The motives which induced my father to undertake the discovery of the West Indies were three.  Natural reason, authority of authors, and the testimony of sailors.  From natural reason my father concluded that the whole sea and land of this world composed a globe or sphere, which might assuredly be gone round, so that men should stand with their feet directly against the feet of other men, in any precisely opposite parts whatever. Secondly, he took it for granted upon the authority of approved authors that a great portion of our globe had been already travelled over and explored; and that it now only remained to discover the whole, so as to make known what was contained in the vacant space which remained, between the eastern boundaries of India which were known to Ptolemy and Marinus, and those our newly discovered western parts of the coast of Africa and the Azores and Cape Verd islands, the most westerly which were yet known. Thirdly, he concluded that this still unknown space, between the eastern limits known to Marinus and the Cape Verds, could not exceed a third part of the circumference of the globe; since Marinus had already described 15 hours towards the east, out of the 24 parts or hours into which the circumference of the world is divided by the diurnal course of the sun; and therefore to return in an easterly direction to the Cape Verd islands from the limits discovered by Marinus, or to proceed westerly from these islands to meet the eastern limits of Marinus, required only to pass over about 8 parts in 24 of the circumference of the earth[1].

He reckoned, fourthly, that as the cosmography of Marinus had given an account of fifteen hours or parts of the circumference of the globe eastwards, and had not yet attained to a knowledge of the eastern extremity of the land, it followed of course that this eastern extremity must be considerably beyond those known limits; and consequently, that the farther it extended eastwards, so much the nearer it must approach to the Cape Verd islands, or the then known western limits of the globe:  And, if this space were sea, it might be easily sailed over in a short time; and if land, that it would be much sooner discovered by sailing to the west, since it must be much nearer to these islands in that direction.  To this may be added what is related by Strabo in his Fifteenth Book, that no army ever penetrated to the eastern bounds of India, which according to Ctesias is as extensive as all the rest of Asia.  Onesicritus affirms that India is a full third part of the world; and Nearchus says that it is four months journey in a straight line from west to east.  Pliny, in the 17th Chap, of his 6th Book, says that India is a third part of the earth, and that consequently it must be nearer Spain in the western than in the eastern direction.