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Updated: May 15, 2025
The geometricians have subjected infinity to the laws of calculation. The circulation of the blood in animals, and of the sap in vegetables, have changed the face of Nature with regard to us. A new kind of existence has been given to bodies in the air-pump. By the assistance of telescopes bodies have been brought nearer to one another.
The more the geometry in mechanism is emphasized, the less can mechanism admit that anything is ever created, even pure form. In so far as we are geometricians, then, we reject the unforeseeable. We might accept it, assuredly, in so far as we are artists, for art lives on creation and implies a latent belief in the spontaneity of nature. But disinterested art is a luxury, like pure speculation.
It is scarcely possible to view the vast steamships of our day without reflecting that to a great master of mechanics, upward of two thousand years since, we in part owe the invention of the machine by which these mighty vessels are propelled upon the wide world of waters. This power is an application of "the Screw of Archimedes," the most celebrated of the Greek geometricians.
It is allowed, say the geometricians, that no mountain in height or sea in depth exceeds ten furlongs, and yet it seems probable that Xenagoras did not take his admeasurement carelessly, but according to the rules of art, and with instruments for the purpose. Here it was that Nasica passed the night.
It is thus, for instance, that the circle seen sideways is changed into that kind of oval which among geometricians is known as an ellipse, and sometimes even into a parabola or a hyperbola, or actually into a straight line, witness the ring of Saturn. The external senses, properly speaking, do not deceive us. It is our inner sense which often makes us go too fast.
Prudence and justice are virtues and excellences of all times and all places; we are perpetually moralists, but are geometricians only by chance. Our intercourse with Intellectual Nature is necessary; our speculations upon Matter are voluntary, and at leisure.
One of these was Isaac Newton, Fellow of Trinity College, and Professor of mathematics. His genius was then in the fullest vigour. The great work, which entitles him to the highest place among the geometricians and natural philosophers of all ages and of all nations, had been some time printing under the sanction of the Royal Society, and was almost ready for publication.
Geometricians, physicians, and astronomers taught, by their example, the severe process of reasoning which was to regenerate all the sciences; and minds of the first order, scattered in various parts of Europe, communicated to each other the results of their labors, and stimulated each other to new exertions.
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.
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.
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