Why do you treat R.'s continued errors with such an effort to find an excuse? His illustrations were corrupted by the published. If he is wrong about something, it's only because we took him at his word.
Have you done the calculations based on RET about what imaginary forces the horseback rider would experience? If so, please present them; otherwise, you don't know about what you're talking. Also please do tell us what if any other forces the rider would experience akin to those you say the FE experiences as the Coriolis Effect.
Rowbotham uses the word 'rapidly' to describe the movement of the horse, as in 'a hurrying pace'. The horse was accelerating.
Rapid typically means to accelerate at a quick pace.
"He swung his fist rapidly into the punching bag"
"New report warns of rapidly increasing carbon emission levels"
"Rapidly rising food costs sting at supermarket"
So when R. says:
"Thus it is demonstrable that, in all cases where a ball is thrown upwards from an object moving at right angles to its path, that ball will come down to a place behind the point from which it was thrown;" (emphasis my own)
He does not mean "in all cases" ? Does he mean "in some cases"? Did "in all cases" mean somethign different in the 19th century? Or are his scientific writing unreliable? He also does not have illustrations that accurately depict his ideas in a book he edited. This is not a good sign.
"Thus it is demonstrable that, in all cases where a ball is thrown upwards from an object moving at right angles to its path, that ball will come down to a place behind the point from which it was thrown"
If the object is moving at right angles to a ball which is in the air, away from it, then the object is accelerating from the ball. I find nothing wrong with the sentence.
He also does not have illustrations that accurately depict his ideas in a book he edited. This is not a good sign.
Even the illustrations show accelerating bodies. Consider the train example from the chapter. The three images of it are not evenly spaced.

The ball falls behind because it is accelerating away.