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Updated: May 10, 2025
Bailly followed the advice of the illustrious geometer, and chose as the subject of his studies, the éloges proposed by several academies, though principally by the French Academy. From the year 1671 to the year 1758, the prize subjects proposed by the French Academy related to questions of religion and morality.
THE PHILOSOPHER: Certainly, since your great everything does not know mathematics, and since all your laws are most profoundly geometrical, there must be an eternal geometer who directs you, a supreme intelligence who presides over your operations. NATURE: You are right; I am water, earth, fire, atmosphere, metal, mineral, stone, vegetable, animal.
They should not be taken for granted. The history of ethical theory appears to make it clear that the "given" of the moralist is not of the same nature as that of the geometer. The ethical philosopher cannot, hence, confine himself to developing deductively the implications of some principle or principles assumed without critical examination. He must establish the validity even of his principles.
The author of the Mécanique Céleste had vowed to the young geometer an unbounded attachment, completely justified, certainly, by the beautiful researches which science already owed to him.
The profound and long-continued researches of the illustrious geometer established with complete evidence that the planetary ellipses are perpetually variable; that the extremities of their major axes make the tour of the heavens; that, independently of an oscillatory motion, the planes of their orbits experienced a displacement in virtue of which their intersections with the plane of the terrestrial orbit are each year directed towards different stars.
The edition of the Mécanique Céleste itself will soon be exhausted. It was painful then to reflect that the time was close at hand when persons engaged in the study of the higher mathematics would be compelled, for want of the original work, to inquire at Philadelphia, at New York, or at Boston for the English translation of the chef d'oeuvre of our countryman by the excellent geometer Bowditch.
These thoughts, in sparkles of light, had appeared often to pious and to poetic souls; but this well-bred, all-knowing Greek geometer comes with command, gathers them all up into rank and gradation, the Euclid of holiness, and marries the two parts of nature. Before all men, he saw the intellectual values of the moral sentiment.
The geometer takes any set of axioms that seem interesting, and deduces their consequences. What defines Geometry, in this sense, is that the axioms must give rise to a series of more than one dimension. And it is thus that Geometry becomes a department in the study of order.
The French Revolution thus threw the learned geometer, whose discoveries I am about to celebrate, far away from the route which destiny appeared to have traced out for him. In ordinary times it would be about Dom Joseph Fourier that the secretary of the Academy would have deemed it his duty to have occupied your attention.
So that, were a trans-Neptunian planet discovered, we should be fully prepared to find it rotating, and surrounded by satellites circulating from east to west. The uniformity of movement, upon the probabilities connected with which the French geometer mainly based his scheme, thus at once vanishes. The excessively rapid revolution of the inner Martian moon is a further stumbling-block.
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