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Updated: May 10, 2025
A third has mastered the laws of proportion mathematically, as he has found them in Euclid or other geometrical treatise. A fourth, with the plain numbers of 1, 2, and 3, sees for himself by simple intuitive force that 1:2=3:6. Of these several kinds of knowledge the third and fourth alone deserve to be called knowledge, the others being no more than opinions more or less justly founded.
By following up this clew with mathematical precision, measuring the exact thickness of the plate and the space between the different rings of color, Young was able to show mathematically what must be the length of pulsation for each of the different colors of the spectrum.
'In these researches he developed mathematically Faraday's theory of molecular induction, and thereby paved the way in great measure for its general acceptance. His ozone apparatus, his telegraph instrument working with alternate currents, and his instrument for translating on and automatically discharging submarine cables also belong to the year 1857.
Yet there will be no use in working out the mathematically correct means to produce certain result, if the real nature of the desired result is underrated; there will be no use in working out laboriously how many ships and tons of coal and oil are needed, if the estimate of the situation, to meet which those ships and coal and oil are needed, is inadequate.
"The unforeseen does not exist," quietly replied Phileas Fogg. "But, Mr. Fogg, eighty days are only the estimate of the least possible time in which the journey can be made." "A well-used minimum suffices for everything." "But, in order not to exceed it, you must jump mathematically from the trains upon the steamers, and from the steamers upon the trains again." "I will jump mathematically."
But this is mathematically and socially impossible for the great majority, and unless a plan of life fits that majority it is best to call the plan what it is, an aristocratic creed, meant for the more able and the more fortunate. The social group, in its descent from the herd, has become an intensely competitive, highly cooperative organization.
True, we only know the minor part of the universe, and it is quite possible, as M. d'Asterac says who is a bit of a fool that this earth is no more than a spot of mud in the infinity of worlds. Maybe the astronomer Copernicus was not altogether dreaming when he taught that, mathematically, the earth is not the centre of creation.
The youngest, with an air of gaiety suggested one of the first chapters of the undertaking, by saying that she would take upon herself to prove mathematically that women who are entirely virtuous were creatures of reason. When the author got home he said at once to his demon: "Come! I am ready; let us sign the compact." But the demon never returned.
There seems to be great confusion; yet we know this is not so. We know those many lines are mathematically correct. If you want to keep your eye on the main line, you mustn't be misled by the lines which touch and cross it, which seem to belong to it, until they suddenly sweep off in another direction.
In the yellow gloom, one might feast one's eyes at leisure upon the centre table, draped in red damask, mystic, wonderful, and on its wealth of mathematically arranged books, the Bible, the "Indian Mutiny" and "Water Babies" in blue and gold. This last had been a gift to Ann and was considered by Mrs. Sykes to be the height of foolishness.
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