The fifth argument which induced the admiral to believe that the distance in a western direction to India was small, was taken from the opinion of Alfragranus and his followers, who computed the circumference of the globe as much less than all other cosmographical writers, as they only allowed 56-2/3 miles to a degree of longitude.  Whence my father inferred, that the whole globe being small, the extent of that third part which remained to be discovered must necessarily be proportionally small likewise; and might therefore be sailed over in a short time.  And, as the eastern bounds of India were not yet discovered, and must lie considerably nearer us towards the west, he therefore considered that the lands which he might discover in his proposed expedition westwards might properly be denominated the Indies.  Hence it appears how much Roderick the archdeacon of Seville was wrong in blaming the admiral for calling those parts the Indies which were not so.  But the admiral did not call them the Indies as having been seen or discovered by any other person; but as being in his opinion the eastern part of India beyond the Ganges, to which no cosmographer had ever assigned any precise limits, or made it to border upon any other country farther to the east, considering those unknown parts of eastern India to border on the ocean.  And because he believed those countries which he expected to discover formed the eastern and formerly unknown lands of India, and had no appropriate name of their own, he therefore gave them the name of the nearest known country, and called them the West Indies.  He was, so much the more induced to choose this appellation that the riches and wealth of India were well known, and he thereby expected the more readily to induce their Catholic Majesties to accede to his proposed undertaking, of the success of which they were doubtful; by saying that he intended to discover the way to India by the west:  And he was desirous of being employed in the service of the crown of Castile, in preference to any other.

The second motive which encouraged the admiral to undertake his great enterprize, and which might reasonably induce him to call the countries he proposed to discover by the name of the Indies, was derived from the authority of learned men; who had affirmed that it was possible to sail from the western coast of Africa and Spain to the eastern bounds of India by the westwards, and that the sea which lay between these limits was of no great extent.  This is affirmed by Aristotle, in his Second Book of the Heaven and of the World, as explained by Averroes; in which he says that a person may sail from India to Cadiz in a few days.  Seneca, in his book of Nature, reflecting upon the knowledge of this world as insignificant in comparison with what shall be attained in a future life, says that a ship may sail in a few days with a fair wind from Spain to India.  And if, as some suppose, the same Seneca were the author of the tragedies, he expresses himself to the same purpose in the following chorus of the Medea: