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Updated: May 28, 2025
A golden text for these gentlemen is that which I so admire in the Buddhist, who never thanks, and who says, "Do not flatter your benefactors." The reason of these discords I conceive to be that there is no commensurability between a man and any gift. You cannot give anything to a magnanimous person. After you have served him he at once puts you in debt by his magnanimity.
There exists between the mean motions of these two great planets a simple relation of commensurability, five times the mean motion of Saturn, being, in fact, very nearly equal to twice the mean motion of Jupiter. It happens, in consequence, that certain terms, which would otherwise be very small, acquire from this circumstance considerable values.
It is plain that the more nearly the mean motions of the two planets approach a relation of commensurability, the smaller will be the displacement of every third conjunction, and consequently the longer will be the duration, and the greater the ultimate accumulation, of the inequality. Translator. Translator.
The properties of commensurability and incommensurability in lines and surfaces, of rational and irrational lines would cease to have any meaning. In fact all that is contained in the tenth book of Euclid would lose its foundation. The atom is made complete by the accidents, without which it cannot be.
A golden text for these gentlemen is that which I admire in the Buddhist, who never thanks, and who says, "Do not flatter your benefactors." The reason of these discords I conceive to be, that there is no commensurability between a man and any gift. You cannot give anything to a magnanimous person. After you have served him, he at once puts you in debt by his magnanimity.
Ricardo, in his theory of rent, has given a magnificent example of the commensurability of values. He has shown that arable lands are to each other as the crops which they yield with the same outlay; and here universal practice is in harmony with theory.
For disturbances recurring time after time owing to commensurability of periods nearly at the same part of the orbit, would have accumulated until the shape of that orbit was notably changed.
Is it not astonishing to find in the commensurability of the mean motions of two planets, a cause of perturbation of so influential a nature; to discover that the definitive solution of an immense difficulty which baffled the genius of Euler, and which even led persons to doubt whether the theory of gravitation was capable of accounting for all the phenomena of the heavens should depend upon the fortuitous circumstance of five times the mean motion of Saturn being equal to twice the mean motion of Jupiter?
His passion for knowing living things was combined with a rapidity of observation, and a capacity to recognize them again and remember everything about them, which all his life it seemed an easy triumph and delight for him to exercise, and which never allowed him to waste a moment in doubts about the commensurability of his powers with his tasks. If ever a person lived by faith, he did.
We can scarcely doubt that this law of commensurability has largely influenced the present distribution of the asteroids. But its effects must have been produced while they were still in an unformed, perhaps a nebular condition.
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