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Now, Laplace has shown that the mean motion of the moon around the earth is connected with the form of the ellipse which the earth describes around the sun; that a diminution of the eccentricity of the ellipse inevitably induces an increase in the velocity of our satellite, and vice versâ; finally, that this cause suffices to explain the numerical value of the acceleration which the mean motion of the moon has experienced from the earliest ages down to the present time.
If a strange comet undertakes to run across Jupiter's bows the latter brings it to, and makes prize of it by throwing it into a relatively small ellipse with the sun for its focus. Thenceforth, unless, as happened to the unhappy comet of Lexell, it encounters Jupiter again in such a way as to be diverted by him into a more distant orbit, it can never get away.
For example, when we have proved with respect to the circle, that a straight line cannot meet it in more than two points, and when the same thing has been successively proved of the ellipse, the parabola, and the hyperbola, it may be laid down as an universal property of the sections of the cone.
Some such teasing notion of their mystical affinity is what haunts you as you make your round of the vast ellipse, with the well-groomed men about you and the well-groomed horses beyond the barrier.
In the lowest range these openings are 13 ft. 4 in. wide, except the four which are at the ends of the two axes of the ellipse, and these are 14 ft. 6 in. wide. The diameter of the columns is 2 ft. 8¾ in. The topmost story, which is considerably more lofty than either of the lower ones, was a nearly solid wall enriched by Corinthian pilasters.
Its path is an immensely elongated ellipse, lying in a plane far apart from that of the planetary movements, carrying it at perihelion considerably within the orbit of Venus, and at aphelion out into space to 5-1/2 times the distance from the sun of Neptune. The entire circuit occupies over 2,000 years, and is performed in a retrograde direction, or against the order of the Signs.
The Gothic, or Pointed, or Christian architecture, as it has been variously called, was the creation of the Middle Ages, and arose nearly simultaneously in Europe after the first Crusade, so that it would seem to be of Eastern origin. But it was a graft on the old Roman arch, in the shape of an ellipse rather than a circle.
On page 182, it is stated, that Newton's proving, that, if a body revolved in an elliptical orbit with the sun as a focus, the force of gravitation toward the sun would always be in the inverse ratio of the square of its distance, "was equivalent to proving, that, if a body in space, free to move, received a single impulse, and at the same moment was attracted to a fixed centre by a force which diminished as the square of the distance at which it operated increased, such a body, thus deflected from its rectilinear path, would describe an ellipse," etc.
The old cell wall seems to offer considerable resistance to the escape of the gonidium, for the latter, which displays remarkable elasticity, is pinched nearly in two while forcing its way through, assuming an hour glass shape when about half out. It immediately assumes the form of an ellipse or oval, and darts off with great speed, revolving on its major axis as it does so.
If the orbit was not a circle, what, then, was it? By a happy stroke of philosophical genius he lit on the ellipse. On bringing his hypothesis to the test of observation, he found it was indeed so; and rising from the case of Mars to universal statement, he generalized the law, that the planetary orbits are elliptical, having the sun for their common focus.
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