“It remains for me to place before your serene majesty a cosmographical description of the voyage. As I have already said, we departed from the desert-rocks, lying in the extreme part of the West known to the ancients, and in the described meridian near the Fortunate Islands, on the thirty-second parallel from the equator of our hemisphere, and sailed from it westwardly to where we found the first land, 1,200 leagues or 4,800 miles, reckoning according to nautical custom four miles to a [marine] league.[409] ... During our voyage we had no lunar eclipses or similar celestial phenomena. We therefore determined our progress from the difference of longitude, which we ascertained by various instruments, taking the sun’s altitude from day to day, and by calculating geometrically the distance run by the ship from one horizon to another. All these observations, as also the ebb and flow of the tide in all places, were noted down in a little book, which may prove serviceable to navigators. They are communicated to your majesty with the hope of promoting science. “My intention in this voyage was to reach Cathay, on the extreme coast of Asia, expecting, however, to find in the newly discovered land some obstacle as I found, yet I did not doubt that I should sail by some passage to the eastern ocean. It was the opinion of the ancients that our eastern ocean of India was an expanse of water without any intervening land. Aristotle supports it by arguments founded on various probabilities, but it is contrary to later belief and false by observation. The discovered country, of which the ancients knew nothing, is another world compared with that which was before known, being evidently larger than our Europe together with Africa, and, perhaps, Asia, if one rightly estimate its extent, as shall now be explained briefly to your majesty.”[410] He then speaks of the Spaniards sailing as far south as the Strait of Magellan and as far north as the twenty-first parallel without finding a termination to the continent....