HKB
the eastern side is computed at just above 9000 stadia, it follows that Babylon is not much more than 1000 stadia east of the passage of [the Euphrates] near Thapsacus.”
We answer, that if the Caspian Gates and the boundary line of Carmania and Persia were exactly under the same meridian, and if right lines drawn in the direction of Thapsacus and Babylon would intersect such meridian at right angles, the inference would be just.[565] For then the line [from the common frontier of Carmania and Persia] to Babylon, if produced to the meridian of Thapsacus, would appear to the eye equal, or nearly equal, to that from the Caspian Gates to Thapsacus. Consequently, Babylon would only be east of Thapsacus in the same proportion as the line drawn from the Caspian Gates to Thapsacus exceeds the line drawn from the frontier of Carmania to Babylon.[566] Eratosthenes, however, does not tell us that the line which bounds the western coast of Ariana follows the direction of the meridian; nor yet that a line drawn from the Caspian Gates to Thapsacus would form right angles with the meridian of the Caspian Gates. But rather, that the line which would form right angles with the meridian, would be one which should follow the course of the Taurus, and with which the line drawn from the Caspian Gates to Thapsacus would form an acute angle. Nor, again, does he ever say that a line drawn from Carmania to Babylon would be parallel to that drawn [from the Caspian Gates] to Thapsacus; and even if it were parallel, this would prove nothing for the argument of Hipparchus, since it does not form right angles with the meridian of the Caspian Gates.
But taking this for granted, and proving, as he imagines, that, according to Eratosthenes, Babylon is east of Thapsacus rather more than 1000 stadia, he draws from this false hypothesis a new argument, which he uses to the following purpose; and says, If we suppose a right line drawn from Thapsacus towards the south, and another from Babylon perpendicular thereto, a right-angled triangle would be the result; whose sides should be, 1. A line drawn from Thapsacus to Babylon; 2. A perpendicular drawn from Babylon to the meridian of Thapsacus; 3. The meridian line of Thapsacus. The hypotenuse of this triangle would be a right line drawn from Thapsacus to Babylon, which he estimates at 4800 stadia. The perpendicular drawn from Babylon to the meridian of Thapsacus is scarcely more than 1000 stadia, the same amount by which the line drawn [from the Caspian Gates] to Thapsacus exceeds that [from the common frontier of Carmania and Persia] to Babylon. The two sides [of the triangle] being given, Hipparchus proceeds to find the third, which is much greater than the perpendicular[567] aforesaid. To this he adds the line drawn from Thapsacus northwards to the mountains of Armenia, one part of which, according to Eratosthenes, was measured, and found to be 1100 stadia; the other, or part unmeasured by Eratosthenes, Hipparchus estimates to be 1000 stadia at the least: so that the two together amount to 2100 stadia. Adding this to the [length of the] side upon which falls the perpendicular drawn from Babylon, Hipparchus estimated a distance of many thousand stadia from the mountains of Armenia and the parallel of Athens to this perpendicular, which falls on the parallel of Babylon.[568] From the parallel of Athens[569] to that of Babylon he shows that there cannot be a greater distance than 2400 stadia, even admitting the estimate supplied by Eratosthenes himself of the number of stadia which the entire meridian contains;[570] and that if this be so, the mountains of Armenia and the Taurus cannot be under the same parallel of latitude as Athens, (which is the opinion of Eratosthenes,) but many thousand stadia to the north, as the data supplied by that writer himself prove.