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Distances In the Mediterranean

For instance, Dicaearchus says that the distance from the Peloponnese to the Pillars is ten thousand stades and still further to the head of the Adriatic; and from the Peloponnesus to the Sicilian straits three thousand; and therefore the remainder, from the Straits to the Pillars, is seven thousand stades. I say nothing about the three thousand stades, whether they are right or wrong; but the seven thousand cannot be made out, whether you measure along the coast or straight across the sea. The coast route is a kind of obtuse angle, contained by two lines resting on the straits and the pillars respectively; so that we have a triangle, of which the apex is Narbo, and the base the straight line representing the course by the open sea; of the two sides of the triangle which contain the obtuse angle, that which extends from the straits to Narbo is more than eleven thousand two hundred stades, the other from Narbo to the Pillars is a little under eight thousand. The longest distance from Europe to Libya across the Tuscan sea is allowed to be not more than three thousand stades, that by the Sardinian sea is somewhat less; but let us call it three thousand stades. Now suppose a perpendicular let down through the gulf of Narbo to the base of the triangle, that is to the straight seacourse, measuring two thousand stades; it requires only a schoolboy's geometry to prove that the coasting voyage is longer than the direct sea voyage by nearly five hundred stades.1 And when the three thousand stades from the Peloponnese to the straits are added, the whole number of the stades even of the straight sea course will be more than double Dicaearchus's reckoning. And if we measure to the head of the Adriatic we must add still more by his own admission; that is to say, from the Peloponnese to Leucas is seven hundred stades, from Leucas to Corcyra seven hundred, from Corcyra to Ceraunia seven hundred, and from Ceraunia along the Illyrian coast six thousand one hundred and fifty. Strabo quotes this reckoning of the distance from the Peloponnese to the head of the Adriatic to prove that Polybius, on his own showing, is wrong in admitting that this distance (8250 stades) is greater than that from the Peloponnese to the Pillars, which Dicaearchus said was 10,000 stades, and which Polybius showed to be 18,765 stades by the shortest route.

In talking such nonsense he might well be regarded as having gone beyond even Antiphanes of Berga, and, in fact, to have left no folly for his successors to commit. . . .

1 Polybius proves his point by the demonstration of the proposition "The square of hypotenuse of a right-angled-triangle is equal to the squares of the sides containing the right angle."

By applying this principle AD = 7745.9 . . and DC = 11019.9 . . . and the whole AC = 18765.8: whereas AB + BC (i.e. the coasting voyage) = 19200 stades (a difference of 434.2 stades, not 500). Add to this the 3000 from the Peloponnese to the Straits, the total coast voyage is 22,200 stades, as against Dicaearchus's 10,000.

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