f degrees. Now then as almost all the lands from
the Cabo Verde islands to the Malucos, are, for the most part quite
distinct from the equinoctial, it will take a much greater number
of degrees when they are transferred and drawn on the spherical
body. Calculating by geometrical proportion, with the arc and chord,
whereby we pass from a plane to a spherical surface, so that each
parallel is just so much less as its distance from the equinoctial
is increased, the number of degrees in the said maps is much greater
than the said pilots confess, and consequently these lands fall by a
greater number of degrees inside their Majesties' limits. In order to
verify the above we must examine the itineraries and navigation routes,
and the angles and intersections made by the routes with the meridians
and parallels encountered, which are styled angles _positionis_ among
cosmographers. This is the most certain method of determining lands
on a spherical body, when calculating them from the plane surface,
as the following will show.

[The distances of these itineraries are shown in evidence of the
preceding. Maps of India made in Portugal "at the time when there was
no suspicion that so great a number of leagues was to be subtracted
as is proved now to have been the case," are cited and distances taken
therefrom in proof of the assertions made by the Castilian deputies. As
a result of these distances it is shown that the distance between
the Moluccas and the island of Sant Antonio would be one hundred and
eighty-four degrees to the eastward, to which number "must be added
the degrees contained in the said three hundred and seventy leagues
from the island of Sant Antonio to the line of demarcation." The
following deductions are made:]

It is quite evident from the above that the distance of the navigation
eastward assigned by the Portuguese in the proceedings is short by more
than fifty degrees, being proved by the said old Portuguese relations
and maps, which are not to be doubted. And it is evident that our
calculation is true, both eastward and westward, and that from the
said divisional line commencing from the island of Sant Antonio,
the distance westward to the Malucos is not more than the said one
hundred and fifty degrees.

[At this point the aid of the old authors, Ptolemaeus and Plinius,
is invoked to prove more conclusively that the distance was shortened
by the Portuguese. The summary of the document is as follows:]

Th