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The theorem was learned at last so that she could make a recitation on it, even if she did not understand it perfectly, and Migwan left it to take up a piece of work which gave her as much pleasure as the other did pain. This was the writing of a story which she intended to send away to a magazine.
In memory of the latter of these discoveries he is said to have offered a public sacrifice to the Gods; and the theorem is still known by the name of the Pythagorean theorem. He ascertained from the length of the Olympic course, which was understood to have measured six hundred of Hercules's feet, the precise stature of that hero.
Kenelm thought that the root of all private benevolence, of all enlightened advance in social reform, lay in the adverse theorem, that in every man's nature there lies a something that, could we get at it, cleanse it, polish it, render it visibly clear to our eyes, would make us love him.
Anaximander invented the sphere, the gnomon, and geographical charts, which required considerable geometrical knowledge. Anaxagoras employed himself in prison in attempting to square the circle. Pythagoras discovered the important theorem that in a right-angled triangle the squares on the sides containing the right angle are together equal to the square on the opposite side of it.
If we then unwind it, keeping it taut the while, its free extremity will describe a spiral similar at all points to the original. The curve will merely have changed places. Jacques Bernouilli, to whom geometry owes this magnificent theorem, had engraved on his tomb, as one of his proudest titles to fame, the generating spiral and its double, begotten of the unwinding of the thread.
To Dutch Spinosa, in the next century, faint, consumptive, with a hold on external things naturally faint, the theorem that God was in all things whatever, annihilating, their differences suggested a somewhat chilly withdrawal from the contact of all alike.
The answer to this question is the binomial theorem. And of this nature are all the theorems of the science of number. They assert the identity of the result of different modes of formation. They affirm that some mode of formation from x, and some mode of formation from a certain function of x, produce the same number. Such, as above described, is the aim and end of the calculus.
The strict decimal relation of the proposition is shown by the following table. It has been tested by Clairaut's theorem, and by other existing expressions, and has been found to agree, far within the probable limits of errors in observation, with the most approved values of the constant.
He spends his nights, not in social dissipation, but in gathering in rats, mice, flying-squirrels, and also birds. When he first brought me a bird, I told him that it was wrong, and tried to convince him, while he was eating it, that he was doing wrong; for he is a reasonable cat, and understands pretty much everything except the binomial theorem and the time down the cycloidal arc.
To the ignorant, indeed, the word of promise is kept to the mind as well as to the ear; but others perceive that, instead of a bull, they have only a piece of sentimental arithmetic, founded upon the elegant theorem, that friendship doubles all our pleasures, and divides all our pains.
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