Greek Texts & Translations

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 ^note 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. ^note From the parallel of Athens ^note 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; ^note 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.

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