The Ten Books on Architecture, 9.1.15

Vitruvius  Parallel editions

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Gwilt translation

15Thus, on a wheel similar to those in use among potters, if seven ants be placed in as many channels round the centre, which are necessarily greater in proportion to their distance therefrom, and the ants are forced to make their circuits in these channels, whilst the wheel moves round in an opposite direction, they will assuredly complete their circuit, notwithstanding the contrary motion of the wheel; and, moreover, that nearest the centre will perform his journey sooner than he who is travelling in the outer channel of the wheel, who, though he move with equal velocity, yet, from the greater extent of his circuit, will require a longer time for its completion. It is even so with the planets, which, each in its particular orbit, revolve in a direction contrary to the motion of the heavens, although, in their diurnal motion, they are carried backwards by its rotation.

Morgan translation

15For example, place seven ants on a wheel such as potters use, having made seven channels on the wheel about the centre, increasing successively in circumference; and suppose those ants obliged to make a circuit in these channels while the wheel is turned in the opposite direction. In spite of having to move in a direction contrary to that of the wheel, the ants must necessarily complete their journeys in the opposite direction, and that ant which is nearest the centre must finish its circuit sooner, while the ant that is going round at the outer edge of the disc of the wheel must, on account of the size of its circuit, be much slower in completing its course, even though it is moving just as quickly as the other. In the same way, these stars, which struggle on against the course of the firmament, are accomplishing an orbit on paths of their own; but, owing to the revolution of the heaven, they are swept back as it goes round every day.