Basically, the fact that the sea rises not only in the directions of the Sun and of the Moon, but also in the opposite directions.
If you think that the Sun and the Moon attract just the sea, but that the Earth does not move, then you would expect the water to bulge only towards them, and not also in the opposite direction.
If you instead think that the whole Earth is falling towards the Moon and the Sun, you have to subtract the motion of the center of the Earth, and you will correctly predict to see the water rise in both directions. The center of the Earth is attracted more than the sea in the opposite side, but less than the sea on the side of the Moon/Sun, so when you subtract you see a high tide in both sides.
In the Placita Philosophorum (probably written by Aetius) it is written that (Ps. Plut. Plac. 3.17):
Seleucus the mathematician attributes a motion to the earth; and thus he pronounceth that the moon in its circumlation meets and repels the earth in its motion; between these two, the earth and the moon, there is a vehement wind raised and intercepted, which rushes upon the Atlantic Ocean, and gives us a probable argument that it is the cause the sea is troubled and moved.
Now, this is very unclear (and the English translation does not help—for example πνεύματος is not “a wind”, the Stoichs used it to mean a much more abstract kind of influence); Galileo was confused by this passage too. But it looks like Seulecus assumed that the Earth moves in order to explain tides.
Basically, the fact that the sea rises not only in the directions of the Sun and of the Moon, but also in the opposite directions.
If you think that the Sun and the Moon attract just the sea, but that the Earth does not move, then you would expect the water to bulge only towards them, and not also in the opposite direction.
If you instead think that the whole Earth is falling towards the Moon and the Sun, you have to subtract the motion of the center of the Earth, and you will correctly predict to see the water rise in both directions. The center of the Earth is attracted more than the sea in the opposite side, but less than the sea on the side of the Moon/Sun, so when you subtract you see a high tide in both sides.
In the Placita Philosophorum (probably written by Aetius) it is written that (Ps. Plut. Plac. 3.17):
Now, this is very unclear (and the English translation does not help—for example πνεύματος is not “a wind”, the Stoichs used it to mean a much more abstract kind of influence); Galileo was confused by this passage too. But it looks like Seulecus assumed that the Earth moves in order to explain tides.