensions. By observation of the two sections of theplane situated on each side of the given line, he showsspace to have at least three dimensions. Abandoningthe system which considers plane as distinct from sohdgeometry, he has recourse to Euclids postulate onlywhen he comes to study the metric properties of geo-metry ; but the young pupil already comprehendsclearly several important geometrical data. However,in this study of the properties of space, we must avoidgiving to proofs the form of theorems. The results are better, generally, when even advancedstudents follow this method and condense their obser-vations into formulae than when they are first told theresult of a theorem and then expected to prove it. The theorem called after Pythagoras—in Enghsh,Proposition 47, Book I.—was the terror of Baccalaureatcandidates. Yet see how simple M. Laissant rendersit in Education founded on Science ! Take two equal squares and from, the four sides of. one of them mark off four equal lengths, then join up thepoints thus obtained (see the figure) so as to form four 8 SCHOOL: A MONTHLY RECORD OF right-angled triangles—as if four set squares had beenplaced at the corners of the square. These right-angledtriangles are such that in each the sum of the sides con-taining the right angle is equal to the side of the . The interior figure is evidently a square, and thissquare is constructed on the hypotenuses of the trianglesin question (i, 2, 3, 4), M Laissant shows that if you make a second figure,A B C D, equal to the figure A B C D, if in this squarethe set squares are so used as to obtain two interior A |-_J oCschoolmonthlyrec06londuoft
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