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Now, what do the laws of Kepler say? They lay down a relation between the areas described by the heliocentric radius-vector of a planet and the time employed in describing them, a relation between the longer axis of the orbit and the time taken up by the course. And what was the principle discovered by Galileo?
The latitude, longitude, and radius-vector of each planet are constantly varying, but they each have a determined value at each moment of time. They may therefore be regarded as functions of the time, and the problem was to express these functions by algebraic formulae. These algebraic expressions would contain, besides the time, the elements of the planetary orbits to be derived from observation.
What the mathematician sought to do was to present the astronomer with a series of algebraic expressions containing t as an indeterminate quantity, and so, by simply substituting for t any year and fraction of a year whatever 1600, 1700, 1800, for example, the result would give the latitude, longitude, or radius-vector of a planet.
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