When, on his third voyage to the New World in 1498, Christopher Columbus encountered the Orinoco River on the coast of present-day Venezuela, he knew just what to make of the voluminous current. There was so much fresh water gushing into the briney Caribbean that he decided that the four rivers of Paradise — the Nile, Euphrates, Tigris, and Ganges — must be nearby. Paradise itself, he reasoned, couldn’t be far.

Had he gone mad? Possibly, but it is very hard to judge him by our own clinical standards, rather than as a European and Christian at the end of the 15th century, trying desperately to understand world geography, but wallowing in terms and concepts dignified by ancient religious and classical usage. Christopher Columbus was not merely a sailor but an omnivorous intellectual — though an intellectual of his own time. He had read widely and absorbed much of what there was to know about the world of his day. And yet, knowing so much meant only that he was as ignorant as those who came before. There was much more of the past to Columbian world geography than the future, more of Aristotle and the Book of Genesis than Gerardus Mercator.

Columbus had begun his career by making himself a skilled sailor, voyaging hither and yon and as far from the familiar lands of Western Europe as Chios in the Aegean to Iceland in the north Atlantic. Such practical experience paid off generously in the pursuit of his transatlantic ambitions. The course he plotted for his 1492 outward voyage and, especially, the one for his 1493 return were too nearly ideal to have been products of pure luck: He must have acquired a lot of hints about the Atlantic wind patterns from practical seamen. You didn’t have to sail all the way to America to learn about, for instance, the Prevailing Westerlies.

But maritime oral tradition didn’t teach him his articles of faith about the locations of major oceans and continents, or about how wide the world was. He got that from the wisemen of his own age, from saints and philosophers, from the Bible, Aristotle, and lesser lights, from minds which were as comfortable issuing statements about world geography as about God. These experts paid more heed to each other than to the few accounts of actual experience by world travelers like Marco Polo, and yet their pronouncements had a very real effect on future experience, helping shape the course of Columbus’s voyage, and, through it, the next several centuries of human history. Those pronouncements, and their very real effects, are the central subject of “The Tropics of Empire” (MIT Press, 616 pages, $49.95), the erudite and readable new study by Nicolás Wey Gómez.

Mr. Gómez’s volume is not an easy one from which to extract brief representative samples, but it does offer tremendous insight into the prevailing medieval understanding of the shape of the world Columbus encountered, and absorbed. Several of the texts that Columbus perused posited a world with five horizontal, that is, latitudinal, zones, each with clear environmental identities and peoples to match. The far north — also the far south, but nobody as yet was paying much attention to the other side of the Equator — was cold, miserable, and inhabited by fair-skinned fierce people who resisted being told what to do. The middle zone, the tropics, was repellently hot, some would say uninhabitable, and populated, when at all, by mild intelligent people who would make good slaves, plus very ugly black and dangerous people, the Ethiopians, who might eat you. In between these two unpleasant zones was a pleasant zone wherein lived sensible clever people who would make excellent governors for the others. Unsurprisingly, Mediterranean Europe was thought an exemplar of this superior zone.

According to Columbus’s experts, geography had a permanent effect on people. Whatever the realities of the lands that Columbus and other Europeans would discover and exploit, they did so with such preconceptions in mind. The West Indian native people, the Tainos, were brownish and trainable, Columbus found, like the Canary Islanders of the same latitude. The West Indian Caribs were darker, tough, and dangerous, quite like the Ethiopians, as the explorers expected.

One of the more influential clichés of medieval geography that attracted Columbus’s interest — and which has arrested Mr. Gómez’s attention — is the quality of south. Europeans started out thinking of the equatorial zone as impossibly hot, that its place quality was poor. But by Columbus’s time, the Portuguese had coasted West Africa for hundreds and hundreds of miles, had made contacts with the peoples who lived there, and had decided that trade with them would indeed be profitable — trade in slaves, for instance. The Spanish state had naively agreed that the lands south of the Canary Islands, and the ocean that lapped their beaches, were Portuguese and off-limits to the Spanish. They knew that the Portuguese, given the opportunity, would certainly want to extend this arrangement westward, claiming the right to any undiscovered lands of the same place quality, in the same latitude, on the far side of the Atlantic. Columbus’s chief motive, Mr. Gómez shows, was not to sail west, discovering whatever he might find there, but to sail south, to establish firmly Spanish claims to that desirable land by planting colonies there.

Indeed, the explorer sailed not simply west but veered south as well. And in his purpose, he succeeded: He established Spanish claims to the many islands of the Caribbean and even to the mainlands beyond. He was not trying to persuade the world that it was round, but to legitimize the claims of Ferdinand and Isabella to a big and quite possibly luscious chunk of its tropics. And if Paradise came along in the bargain, so be it.

Mr. Crosby is a professor emeritus of the University of Texas, and author of “The Columbian Exchange” and “Ecological Imperialism.”