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For this reason he recommends the paeon, and says that every person makes use of it, even without being sensible when he does so. He likewise observes that it is a proper medium between the different feet above-mentioned: the proportion between the long and short syllables, in every foot, being either sesquiplicate, duple, or equal.
"Moreover, since the satellites of Jupiter perform their revolutions in times which observe the sesquiplicate proportion of their distances from Jupiter's centre, their accelerative gravities towards Jupiter will be reciprocally as the square of their distances from Jupiter's centre that is, equal, at equal distances.
The third and fourth causes compensate each other in a comparison of different planets; the simple and subduplicate proportion compound the sesquiplicate proportion, which therefore is the ratio of the periodic times."
In his own words, "The proportion existing between the periodic times of any two planets is exactly the sesquiplicate proportion of the mean distances of the orbits," or as generally given, "the squares of the periodic times are proportional to the cubes of the mean distances."
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