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Updated: May 10, 2025
Such is the happy combination by the aid of which Laplace has solved the great, the celebrated problem of parallax. It is thus that the illustrious geometer found for the mean distance of the sun from the earth, expressed in radii of the terrestrial orbit, a value differing only in a slight degree from that which was the fruit of so many troublesome and expensive voyages.
As plants convert the minerals into food for animals, so each man converts some raw material in nature to human use. The inventors of fire, electricity, magnetism, iron; lead, glass, linen, silk, cotton; the makers of tools; the inventor of decimal notation; the geometer; the engineer; musician, severally make an easy way for all, through unknown and impossible confusions.
So, too, all thinkers, using the actual world in their processes, are at a disadvantage. The figures of the geometer, the quantities of the chemist, the measurements of the astronomer, are inexact approximations to their equivalent in the mind. Art, as an embodiment in mortal images, is subject to the conditions of mortality.
The great names belonging to this period are Hippias of Elis, Hippocrates of Chios, and Democritus. Hippocrates of Chios is mentioned by Aristotle as an instance to prove that a man may be a distinguished geometer and, at the same time, a fool in the ordinary affairs of life. He occupies an important place both in elementary geometry and in relation to two of the higher problems above mentioned.
He has an insurmountable antipathy towards men, who have in the face of the world gained the honourable titles of historian, geometer, mechanician, astronomer, physician, chemist, or geologist, &c.... His desire, his will, is to speak on every thing. He requires, therefore, colleagues who cannot contradict him.
On the contrary, we cannot but be surprised at the multitude of literary and scientific labours that he accomplished in a few years. Bailly's earliest researches on Jupiter's satellites began in 1763. The subject was happily chosen. Studying it in all its generalities, he showed himself both an indefatigable computer, a clear-sighted geometer, and an industrious and able observer.
True, the theologian commonly dreads a critic more than does the geometer, but this happens only because the theologian has probably not developed the import of his facts with any austerity or clearness, but has distorted that ideal interpretation with all sorts of concessions and side-glances at other tenets to which he is already pledged, so that he justly fears, when his methods are exposed, that the religious heart will be alienated from him and his conclusions be left with no foothold in human nature.
For if it happened that an individual, even when asleep, had some very distinct idea, as, for example, if a geometer should discover some new demonstration, the circumstance of his being asleep would not militate against its truth; and as for the most ordinary error of our dreams, which consists in their representing to us various objects in the same way as our external senses, this is not prejudicial, since it leads us very properly to suspect the truth of the ideas of sense; for we are not infrequently deceived in the same manner when awake; as when persons in the jaundice see all objects yellow, or when the stars or bodies at a great distance appear to us much smaller than they are.
In connection with the idea that God was a Geometer, must be taken the contention held by the Egyptians, and after them the Greeks and Arabs, that the Right-Angled Triangle symbolised the nature of the Universe; it was called the law of the three squares, because in every Right-Angled Triangle, as expounded by the Pythagorean Theorem, the squares, formed on the two sides containing the Right Angle, must together be exactly equal to the square on the third side, whatever the shape of the triangle may be.
"You will certainly not set off for some months to come," said the illustrious geometer; "you could, therefore, take my place temporarily." "Your proposal," I replied, "flatters me infinitely; but I do not know whether I ought to accept it.
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