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Updated: May 17, 2025
It is not that the mind does not take this method, but it does so silently, naturally, and without conscious art. The perception of the process belongs only to a few minds, and those of the highest order. . . . Geometers, who are only geometers, are sure to be right, provided the subject come within their scope, and is capable of explanation by definition and principles.
The varieties of physical phenomena with which those sciences are conversant, have been found to answer to determinable varieties in the quantity of some circumstance or other; or at least to varieties of form or position, for which corresponding equations of quantity had already been, or were susceptible of being, discovered by geometers.
She craves, if not the gaudy furbelows borrowed from rhetoric's wardrobe, at least a vine leaf. The geometers alone have the right to refuse her that modest garment; in theorems, plainness suffices. The others, especially the naturalist, are in duty bound to drape a gauze tunic more or less elegantly around her waist. Suppose I say: 'Baptiste, give me my slippers.
The disturbance of their motions by their giant neighbours afforded a more accurate knowledge of the Jovian mass, which Laplace had taken about 1/50 too small; the anomalous character of their orbits presented geometers with highly stimulating problems in the theory of perturbation; while the exigencies of the first discovery had produced the Theoria Motus, and won Gauss over to the ranks of calculating astronomy.
The remarkable thing about the earliest geometers is, in fact, that they did not formulate the conception of Space, which seems to us at the present day fundamental. They were able to avoid it because they possessed the conception of Matter, and regarded Air as the normal state of the material substratum.
These "Elements" soon became the universal study of geometers throughout the civilized world; they were translated into the Arabic, and through the Arabians were made known to mediaeval Europe.
Among those who often come to look at new books and converse familiarly among themselves there are historians as learned as Tillemont, sacred orators the equals of Bossuet and Bourdaloue in eloquence, comic and tragic poets, theologians who unite purity of morals with solidity of doctrine, the esteemed authors of "Spanish" novels, geometers and philosophers capable, like M. Descartes, of measuring and weighing the universe.
"Father," cried Magis, "notice how each one advances with his nose pointed towards the centre of gravity of that young damsel now that the centre is covered by a garment. The sphere inspires the meditations of geometers by the number of its properties.
Literature, the fine arts, and the sciences appeared for a moment to flourish under the auspicious influence of the French Revolution. Observe, for example, with what grandeur of conception the reformation of weights and measures was planned; what geometers, what astronomers, what eminent philosophers presided over every department of this noble undertaking!
The Greek tongue was extraordinarily well adapted as a vehicle of scientific thought. The language of the Greek geometers is also wonderfully concise, notwithstanding all appearances to the contrary. And, to say nothing of the perfect finish of Archimedes's treatises, we shall find in Heron, Ptolemy and Pappus veritable models of concise statement.
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