Book 10
1.60
Further, we must not assert up or down of that which is unlimited, as if there were a zenith or nadir.Objection was taken by Aristotle to the atomic motion of Democritus, on the ground that it implied a point or region absolutely high, and an opposite point or region absolutely low, these terms being unmeaning in infinite space (Aristotle, Phys. iii. 5. 205 b 30; iv. 8. 215 a 8). See Classical Review, xxxv. p. 108. As to the space overhead, however, if it be possible to drawThis verb (ἄγειν) is technical in Euclid. a line to infinity from the point where we stand, we know that never will this space —or, for that matter, the space below the supposed standpoint if produced to infinity—appear to us to be at the same time up and down with reference to the same point; for this is inconceivable. Hence it is possible to assume one direction of motion, which we conceive as extending upwards ad infinitum, and another downwards, even if it should happen ten thousand times that what moves from us to the spaces above our heads reaches the feet of those above us, or that which moves downwards from us the heads of those below us. None the less is it true that the whole of the motion in the respective cases is conceived as extending in opposite directions ad infinitum.
