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Updated: May 26, 2025
But if to compare involve the sense of its etymon, and involve the sense of parity, I utterly deny that I do at all compare them; and, in truth, in no conceivable sense of the word is it applicable, any more than a geometrician can be affirmed to compare a polygon to a point, because he generates the line out of the point.
For thousands of years they have constructed their marvellous combs, whereto we can add nothing, wherefrom we can take nothing, combs that unite in equal perfection the science of the chemist, the geometrician, the architect, and the engineer; but on the sarcophagi, on Egyptian stones and papyri, we find drawings of combs that are identical in every particular.
Do not expect to find in this young geometrician, so soon consumed by disease and passion, the breadth, surface, and infinite variety of Bossuet, who, supported by vast and uninterrupted study, rose and rose until he gained the loftiest reaches of intellect and art, and commanded at pleasure every tone and every style. Pascal did not fulfil all his destiny.
She nodded her head with one of those sudden gestures whose graceful vivacity is not to be translated into words. "My good friend, don't go away," cried the geometrician. "This is my wife!" I bowed for the second time! Oh, Coulon! Why wert thou not present to applaud the only one of thy pupils who understood from that moment the expression, "anacreontic," as applied to a bow?
Exactly so. Clearly, he said, we are concerned with that part of geometry which relates to war; for in pitching a camp, or taking up a position, or closing or extending the lines of an army, or any other military manoeuvre, whether in actual battle or on a march, it will make all the difference whether a general is or is not a geometrician.
In allusion to the study which Cauchy had made of the mechanistic theory of the reflection of light, Père Gratry threw out the suggestion that one on the greatest intellectual joys of the great geometrician in the future life would be to penetrate into the secret of light.
He was a gambler and libertine, yet with some tincture of science and professed interest in its progress. In his correspondence there is a letter to Pascal, in which he makes free in a somewhat ridiculous manner with the young geometrician already so distinguished. Other names still less reputable—those of Miton and Desbarreaux, for example—have been associated with Pascal during this period.
To quote Pascal again, I see no objection, at this stage, to defining the process by the curve which that geometrician studied under the name of roulette or cycloid, the curve traced by a point in the circumference of a wheel when the carriage is advancing in a straight line: this point turns like the wheel, though it advances like the carriage.
A geometrician does a good service when he declares and explicates the nature of the triangle, an object suggested by many casual and recurring sensations. His service is not less real, even if less obvious, when he arrests some fundamental concretion in discourse, and formulates the first principles of logic.
As for the vulgar who never reason, the arguments of an Atheist are no more fit for them than the systems of a natural philosopher, the observations of an astronomer, the experiments of a chemist, the calculations of a geometrician, the researches of a physician, the plans of an architect, or the pleadings of a lawyer, who all labour for the people without their knowledge.
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