ly: "Nota quod sepius navigando
ex Ulixbona ad Austrum in Guineam, notavi cum diligentia viam,
ut solitum naucleris et malineriis, et preteria accepi
altitudinem solis cum quadrante et aliis instrumentis plures
vices, et inveni concordare cum Alfragano, videlicet respondere
quemlibet gradum milliariis 56-2/3. Quare ad hanc mensuram
fidem adhibendam. Tunc igitur possumus dicere quod circuitus
Terrae sub arae equinoctiali est 20,400 milliariorum. Similiter
que id invenit magister Josephus phisicus et astrologus et alii
plures missi specialiter ad hoc per serenissimum regem
Portugaliae," etc.; _anglice_, "Observe that in sailing often
from Lisbon southward to Guinea, I carefully marked the course,
according to the custom of skippers and mariners, and moreover
I took the sun's altitude several times with a quadrant and
other instruments, and in agreement with Alfragan I found that
each degree [i. e. of longitude, measured on a great circle]
answers to 56-2/3 miles. So that one may rely upon this
measure. We may therefore say that the equatorial circumference
of the earth is 20,400 miles. A similar result was obtained by
Master Joseph, the physicist [or, perhaps, physician] and
astronomer, and several others sent for this special purpose by
the most gracious king of Portugal."--Master Joseph was
physician to John II. of Portugal, and was associated with
Martin Behaim in the invention of an improved astrolabe which
greatly facilitated ocean navigation.--The exact agreement with
Ptolemy's figures shows that by a mile Columbus meant a
geographical mile, equivalent to ten Greek stadia.]

[Footnote 464: One seventh of 18,000 is 2,571 geographical
miles, equivalent to 2,963 English miles. The actual length of
Columbus's first voyage, from last sight of land in the
Canaries to first sight of land in the Bahamas, was according
to his own dead reckoning about 3,230 geographical miles. See
his journal in Navarrete, _Coleccion_, tom. i. pp. 6-20.

I give here in parallel columns the passage from Bacon and the
one from Alliacus upon which Columbus placed so much reliance.
In the Middle Ages there was a generous tolerance of muc