among his own papers respecting this matter.

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