The Earth being a sphere was not new in Columbus' time, but no one really believed the astronomers....................

Geographical considerations

Washington Irving's 1828 biography of Columbus popularized the idea that Columbus had difficulty obtaining support for his plan because many Catholic theologians insisted that the Earth was flat.^[26] In fact, most educated Westerners had understood that the Earth was spherical at least since the time of Aristotle, who lived in the 4th century BC and whose works were widely studied and revered in Medieval Europe.^[27][25]

The sphericity of the Earth is also accounted for in the work of Ptolemy, on which medieval astronomy was largely based. Christian writers whose works clearly reflect the conviction that the Earth is spherical include Saint Bede the Venerable in his Reckoning of Time, written around AD 723. In Columbus' time, the techniques of celestial navigation, which use the position of the sun and the stars in the sky, together with the understanding that the Earth is a sphere, had long been in use by astronomers and were beginning to be implemented by mariners.^[28]

As far back as the 3rd century BC, Eratosthenes had correctly computed the circumference of the Earth by using simple geometry and studying the shadows cast by objects at two different locations: Alexandria and Syene (modern-day Aswan).^[29] Eratosthenes's results were confirmed by a comparison of stellar observations at Alexandria and Rhodes, carried out by Posidoniusin the 1st century BC. These measurements were widely known among scholars, but confusion about the old-fashioned units of distance in which they were expressed had led, in Columbus's day, to some debate about the exact size of the Earth.

Toscanelli's notions of the geography of the Atlantic Ocean, which directly influenced Columbus' plans

From d'Ailly's Imago Mundi Columbus learned of Alfraganus's estimate that a degree of latitude (or a degree of longitude along the equator) spanned 56⅔ miles, but did not realize that this was expressed in the Arabic mile rather than the shorter Roman mile with which he was familiar (1,480 m).^[30] He therefore estimated the circumference of the Earth to be about 30,200 km, whereas the correct value is 40,000 km (25,000 mi).

Furthermore, most scholars accepted Ptolemy's estimate that Eurasia spanned 180° longitude, rather than the actual 130° (to the Chinese mainland) or 150° (to Japan at the latitude of Spain). Columbus, for his part, believed the even higher estimate of Marinus of Tyre, which put the longitudinal span of the Eurasian landmass at 225°, leaving only 135° of water. He also believed that Japan (which he called "Cipangu", following Marco Polo) was much larger, farther to the east from China ("Cathay"), and closer to the equator than it is, and that there were inhabited islands even farther to the east than Japan, including the mythicalAntillia, which he thought might lie not much farther to the west than the Azores. In this, he was influenced by the ideas of Florentine astronomer Toscanelli, who corresponded with Columbus before his death in 1482 and who also defended the feasibility of a westward route to Asia.^[31]

Columbus therefore estimated the distance from the Canary Islands to Japan to be about 3,000 Italian miles (3,700 km, or 2,300 statute miles). The true figure is now known to be vastly larger: about 12,500 km. No ship in the 15th century could have carried enough food and fresh water for such a long voyage, and the dangers involved in navigating through the uncharted ocean would have been formidable. Most European navigators reasonably concluded that a westward voyage from Europe to Asia was unfeasible. The Catholic Monarchs, however, having completed an expensive war in the Iberian Peninsula, were eager to obtain a competitive edge over other European countries in the quest for trade with the Indies. Columbus's project, though far-fetched, held the promise of such an advantage.