So far as acquaintance with the world was concerned, we have sufficient evidence 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 place to stand on and I will move the world.”  What he and others had learned concerning fluid pressure, or concerning pulleys, levers, and other mechanical devices, had not been lost by the Greeks and had been borrowed from them for full practical use by the Romans.  They knew how to lift huge weights, and how to hurl heavy missiles by the artillery previously mentioned.  Experiments had been made at Alexandria in the use of steam-power, but had led to nothing practical.