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The World's Greatest Books [Volumes 1-15, 17-20]
- Автор: Gutenberg
- Год: 1910
- Язык: английский
- Жанр: Культурология
Электронная книга - «The World's Greatest Books [Volumes 1-15, 17-20]». Краткое содержание книги:
The World's Greatest Books — Volume 01 — Fiction от Неизвестный
The World's Greatest Books — Volume 02 — Fiction от Неизвестный
The World's Greatest Books — Volume 03 — Fiction от Неизвестный
The World's Greatest Books — Volume 04 — Fiction от Неизвестный
The World's Greatest Books — Volume 05 — Fiction от Неизвестный
The World's Greatest Books — Volume 06 — Fiction от Неизвестный
The World's Greatest Books — Volume 07 — Fiction от Неизвестный
The World's Greatest Books — Volume 08 — Fiction от Неизвестный
The World's Greatest Books — Volume 09 — Lives and Letters от Неизвестный
The World's Greatest Books — Volume 10 — Lives and Letters от Неизвестный
The World's Greatest Books — Volume 11 — Ancient and Mediæval History от Неизвестный
The World's Greatest Books — Volume 12 — Modern History от Неизвестный
The World's Greatest Books — Volume 13 — Religion and Philosophy от Неизвестный
The World's Greatest Books — Volume 14 — Philosophy and Economics от Неизвестный
The World's Greatest Books — Volume 15 — Science от Неизвестный
The World's Greatest Books — Volume 17 — Poetry and Drama от Неизвестный
The world's greatest books от Mee, Arthur, 1875-1943, joint editor & Hammerton, John Alexander, Sir, 1871-1949, joint editor & McClure, S. S. (Samuel Sidney), 1857-1949, joint editor
The World's Greatest Books — Volume 19 — Travel and Adventure от Неизвестный
The World's Greatest Books — Volume 20 — Miscellaneous Literature and Index от Неизвестный
Upon this subject I had (he says) composed the third book in a popular method, that it might be read by many, but afterward, considering that such as had not sufficiently entered into the principles could not easily discern the strength of the consequences, nor lay aside the prejudices to which they had been many years accustomed, therefore, to prevent the disputes which might be raised upon such accounts, I chose to reduce the substance of this book into the form of Propositions (in the mathematical way). So that this third book is composed both "in popular method" and in the form of mathematical propositions.
Books I and II
The principle of universal gravitation, namely, "That every particle of matter is attracted by or gravitates to every other particle of matter with a force inversely proportional to the squares of their distances," is the discovery which characterises the "Principia." This principle the author deduced from the motion of the moon and the three laws of Kepler; and these laws in turn Newton, by his greater law, demonstrated to be true.
From the first law of Kepler, namely, the proportionality of the areas to the times of their description, Newton inferred that the force which retained the planet in its orbit was always directed to the sun. From the second, namely, that every planet moves in an ellipse with the sun as one of foci, he drew the more general inference that the force by which the planet moves round that focus varies inversely as the square of its distance therefrom. He demonstrated that a planet acted upon by such a force could not move in any other curve than a conic section; and he showed when the moving body would describe a circular, an elliptical, a parabolic, or hyperbolic orbit. He demonstrated, too, that this force or attracting, gravitating power resided in even the least particle; but that in spherical masses it operates as if confined to their centres, so that one sphere or body will act upon another sphere or body with a force directly proportional to the quantity of matter and inversely as the square of the distance between their centres, and that their velocities of mutual approach will be in the inverse ratio of their quantities of matter. Thus he outlined the universal law.
The System of the World
It was the ancient opinion of not a few (writes Newton in Book III.) in the earliest ages of philosophy that the fixed stars stood immovable in the highest parts of the world; that under the fixed stars the planets were carried about the sun; that the earth, as one of the planets, described an annual course about the sun, while, by a diurnal motion, it was in the meantime revolved about its own axis; and that the sun, as the common fire which served to warm the whole, was fixed in the centre of the universe. It was from the Egyptians that the Greeks derived their first, as well as their soundest notions of philosophy. It is not to be denied that Anaxagoras, Democritus and others would have it that the earth possessed the centre of the world, but it was agreed on both sides that the motions of the celestial bodies were performed in spaces altogether free and void of resistance. The whim of solid orbs was[1] of later date, introduced by Endoxus, Calippus and Aristotle, when the ancient philosophy began to decline.
As it was the unavoidable consequence of the hypothesis of solid orbs while it prevailed that the comets must be thrust down below the moon, so no sooner had the late observations of astronomers restored the comets to their ancient places in the higher heavens than these celestial spaces were at once cleared of the encumbrance of solid orbs, which by these observations were broken to pieces and discarded for ever.
Whence it was that the planets came to be retained within any certain bounds in these free spaces, and to be drawn off from the rectilinear courses, which, left to themselves, they should have pursued, into regular revolutions in curvilinear orbits, are questions which we do not know how the ancients explained; and probably it was to give some sort of satisfaction to this difficulty that solid orbs were introduced.
The later philosophers pretend to account for it either by the action of certain vortices, as Kepler and Descartes, or by some other principle of impulse or attraction, for it is most certain that these effects must proceed from the action of some force or other. This we will call by the general name of a centripetal force, as it is a force which is directed to some centre; and, as it regards more particularly a body in that centre, we call it circum-solar, circum-terrestrial, circum-jovial.
Centre-Seeking Forces
That by means of centripetal forces the planets may be retained in certain orbits we may easily understand if we consider the motions of projectiles, for a stone projected is by the pressure of its own weight forced out of the rectilinear path, which, by the projection alone, it should have pursued, and made to describe a curve line in the air; and through that crooked way is at last brought down to the ground, and the greater the velocity is with which it is projected the further it goes before it falls to earth. We can, therefore, suppose the velocity to be so increased that it would describe an arc of 1, 2, 5, 10, 100, 1,000 miles before it arrived at the earth, till, at last, exceeding the limits of the earth, it should pass quite by it without touching it.
And because the celestial motions are scarcely retarded by the little or no resistance of the spaces in which they are performed, to keep up the parity of cases, let us suppose either that there is no air about the earth or, at least, that it is endowed with little or no power of resisting.
And since the areas which by this motion it describes by a radius drawn to the centre of the earth have previously been shown to be proportional to the times in which they are described, its velocity when it returns to the point from which it started will be no less than at first; and, retaining the same velocity, it will describe the same curve over and over by the same law.
But if we now imagine bodies to be projected in the directions of lines parallel to the horizon from greater heights, as from 5, 10, 100, 1,000 or more miles, or, rather, as many semi-diameters of the earth, those bodies, according to their different velocity and the different force of gravity in different heights, will describe arcs either concentric with the earth or variously eccentric, and go on revolving through the heavens in those trajectories just as the planets do in their orbs.
As when a stone is projected obliquely, the perpetual deflection thereof towards the earth is a proof of its gravitation to the earth no less certain than its direct descent when suffered to fall freely from rest, so the deviation of bodies moving in free spaces from rectilinear paths and perpetual deflection therefrom towards any place, is a sure indication of the existence of some force which from all quarters impels those bodies towards that place.
That there are centripetal forces actually directed to the bodies of the sun, of the earth, and other planets, I thus infer.
The moon revolves about our earth, and by radii drawn to its centre describes areas nearly proportional to the times in which they are described, as is evident from its velocity compared with its apparent diameter; for its motion is slower when its diameter is less (and therefore its distance greater), and its motion is swifter when its diameter is greater.