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Apollonius of Perga, probably about forty years younger than Archimedes, and his equal in mathematical genius, was the most fertile and profound writer among the ancients who treated of geometry. He was called the Great Geometer.
We have seen D'Alembert, ever since the year 1763, encouraging Bailly to exercise himself in a style of literary composition then much liked, the style of éloge, and holding out to him in prospect the situation of Perpetual Secretary of the Academy of Sciences. Six years after, the illustrious geometer gave the same advice, and perhaps held out the same hopes, to the young Marquis de Condorcet.
Every evening the great geometer entered my room, and we passed entire hours in conversing on politics and mathematics, which is certainly not quite the same thing. In the course of 1804, the school was a prey to political passions, and that through the fault of the government.
Is it unreasonable to believe that the exceeding beauty of animated forms, and of the highest, the human form, arises from the fact that these forms are the result of some simple intellectual law, a simple conception of the Divine Geometer, assuming varied developments in the great series of animated beings?
It was natural that a geometer who had so elegantly connected the laws of simple refraction which light undergoes in its passage through the atmosphere, and the laws of double refraction which it is subject to in the course of its passage through certain crystals, with the action of attractive and repulsive forces, should not have abandoned this route, before he recognized the impossibility of arriving by the same path, at plausible explanations of the phenomena of diffraction and polarization.
Accordingly I wrote to Professor Miller, of Cambridge, and this geometer has kindly read over the following statement, drawn up from his information, and tells me that it is strictly correct:
An observing geometer who, from his infancy, had never quitted his chamber of study, and who had never viewed the heavens except through a narrow aperture directed north and south, in the vertical plane in which the principal astronomical instruments are made to move, to whom nothing had ever been revealed respecting the bodies revolving above his head, except that they attract each other according to the Newtonian law of gravitation, would, however, be enabled to ascertain that his narrow abode was situated upon the surface of a spheroidal body, the equatorial axis of which surpassed the polar axis by a three hundred and sixth part; he would have also found, in his isolated immovable position, his true distance from the sun.
M. de Laplace, at the moment of voting, took two plain pieces of paper; his neighbour was guilty of the indiscretion of looking, and saw distinctly that the illustrious geometer wrote the name of Fourier on both of them.
The primitive geometer, then, was a surveyor. The Egyptian records, as now revealed to us, show that the science had not been carried far in the land of its birth. The Egyptian geometer was able to measure irregular pieces of land only approximately.
Such can be found, I think, by turning to two truths dwelt upon in what has preceded: the truth that the moralist should not assume that he is possessed of a "given" analogous to that of the geometer a standard in no need of criticism; and the equally important truth that the moralist cannot hope to frame a code which will simply replace the codes of individual communities and will prescribe the details of human conduct while ignoring such codes altogether.
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