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Updated: May 15, 2025
Now, the three great problems of antiquity which engaged the attention and wonderment of geometricians throughout the Middle Ages, were "the Squaring of the Circle," "the Duplication of the Cube," and lastly, "the Trisection of an Angle," even Euclid being unable to show how to do it; and yet it will be seen that the diagonal of one of the subsidiary figures in the tri-subdivision, together with the diagonal of the whole figure, actually trisect the angle at the corner of the rectangle.
The geometricians and the chemists bring the one from the dry bones of their diagrams, and the other from the soot of their furnaces, dispositions that make them worse than indifferent about those feelings and habitudes which are the supports of the moral world.
If in our fancy we strip the buildings of Chaldæa and Assyria of all their accessories, if we take from them their surface ornament and the salience of their roofs, the bare edifice that remains is what geometricians call a rectangular parallelopiped. Of all the types created by this architecture, the only one of which we still possess a few fairly well preserved examples is that of the palace.
For if you investigate the method of these little geometricians, you discover at once that they have retained only the exact impression of the diagram and the words of the demonstration. Upon the least new objection they are puzzled. Their knowledge is only of the sensation; nothing has become the property of their understanding.
But with the dimensions of matter it is not thus: the ternary number is determined for it not by the reason of the best, but by a geometrical necessity, because the geometricians have been able to prove that there are only three straight lines perpendicular to one another which can intersect at one and the same point.
WARING, England has produced no great geometricians since the death of MACLAURIN, STERLING, and SIMPSON. The French tables of Logarithms, printed stereotypically, are cleared of all the errors which afflicted calculators of every country. Those of other nations will owe this obligation to Frenchmen.
So the Khalif wrote to the Viceroy of Bassora, to send him Ibrahim ben Siyyar the poet, who was the first man of his day in argument and eloquence and poetry and logic, and bade him bring with him readers of the Koran and doctors of the law and physicians and astrologers and sages and geometricians and philosophers; and Ibrahim was more learned than all.
Has not each cell in a honey comb six sides, or as many as a bee has feet, the art of which arrangement appears in the teaching of the geometricians that of all polygons the hexagon covers the largest area within a circle.
Even among the ancients, though many of their geometricians had acknowledged the sphericity of the globe, it was for a long time imagined that the earth was a third longer than it was broad, and thence arose the terms of longitude and latitude. St. Athanasius expresses himself most warmly against astronomers.
While setting down my figures, methought I was still at Chambery, still in my days of happiness how far had I to look back for them! The colored plans of our geometricians had given me a taste for drawing: accordingly I bought colors, and began by attempting flowers and landscapes.
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