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Updated: May 17, 2025


The ingenuity and experience of mechanics working such an instrument enabled them to add many improvements to it; until the skilful artisan at length produced not merely circular turning of the most beautiful and accurate description, but exquisite figure-work, and complicated geometrical designs, depending upon the cycloidal and eccentric movements which were from time to time added to the machine.

There is no apparent connection between duration and the cycloidal arch, the properties of which duly attended to, have furnished us with our best regulated methods of measuring time: and he who has made himself master of the nature and affections of the logarithmick curve, is not aware that he has advanced considerably towards ascertaining the proportionable density of the air at its various distances from the surface of the earth.

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.

As I sat painting, I would see the gray eagle come down, with his long cycloidal swoop, skimming along the surface of the water, and catch, as he passed, the trout that sunned itself on the surface; or the osprey seizing it with his direct plunge into the lake, from which, after a struggle that lasted sometimes a minute, the only sign of his presence being the agitated water, he would emerge with the fish in his claws and sail aloft, hurrying to escape to the forest with his prey lest the eagle, always watching from the upper air, should rob him of his hard-earned booty.

"De Queechy should have known her," continued Madame. "He always loved everything out of the common. Well, and now for the prophecy. What is all this, Mr. Vivian?" "The result of last night's observation," said the Prophet. "Do you call that a cycloidal curve?" asked Madame, with a contralto laugh that shook the library. "Look, Jupiter!" Mr. Sagittarius glanced over his wife's heaving shoulder.

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.

In the pendulum of clocks, therefore, a small arc is preferred, as there is, in that case, no sensible deviation from the cycloidal curve, but in other respects the size of the arc does not signify. Q. If then the length of a pendulum be given, can the number of vibrations in a given time be determined?

Jupiter, this gentleman is not practical. This report" she struck the paper on which the Prophet had dotted down his notes "is badly written. The cycloidal curve might have been made by a Board School child. The deductions drawn deductio ad absurdibus reveal no talent, none of the prophetic feu de joie at all. But this mystery of the dressed Crab may mean much.

Many even of the truths of geometry were generalizations from experience before they were deduced from first principles. The quadrature of the cycloid is said to have been first effected by measurement, or rather by weighing a cycloidal card, and comparing its weight with that of a piece of similar card of known dimensions.

The large stamps issued in the United States in 1865, for the payment of postage on newspapers and periodicals, are examples of this work. Cycloidal ruling in its simplest form resembles a series of loops. It is produced by a fixed point which is held against a plate while the latter is moved in a circle and, at the same time, forward.

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