tatem sancti
sancti habuerunt illum librum habuerunt in reverentia."
in usu et confirmant veritates
sacras per illum librum."

Columbus must either have carried the book of Alliacus with him
on his voyages, or else have read his favourite passages until
he knew them by heart, as may be seen from the following
passage of a letter, written from Hispaniola in 1498 to
Ferdinand and Isabella (Navarrete, tom i. p. 261):--"El
Aristotel dice que este mundo es pequeno y es el agua muy poca,
y que facilmente se puede pasar de Espana a las Indias, y esto
confirma el Avenryz [Averroes], y le alega el cardenal Pedro de
Aliaco, autorizando este decir y aquel de Seneca, el qual
conforma con estos.... A esto trac una autoridad de Esdras del
tercero libro suyo, adonde dice que de siete partes del mundo
las seis son descubiertas y la una es cubierta de agua, la cual
autoridad es aprobada por Santos, los cuales dan autoridad al
3^o e 4^o libro de Esdras, ansi come es S. Agustin e S.
Ambrosio en su _exameron_," etc.--"Singular period," exclaims
Humboldt, "when a mixture of testimonies from Aristotle and
Averroes, Esdras and Seneca, on the small extent of the ocean
compared with the magnitude of continental land, afforded to
monarchs guarantees for the safety and expediency of costly
enterprises!" _Cosmos_, tr. Sabine, vol. ii. p. 250. The
passages cited in this note may be found in Humboldt, _Examen
critique_, tom. i. pp. 65-69. Another interesting passage from
_Imago Mundi_, cap. xv., is quoted on p. 78 of the same work.]

[Sidenote: Fortunate mixture of truth and error.]

[Sidenote: The whole point and purport of Columbus's scheme.]

Thus did Columbus arrive at his decisive conclusion, estimating the
distance across the Sea of Darkness to Japan at something less than the
figure which actually expresses the distance to the West Indies. Many a
hopeful enterprise has been ruined by errors in figuring, but this wrong
calculation was certainly a great help to Columbus. When we consider
how difficult he found it to obtain men and ships for a voyage supposed
to be not more than 2,500 miles in this new and untried direction, we
must admit that his chances would have been poor indeed if he had
proposed to sail westward on