e that the trader knew his way very well down the
African coast as far as Zanzibar, and along the southern shores of
Asia as far as Cape Comorin. With Ceylon his acquaintance was vague,
and only by tradition did he know of Further India by way of the sea
and of China by way of the land. In the interior of Africa the
caravans reached the Oases, and by way of Nile or caravan there was
trade with the Soudan. Outside the Straits of Gibraltar, the Canary
Islands and Madeira--known indiscriminately as the "Fortunate Isles,"
or "Isles of the Blest"--were in touch with the port of Cadiz. The
shape of Great Britain beyond England was indefinite, although it was
known to be an island, with the Shetlands lying beyond. Ireland was
also recognised as an island and its relative size was not greatly
misconceived. The chief misconception in this corner of Europe was
that of orientation, Britain being placed either far too near or far
too parallel to Spain (through a large error as to the shape of the
Bay of Biscay). Meanwhile the coast of the Netherlands and Germany was
made to run in a line much too closely parallel to the eastern shores
of Britain. Scandinavia was known from navigating explorers and from
the amber trade, but was commonly regarded as a large island.
Knowledge of the Baltic did not extend beyond about the modern Riga,
and of the whole region thence to the Caspian only the dimmest notions
were entertained.

From what has been said concerning the calculation of the earth's
diameter and of the distances of the sun and moon, it may be readily
understood that the ancient mathematician had arrived at great
proficiency in the geometrical branch of mathematics. This should
cause no surprise when we remember what is meant by "Euclid." That
eminent genius had lived at Alexandria three centuries and a half
before the age of Nero, and he by no means represents all that was
known of such mathematics at the latter date. The ancients were quite
sufficiently versed in the solution of triangles to have made the
necessary calculations in geography and astronomy, if they had but
possessed the right instruments. Perhaps only an expert should
deal--even in the few sentences required for our purpose--with such
matters as the calculation of the capacity and proportional relations
of cylinders, or with the mechanics and hydrostatics of Archimedes.
That philosopher so far understood the laws of applied force that he
had boasted: "Give me a pl