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Updated: May 10, 2025
First, The Immediateness of a judgment, is no proof of its being innate; long practice or familiarity has the same effect. In proportion as we are habituated to any subject, or any class of operations, our decisions are rapid and independent of deliberation. An expert geometer sees at a glance whether a demonstration is correct.
But, as was candidly observed by Professor Playfair in concluding his report "It is not from theoretical men that the most valuable information in such a case as the present is to be expected. When a mechanical arrangement becomes in a certain degree complicated, it baffles the efforts of the geometer, and refuses to submit to even the most approved methods of investigation.
The result of this view of knowledge was that, although during the fifteen centuries following the death of the geometer of Syracuse great universities were founded at which generations of professors expounded all the learning of their time, neither professor nor student ever suspected what latent possibilities of good were concealed in the most familiar operations of Nature.
Let us now, after the example of Laplace, take from the standard tables the least considerable values, if you choose, of the expansions or contractions which solid bodies experience from changes of temperature; search then the annals of Grecian, Arabian, and modern astronomy for the purpose of finding in them the angular velocity of the moon, and the great geometer will prove, by incontrovertible evidence founded upon these data, that during a period of two thousand years the mean temperature of the earth has not varied to the extent of the hundredth part of a degree of the centigrade thermometer.
It was the geometer Cousin, member of this academy, who by his incessant solicitations got Madame Bailly's name inserted at the Board of Charity in his arrondissement. The support was distributed in kind. Cousin used to receive the articles at the Hôtel de Ville, where he was a Municipal Councillor, and carried them himself to the street de la Sourdière.
Accordingly, in 1470, when eighteen years old, Leonardo was placed under the care of Verrocchio, who was like a kind father to his pupils: he was not only a painter, but also an architect and sculptor, a musician and a geometer, and he especially excelled in making exquisite cups of gold and silver, crucifixes and statuettes such as were in great demand for the use of the priesthood in those days.
What I regret most is, the chapter in which Bailly might have related how certain adepts of Mesmer's had the hardihood to magnetize the moon, so as, on a given day, to make all the astronomers devoted to observing that body fall into a syncope; a perturbation, by the way, that no geometer, from Newton to Laplace, had thought of.
His position as a geometer is perhaps better understood from the assertion made respecting him by a modern mathematician, that he came as near to the discovery of the Differential Calculus as can be done without the aid of algebraic transformations.
He knew that the earth was a gigantic object, but, large as it may have been, he knew that it was only a particle in comparison with the celestial sphere, yet he apparently believed, and certainly succeeded in persuading other men to believe, that the celestial sphere did actually perform these movements. Ptolemy was an excellent geometer.
Father Lozeran de Fiesc and the Count of Créqui were rewarded with the high honour of seeing their names inscribed beside that of the illustrious geometer, although it would be impossible in the present day to discern in their memoirs any kind of merit, not even that of politeness, for the courtier said rudely to the Academy: "the question, which you have raised, interests only the curiosity of mankind."
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