Most of this proof is answered in my last post Water Flows Downward. In fact, the proof is pretty much identical to the last one, except the author just picks out downhill water flow specifically and saves the other points about the movement of Earth to discuss again later.
“5) One portion of the Nile River flows for a thousand miles with a fall of only one foot. Parts of the West African Congo, according to the supposed inclination and movement of the ball-Earth, would be sometimes running uphill and sometimes down. This would also be the case for the Parana, Paraguay and other long rivers.”
There are two problems with the statement. The first is easily understood by anyone who has ridden a roller coaster. If something rolls down a hill fast enough, it can go up another hill.
After going up a very large hill, building up potential energy, the roller coaster occupant then goes through a series of ups and downs until the potential energy is lost to friction with the track.
More importantly, the author does not understand gravity. Here is the water cycle:
Energy from the sun heats up and evaporates water which is able to climb in the atmosphere. Once released as rain, it hits mountains, hills, or even slightly inclined plains and flows downhill toward a body of water. Because gravity is pulling toward the center of the planet no matter which area of the ball Earth rain hits, water will flow downhill from a position of higher elevation to a position of lower elevation. Meaning each of these representations works the same way:
People on the southern half of the ball Earth are not falling off because of the effects of gravity. Up and down is relative to where you are standing. So while rivers may go uphill if there is enough energy built up from a steep downhill; rivers in general travel from a point of higher elevation to a point of lower elevation no matter which side of the ball Earth they are on.