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Why should one waste a lot of time, he had thought, and be bored during the wasting, by studying grammar if one could already talk intelligibly to people? And why should one not revel in complicated problems of figures and geometrical designs that really took some hard thinking to work out, if hard thinking was just what one liked to do?
Juxtaposition and arrangement are the geometrical operations which typify the work of knowledge in such a case; or else we must fall back on metaphors from some mental chemistry, such as proportioning and combination. In all cases, the method is still that of alignment and blending of pre-existent concepts.
It is boasted that the geometrical policy has been adopted, that all local ideas should be sunk, and that the people should be no longer Gascons, Picards, Bretons, Normans, but Frenchmen, with one country, one heart, and one Assembly. But, instead of being all Frenchmen, the greater likelihood is that the inhabitants of that region will shortly have no country.
The disciples of Plato invented conic sections, and discovered the geometrical foci. It was however reserved for Euclid to make his name almost synonymous with geometry. He was born 323 B.C., and belonged to the Platonic sect, which ever attached great importance to mathematics. His "Elements" are still in use, as nearly perfect as any human production can be. They consist of thirteen books.
Few perhaps would have detected the profound significance the curious words he next used unquestionably concealed. Henriot's mind rejected them, but his heart accepted. For the ancient soul in him was listening and aware. "Life, using matter to express itself in bodily shape, first traces a geometrical pattern.
It is probable that this number will increase, as it has hitherto done, in a geometrical ratio, which will give 6,000,000, in 1875, of a people dangerous from numbers merely, but doubly, trebly so in their consciousness of oppression, and in the passions which may incite them to a terrible revenge.
This is also the time when object lessons may be given with great advantage. The forms and names of geometrical solids may be taught. Exercises may be introduced tending to develop those powers by which we comprehend the qualities of color, size, density, form, and weight. Important moral truths may be presented with the aid of suitable illustrations.
Now, their significance as a geometrical test of tabular accuracy is altogether overshadowed by the interest attaching to the physical observations for which they afford propitious occasions. This change may be said to date, in its pronounced form, from the great eclipse of 1842.
Similar to this sameness of form is sameness of direction or parallelism of lines. Another kind of harmonious unification of lines is continuity, where out of different lines or shapes a single line is made. The classical geometrical forms of composition, as the circular or pyramidal, are good examples of this.
Geometry seems to have acted as a febrifuge, for beautiful geometrical designs are introduced amidst the tumult of the hunt; and there is no more seeing double, nor ghastly monstrosity of conception; no more ending of everything in something else; no more disputing for spare legs among bewildered bodies; no more setting on of heads wrong side foremost.
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