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Intellectual love! intellectual love! what is this intellectual love? Something of the nature of a red flavour, or a bitter sound, or an aromatic colour, or rather something of the same sort as a love-stricken triangle or an enraged ellipse a pure metaphor, but a tragic metaphor. And a metaphor corresponding tragically with that saying that the heart also has its reasons.
It seemed natural to assume, that this was exactly the case, in which event each of the two foci of the ellipse would have had a special significance in relation to the movement of the planet.
This discovery had been arrived at from the interpretation of observations. Kepler had himself assigned no reason why the orbit of a planet should be an ellipse rather than any other of the infinite number of closed curves which might be traced around the sun.
We could view the enclosed ellipse longitudinally, and note nearly every movement made by those inside. Even should we be detected in our espionage, it would pass without suspicion as to our real object. What more natural than that we should desire to witness the spectacle of the dance? The act would be construed as springing from mere savage curiosity?
Then the whole line DC is 141,289; and CP, which is a mean proportional between DC and CN, since MD touches the Ellipse, will be 105,032. But OC is 62,479 of these same parts of which CM is 100,000, because it is equal to MN, the sine of the angle MCP, which is 38 degrees 40 minutes. Then the whole line CZ is 139,655; and CS, which is a mean proportional between CZ and CO will be 93,410.
Decreasing the angle minute by minute, the ellipse becomes first perceptibly eccentric, then manifestly so, and by and by acquires so immensely elongated a form, as to bear no recognizable resemblance to a circle. By continuing this process, the ellipse passes insensibly into a parabola; and, ultimately, by still further diminishing the angle, into an hyperbola.
Supposing then, in the next figure, as previously, the surface of the crystal gG, the Ellipse GPg, and the line N; and CM the refraction of the perpendicular ray FC, from which it diverges by 6 degrees 40 minutes. Now let there be some other ray RC, the refraction of which must be found.
I found afterward that the elliptical wall as well was of black marble, absorbing the little light that reached it. The roof was the long half of an ellipsoid, and the opening in it was over one of the foci of the ellipse of the floor. I fancied I caught sight of reddish lines, but when I would have examined them, they were gone.
He made the general body of the arch an ellipse, 150 feet on the chord-line and 35 feet rise, while the voussoirs, or external archstones, being in the form of a segment, have the same chord, with only 13 feet rise. "This complex form," says Mr.
Thus the properties of the ellipse, the hyperbola, and the parabola, continued to be studied by after mathematicians; but no use was made of this knowledge till nearly two thousand years later, when Kepler crowned the labours of Apollonius with the great discovery that the paths of the planets round the sun were conic sections.
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