Geography

​Therefore, one should not say this to Eratosthenes, but rather that there must be some limit for sizes and shapes that are spoken of in terms of width, and that we must allow more in one place and less in another. For if the width of the mountains extending towards the equinoctial sunrise is assumed to be three thousand stadia, and likewise that of the sea as far as the Pillars, one would more readily allow the parallels drawn within that same width to be examined as if on a single line, rather than those that intersect; and of the intersecting ones, those having their intersection within that very width rather than those outside; likewise, those diverging up to the point of not exceeding the width rather than those exceeding it, and those over a greater length rather than those over a smaller. For the inequality of the lengths and the dissimilarity of the shapes would be more concealed; as, for example, within the width of the entire Taurus and the sea as far as the Pillars, with three thousand stadia being assumed, a single parallelogrammic region is conceived, which circumscribes both the entire mountain and the aforementioned sea. If, then, you divide the length into several parallelograms, and take the diagonal of both this whole and the parts, the diagonal of the whole would more easily be calculated as the same as the side along the length than the diagonal in the parts; and indeed, the smaller the parallelogram taken as a part, the more this would happen. For the obliquity of the diagonal and the inequality of the length are less exposed in large dimensions, so that one would not hesitate to call the diagonal the length of the shape in their case. If, then, you make the diagonal more oblique, so that it falls outside either of the sides, or at least one of them, these things would no longer happen in the same way; this is the kind of limit I mean for things spoken of in terms of width. But Eratosthenes, while taking the line from the Caspian Gates through the mountains themselves as if drawn on the same parallel as far as the Pillars, and the one inclining towards Thapsacus as immediately far outside the mountains, and again extending another line from Thapsacus to Egypt, which occupies so much width, then measures the length of the region by the length of this latter line, and thus would seem to measure the length of a square by the diagonal of the square. And when the line is not even a diagonal but a broken line, he would seem to err much more; for the line drawn from the Caspian Gates through Thapsacus to the Nile is indeed a broken line. So much for Eratosthenes.

​On the other hand, against Hipparchus we must also say this, that just as he has made an accusation against what was said by Eratosthenes, so he ought also to have made some correction of the errors—which is what we are doing. But he, even if he has thought of this somewhere, bids us attend to the ancient maps, which stand in need of a vastly greater correction than Eratosthenes’ map requires. And the argument that is brought forward next also suffers from the same defect. For he takes as an assumption what was constructed from ungranted premises, as we have proved, namely, that Babylon is not more than a thousand stadia further east than Thapsacus; so that even if it is fully concluded from Eratosthenes’ statements that Babylon is more than two thousand four hundred stadia further east—since he says that from Thapsacus to the crossing of the Tigris, where Alexander crossed, is a short cut of two thousand four hundred stadia, and that the Tigris and the Euphrates, having encircled Mesopotamia, flow for a while towards the east, and then turn towards the south and then approach both each other and Babylon at the same time—no absurdity results for his argument.