The ball passing from A to C, by the force of gravity, and having, at the moment of its liberation, received a momentum . from the moving ship in the direction A, B, will, by the conjoint action of the two forces A, B, and A, C, take the direction A, D, falling at D, just as it would have fallen at C, had the vessel remained at rest.
It is argued by those who hold that the earth is a revolving globe, that if a ball is dropped from the mouth of a deep mine, it reaches the bottom in an apparently vertical direction, the same as it would if the earth were motionless. In the same way, and from the same cause, it is said that a ball allowed to drop from the top of a tower, will fall at the base. Admitting the fact that a ball dropped down a mine, or let fall from a high tower, reaches the bottom in a direction parallel to the side of either, it does not follow therefrom that the earth moves. It only follows that the earth might move, and yet allow of such a result. It is certain that such a result would occur on a stationary earth; and it is mathematically demonstrable that it would also occur on a revolving earth; but the question of motion or non-motion--of which is the fact it does not decide. It gives no proof that the ball falls in a vertical or in a diagonal direction. Hence, it is logically valueless. We must begin the enquiry with an experiment which does not involve a supposition or an ambiguity, but which will decide whether motion does actually or actually does not exist. It is certain, then, that the path of a ball, dropped from the mast-head of a stationary ship will be vertical.
No. the ball does not receive its momentum from the ship, or at the moment of its liberation. The ball has its horizontal momentum when it "went on board".
Since the ball, the top of the mine (or tower), and the bottom of the tower all are traveling horizontally at the same velocity (Technically the top of a one-mile-high tower travels 0.00000160868 mph faster) RET agrees with reality.
Finally, R. makes his all-too-typical error in reasoning. If he can't find evidence of RET, especially failing to do the math involved, RET must be false. Failing to find evidence to support a thesis does not disprove the thesis.
With yet another page destroyed with such little effort and demonstrating R.'s failure to reason, I increasingly have to wonder why FEers reference this text.