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Updated: June 18, 2025
Rousseau once wrote, in a letter about Rivière's book, that the great problem in politics, which might be compared with the quadrature of the circle in geometry, is to find a form of government which shall place law above man.
So, too, of those quarto civilians and canonists of Leyden and Amsterdam, with their smooth white vellum coats, bearing so generic a resemblance to Dutch cheeses, that they might be supposed to represent the experiments of some Gouda dairyman on the quadrature of the circle. An easy life and an established position in society are the secret of their excellent preservation and condition.
After gaining the Neapolitan frontier, he took the road to Gaeta. The illusion of the Pope Liberator ended with the Encyclical; the illusion of the Constitutional Pope ended with the flight to Gaeta. Pius IX. was only in a limited degree responsible for his want of success, because the task he had set before him was the quadrature of the circle in politics.
A few years later an astronomer of Dantzig, Hevelius by operations which were only exact twice a month, at the first and second quadrature reduced Galileo's heights to one-twenty-sixth only of the lunar diameter. This was an exaggeration the other way. But it is to this savant that the first map of the moon is due.
Nay, Aristotle would not have missed the quadrature of the circle, if only baleful conflicts had spared the books of the ancients, who knew all the methods of nature.
Because some years previously in 1886 when occupied with the problem of the quadrature of the circle he had learned of the existence of a number computed to a relative degree of accuracy to be of such magnitude and of so many places, e.g., the 9th power of the 9th power of 9, that, the result having been obtained, 33 closely printed volumes of 1000 pages each of innumerable quires and reams of India paper would have to be requisitioned in order to contain the complete tale of its printed integers of units, tens, hundreds, thousands, tens of thousands, hundreds of thousands, millions, tens of millions, hundreds of millions, billions, the nucleus of the nebula of every digit of every series containing succinctly the potentiality of being raised to the utmost kinetic elaboration of any power of any of its powers.
When, three hours after sunset, on the 23d of March, the Gallian moon rose upon the western horizon, it was observed that she had entered upon her last quarter. She had taken only four days to pass from syzygy to quadrature, and it was consequently evident that she would be visible for little more than a week at a time, and that her lunation would be accomplished within sixteen days.
Many even of the truths of geometry were generalizations from experience before they were deduced from first principles. The quadrature of the cycloid is said to have been first effected by measurement, or rather by weighing a cycloidal card, and comparing its weight with that of a piece of similar card of known dimensions.
Such a book is the sport of a geometrical giant wantonly amusing himself with his strength. Among his mathematical investigations must not be omitted the quadrature of the parabola. His fame depends, however, not so much on his mathematical triumphs as upon his brilliant discoveries in physics and his mechanical inventions.
Professor Max Mueller after a lifetime of arduous labor in this field frankly confesses: "Modern words are round, ancient words are square, and we may as well hope to solve the quadrature of the circle, as to express adequately the ancient thought of the Vedas in modern English." Without a commentary it is practically impossible to understand either the spirit or the meaning of the Upanishads.
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