How high up can one extend the applicability of Descartes' fundamental mechanical dictum that "each part of matter, considered individually, tends to continue its movement along straight lines?"" Not very far, if one judges by Descartes' own celestial speculations: "the matter of heaven, in which the planets are situated, unceasingly revolves."" And how explanatorily powerful are Kepler's suppositions that "the power that moves the planets resides in the body of the sun"'" and that "the power that moves the planet in a circle diminishes with the removal from its source?""74 Not very much-at least they do not assist Kepler in his primary task of calculating the planetary orbits. And how instructive is "the beautiful agreement between this thought [concerning the parabolic path produced by gravity and violent motion] of the Author [Galileo] and the views of Plato concerning the origins of the various speeds with which the heavenly bodies revolve?"" It isn't at all, at least it wasn't for Galileo, who never pursued it. The first time that these spectacular possibilities were explored together and the question of planetary motions formulated at the same time in causal, mechanical and mathematical terms is in the following passage: