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Updated: June 27, 2025
To the sphere of the same which was undivided he gave dominion, but the sphere of the other or diverse was distributed into seven unequal orbits, having intervals in ratios of twos and threes, three of either sort, and he bade the orbits move in opposite directions to one another three of them, the Sun, Mercury, Venus, with equal swiftness, and the remaining four the Moon, Saturn, Mars, Jupiter, with unequal swiftness to the three and to one another, but all in due proportion.
In the same manner, 6 pounds weight of coal are equivalent to 32 pounds weight of zinc. The numbers representing chemical equivalents express very general ratios of effects, comprehending for all bodies all the actions they are capable of producing.
Symbols and ratios carry us and bring us forth and beat us down; gravity that swings the incommensurable suns and worlds through space, is but a figment varying inversely as the squares of distances; and the suns and worlds themselves, imponderable figures of abstraction, NH3, and H2O. Consideration dares not dwell upon this view; that way madness lies; science carries us into zones of speculation, where there is no habitable city for the mind of man.
Probably its amount of pleasure its capability of enjoyment is in a direct proportion to the pain which it endures; and it is highly probable that this double line of ratios runs in an ascending scale throughout the vegetable kingdom, gradually joining on to what is more strictly termed the "animal."
Now, there is a clear logic of proportion. Certain things are evidently not to be thought of, though next neighbors do have them; and we must resign ourselves to find some other way of living." "My dear," said my wife, "I think there is a peculiar temptation in a life organized as ours is in America. There are here no settled classes, with similar ratios of income.
Uniting with the ever-flowing current, they shake the courses of the soul, stopping the revolution of the same and twisting in all sorts of ways the nature of the other, and the harmonical ratios of twos and threes and the mean terms which connect them, until the circles are bent and disordered and their motion becomes irregular.
Symbols and ratios carry us and bring us forth and beat us down; gravity, that swings the incommensurable suns and worlds through space, is but a figment varying inversely as the squares of distances; and the suns and worlds themselves, imponderable figures of abstraction, NH and H O. Consideration dares not dwell upon this view; that way madness lies; science carries us into zones of speculation, where there is no habitable city for the mind of man.
Then comes Mr. Malthus forward with the geometrical and arithmetical ratios in his hands, and holds them out to his affrighted contemporaries as the only means of salvation.
You certainly have less respect and affection for your relatives than any man I ever saw." "Which fact is entirely attributable to my thorough knowledge of their characters. I have generally found that high appreciation and intimate acquaintance are in inverse ratios. As for Clinton Allston, were he my father's son, instead of his nephew.
At the beginning of his career he had a defective sense of the harmonic ratios upon which a really musical building may be constructed out of mere bricks and mortar such, for example, as the Church of S. Giustina at Padua.
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