Contrary to the commonly held view that people in Columbus’s time that the earth was flat, it was accepted by experts that it was indeed a sphere.
Regiomontanus’s work was used to teach both Copenernicus’ teacher, and Copernicus himself since Regiomontanus had arrived at the concept that the Sun was the center of our solar system, not the earth, and all of his work and accomplishments regarding the appearance and locations of heavenly bodies such as comets and planets followed from that concept of the planets rotating around the sun, not the earth.
What I don’t know is if Columbus derived the eclipse from the data provided by Regiomontanus (since he had Regiomontanus’book with him, apparently it was similar to the modern US Navy (probably at least up to the 1970’s) where you wouldn’t go to sea unless you had a copy of Bowdich (The American Practical Navigator) with you.) or if it were in the book itself.
Columbus was a very smart guy. He doesn’t get any credit from many of his detractors for that. They think he simply stood on the shoulders of others...which he did. But he enabled his own path.
One of the best and most enjoyable books on the subject is “Admiral of the Ocean Sea: A Life of Christopher Columbus” by Samuel Eliot Morison. Great and enjoyable book, along with his “The European Discovery of America” volumes 1 and 2, and “The Great Explorers”.
Besides being incredibly informative, he writes in an engaging manner, and has sailed the waters of North America and the Caribbean extensively and often compares what he saw to what those early explorers saw.
Very cool stuff!