[29]

But here, for the formation of his right-angled triangle, Hipparchus not only makes use of propositions already overturned, but assumes what was never granted, namely, that the hypotenuse subtending his right angle, which is the straight line from Thapsacus to Babylon, is 4800 stadia in length. What Eratosthenes says is, that this route follows the course of the Euphrates, and adds, that Mesopotamia and Babylon are encompassed as it were by a great circle formed by the Euphrates and Tigris, but principally by the former of these rivers. So that a straight line from Thapsacus to Babylon would neither follow the course of the Euphrates, nor yet be near so many stadia in length. Thus the argument [of Hipparchus] is overturned. We have stated before, that supposing two lines drawn from the Caspian Gates, one to Thapsacus, and the other to the mountains of Armenia opposite Thapsacus, and distant therefrom, according to Hipparchus's own estimate, 2100 stadia at the very least, neither of them would be parallel to each other, nor yet to that line which, passing through Babylon, is styled by Eratosthenes the southern side [of the third section]. As he could not inform us of the exact length of the route by the mountains, Eratosthenes tells us the distance between Thapsacus and the Caspian Gates; in fact, to speak in a general way, he puts this distance in place of the other; besides, as he merely wanted to give the length of the territory between Ariana and the Euphrates, he was not particular to have the exact measure of either route. To pretend that he considered the lines to be parallel to each other, is evidently to accuse the man of more than childish ignorance, and we dismiss the insinuation as nonsense forthwith.

1 Or second side.

2 Hipparchus found by this operation that the distance from the parallel of Babylon to that of the mountains of Armenia was 6795 stadia.

3 See Humboldt, Cosmos ii. p. 556, note, Bohn's edition.

4 Eratosthenes estimated 252,000 stadia for the circumference of the earth.