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Excerpt of Over the Edge of the World by Laurence Bergreen
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The result of endless compromises, the treaty created more problems than it solved. It was impossible to fix the line's location because cosmologists did not yet know how to determine longitude — nor would they for another two hundred years. To further complicate matters, the treaty failed to specify whether the line of demarcation extended all the way around the globe or bisected just the Western Hemisphere. Finally, not much was known about the location of oceans and continents. Even if the world was round, and men of science and learning agreed that it was, the maps of 1494 depicted a very different planet from the one we know today. They mixed geography with mythology, adding phantom continents while neglecting real ones, and the result was an image of a world that never was. Until Copernicus, it was generally assumed that the earth was at the absolute center of the universe, with the perfectly circular planets — including the sun — revolving around it in perfectly circular, fixed orbits; it is best to conceive of the earth as nested in the center of all these orbits.

Even the most sophisticated maps revealed the limitations of the era's cosmology. In the Age of Discovery, cosmology was a specialized, academic field that concerned itself with describing the image of the world, including the study of oceans and land, as well as the world's place in the cosmos. Cosmologists occupied prestigious chairs at universities, and were held in high regard by the thrones of Europe. Although many were skilled mathematicians, they often concerned themselves with astrology, believed to be a legitimate branch of astronomy, a practice that endeared them to insecure rulers in search of reassurance in an uncertain world. And it was changing faster than cosmologists realized. Throughout the sixteenth century, the calculations and theories of the ancient Greek and Egyptian mathematicians and astronomers served as the basis of cosmology, even as new discoveries undermined time-honored assumptions. Rather than acknowledge that a true scientific revolution was at hand, cosmologists responded to the challenge by trying to modify or bend classical schemes, especially the system codified by Claudius Ptolemy, the Greco-Egyptian astronomer and mathematician who lived in the second century A.D.

Ptolemy's massive compendium of mathematical and astronomical calculations had been rediscovered in 1410, after centuries of neglect. The revival of classical learning pushed aside medieval notions of the world based on a literal-yet magical-interpretation of the Bible, but even though Ptolemy's rigorous approach to mathematics was more sophisticated than monkish fantasies of the cosmos, his depiction of the globe contained significant gaps and errors. Following Ptolemy's example, European cosmologists disregarded the Pacific Ocean, which covers a third of the world's surface, from their maps, and they presented incomplete renditions of the American continent based on reports and rumors rather than direct observations. Ptolemy's omissions inadvertently encouraged exploration because he made the world seem smaller and more navigable than it really was. If he had correctly estimated the size of the world, the Age of Discovery might never have occurred.

Amid the confusion, two kinds of maps evolved: simple but accurate "portolan" charts based on the actual observations of pilots, and far more elaborate concoctions of cosmographers. The charts simply showed how to sail from point to point; the cosmographers tried to include the entire cosmos in their schemes. The cosmographers relied primarily on mathematics for their depictions, but the pilots relied on experience and observation. The pilots' charts covered harbors and shorelines; the cosmographers' maps of the world, filled with beguiling speculation, were often useless for actual navigation. Neither approach successfully applied the terms of the Treaty of Tordesillas to the real world.