Now at last, at long last, after six years of incredible labour, he held the secret of the Martian orbit. He was able to express the manner in which the planet’s distance from the sun varied with its position, in a simple formula, a mathematical Law of Nature. But he still did not realize that this formula specifically defined the orbit as an ellipse.* Nowadays, a student with a little knowledge of analytical geometry would realize this at a glance; but analytical geometry came after Kepler. He had discovered his magic equation empirically, but he could no more identify it as the shorthand
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