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'Tis absurd to imagine that motion in a circle, for instance, should be nothing but merely motion in a circle; while motion in another direction, as in an ellipse, should also be a passion or moral reflection; that the shocking of two globular particles should become a sensation of pain, and that the meeting of the triangular ones should afford a pleasure.
Instead of saying, the successive places of Mars are so and so, he summed them up in the statement, that the successive places of Mars are points in an ellipse. It is true, this statement, as Dr. Whewell says, was not the sum of the observations merely; it was the sum of the observations seen under a new point of view. But it was not the sum of more than the observations, as a real induction is.
Beyond the hill, and through the opening in the ellipse, we could see to another new country of hills and meadows and forest groves. In this clear air they were microscopically distinct. No blue of atmosphere nor shimmer of heat blurred their outlines. They were merely made small. Our camp was made in the open above a tiny stream.
I believe she is trying to idealize what we vulgarly call deformity, which she strives to look at in the light of one of Nature's eccentric curves, belonging to her system of beauty, as the hyperbola, and parabola belong to the conic sections, though we cannot see them as symmetrical and entire figures, like the circle and ellipse.
The great majority of cometary orbits are classed as parabolic; and it is ordinarily inferred that they are visitors from remote space, and will never return. But are they rightly classed as parabolic? Observations on a comet moving in an extremely eccentric ellipse, which are possible only when it is comparatively near perihelion, must fail to distinguish its orbit from a parabola.
Then he interested their minds by forming before them, with his body, definite figures, such as the circle, the ellipse, and the spiral, the wonderful properties of which have since been recognised by the Greeks. Adam meditated on these figures more than Eve did.
Pass the needle upward through the hole marked 0, and tie a knot in the end of the thread to prevent its slipping through. The apparatus is now ready for immediate use. It only remains to set it to the size of the oval desired. Suppose it is required to describe an ellipse the longer diameter of which is 8 inches, and the distance between the foci 5 inches.
It was a long time before it dawned upon Kepler that the simplest figure falling within the circle except at the two extremities of the diameter, was an ellipse, and it is not clear why his first attempt with an ellipse should have been just as much too narrow as the circle was too wide.
The ellipse was some ten miles long by four or five wide, and its surface rolled in easy billows to a narrow neck at the lower end. There we could just make out in the far distance a conical hill partly closing the neck. Atop the hill was a Masai manyatta, very tiny, with indistinct crawling red and brown blotches that meant cattle and sheep.
It is thus, for instance, that the circle seen sideways is changed into that kind of oval which among geometricians is known as an ellipse, and sometimes even into a parabola or a hyperbola, or actually into a straight line, witness the ring of Saturn. The external senses, properly speaking, do not deceive us. It is our inner sense which often makes us go too fast.
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