That's like saying the bible is true because it's written down.
A couple of quotes of his:
"There are rivers that flow for hundreds of miles towards the level of the sea without falling more than a few feet — notably, the Nile, which, in a thousand miles, falls but a foot. A level expanse of this extent is quite incompatible with the idea of the Earth's convexity. It is, therefore, a reasonable proof that Earth is not a globe."
By this logic the fact that there are mountains proves that the Earth is round because the highest of the rises to 29,000 feet over a very short span.
"If the Earth were a globe, a small model globe would be the very best - because the truest - thing for the navigator to take to sea with him. But such a thing as that is not known: with such a toy as a guide, the mariner would wreck his ship, of a certainty!, This is a proof that Earth is not a globe."
Such a thing as a model globe is not known? The earliest globe known of dates from the same period of time in which the Earth was established as a sphere. Was he just no looking in the right places to find this magical thing or was it one of the things he chose to ignore to bolster his claim?
You obviously completely misinterpreted Rowbothams points there.
A mountain has no bearing on a river. A river has a high point and flows towards sea level. If a river goes across a thousand miles it would inevitably have to conquer the convexity in the form of a hill at some point (flowing up and over)
As far as the globe, what he was saying was that no navigator uses a model globe to travel at sea. They use maps, and celestial methods to do it, if the globe were a true representation they would only need a model globe to navigate.
If that is a representation of your take away from 100 proofs then you clearly have a hard time understanding it at all.
A mountain has as much bearing on the topic at hand as a river. It's a matter of following logic. If the perceived flatness of a river proves a flat earth, the perceive rise of a mountain proves a round earth.
Regarding a globe representation, keeping in mind the limited space available on ships (today and especially in the past):
1. Globes are a scaled representation of the earth.
2. Most globes represent thousands of miles in mere inches.
3. A globe can be scaled to represent those thousands of miles in a usable way but it would have to be extremely large, probably on the order of a ten foot diameter (possibly quite larger to accommodate resolution of oceanic features), to be truly useful which would necessitate an independent, specialized room in each and every ship to accommodate it.
1. Maps are scaled representations of the earth.
2. Maps also represent thousands of miles (typical world map) in mere inches but their resolution is easily changed to give a more accurate representation (typical topo grid map).
3. Maps take up very little space. Even if every ship was required to have 100 maps of differing resolutions and areas the space they take up is a matter of feet (a cabinet not much larger than a typical office desk).
Do you honestly believe that ship builders, navies and naval merchants are or were going to build their ships around a useable globe representation when maps served the purpose just as well? Do you honestly believe that any of them would give up valuable space to a useable globe representation when a smaller, viable option was/is available?
Prior to the advent of GPS maps were the only available source for navigation (from nation scale to community scale). Try to imagine how large a globe representation would have to be to give useable navigation information on a national scale and even more so on a community scale.
The fact that maps are used is, in no way, proof of a flat earth.
Who said a river was flat? It's obvious they aren't, because they flow toward the lowest area, as fluids are known to do, in particular sea level. Which is what all water does. It flows from the higher elevation to lower elevation. But there is a vast ocean in which not only does this not happen, it actually bends and contorts and bulges to form a giant spherical surface.
Interesting though, that a paper map has high enough resolution because of a typographical grid that apparently doesn't work on a globe. Also interesting most modern ships don't have anywhere near enough room for a 10 foot globe.
https://www.google.com/search?q=allure+of+the+seas+lobby&biw=1600&bih=765&source=lnms&tbm=isch&sa=X&ved=0ahUKEwixjsqD-rLLAhXIdD4KHRbAC48Q_AUIBigB
Reread the conversation regarding rivers and the quote from Rowbotham. The gist (one foot of drop in a thousand miles is miniscule) of his statement is that the Nile is running flat.
A topographical grid does work on a globe but the topographical grid is not what makes a map, or a globe for that matter, scalable.
Regarding maps and scaling them:
1. World map drawn on a sheet of paper that is 4 foot by 3 foot. You can see information on a gross scale, i.e. continents, mountains and some major rivers.
2. Another map drawn on the same size paper representing the Americas. You can now see information not only on a gross scale but also at a slightly finer scale.
3. Another map drawn on the same size paper representing only North America. You can now see even finer detail.
4. Another map drawn on the same size paper representing only the United States. You can now see even finer detail.
5. Another map drawn on the same size paper representing only the area bounded by the Rocky mountains and the Mississippi river. You can now see even finer detail.
6. Another map drawn on the same size paper representing only the state of Oklahoma. You can now see even finer detail.
7. Another map drawn on the same size paper representing only the western half of Oklahoma. You can now see even finer detail.
These scaling steps can go on to the point that the user of the map needs. At any point along the way topographical markings can be made to represent pertinent information. Just from this example you've got a series of maps that provide information from the gross to the relatively fine which are easily transportable, storable, usable and provide a vast wealth of information.
Scaling a globe works for scaling a globe. What I mean by this is that you can scale the globe to large or small as needed but you can NOT scale the Americas, North America, the United States, the area bounded by the Rocky mountains and Mississippi river, Oklahoma or the western half of Oklahoma to their own, independent, globe.
Regarding ships not having room:
How big is the mechanism to mount that ten foot globe?
Is the globe stationary and people have to move around it to use it?
If mobile, how big is the mechanism to drive it in multiple dimensions?
If static, how large is the structure to allow people to use it without issue?
There are many other aspects to consider which drive the amount of space a ten foot globe would actually take up. Go talk to that cruise line and see how agreeable they would be to taking away from passenger space to fit this instrument in their ship when they can accomplish much more with maps that take up far, far less space. Do the same with military and merchant ships. Talk them in to giving up valuable space for this model globe mechanism. You've gained nothing with that comment.