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 We will now return at once to Hipparchus, and see what comes next. Continuing to palm assumptions of his own [upon Eratosthenes], he goes on to refute, with geometrical accuracy, statements which that author had made in a mere general way. ‘Eratosthenes,’ he says, ‘estimates that there are 6700 stadia between Babylon and the Caspian Gates, and from Babylon to the frontiers of Carmania and Persia above 9000 stadia; this he supposes to lie in a direct line towards the equinoctial rising,1 and perpendicular to the common side of his second and third sections. Thus, according to his plan, we should have a right-angled triangle, with the right angle next to the frontiers of Carmania, and its hypotenuse less than one of the sides about the right angle! Consequently Persia should be included in the second section.’2 To this we reply, that the line drawn from Babylon to Carmania was never intended as a parallel, nor yet that which divides the two sections as a meridian, and that therefore nothing has been laid to his charge, at all events with any just foundation. In fact, Eratosthenes having stated the number of stadia from the Caspian Gates to Babylon as above given,3 [from the Caspian Gates] to Susa 4900 stadia, and from Babylon [to Susa] 3400 stadia, Hipparchus runs away from his former hypothesis, and says that [by drawing lines from] the Caspian Gates, Susa, and Babylon, an obtuse-angled triangle would be the result, whose sides should be of the length laid down, and of which Susa would form the obtuse angle. He then argues, that ‘according to these premises, the meridian drawn from the Gates of the Caspian will intersect the parallel of Babylon and Susa 4400 stadia more to the west, than would a straight line drawn from the Caspian to the confines of Carmania and Persia; and that this last line, forming with the meridian of the Caspian Gates half a right angle, would lie exactly in a direction midway between the south and the equinoctial rising. Now as the course of the Indus is parallel to this line, it cannot flow south on its descent from the mountains, as Eratosthenes asserts, but in a direction lying between the south and the equinoctial rising, as laid down in the ancient charts.’ But who is there who will admit this to be an obtuse-angled triangle, without also admitting that it contains a right angle? Who will agree that the line from Babylon to Susa, which forms one side of this obtuse-angled triangle, lies parallel, without admitting the same of the whole line as far as Carmania? or that the line drawn from the Caspian Gates to the frontiers of Carmania is parallel to the Indus? Nevertheless, without this the reasoning [of Hipparchus] is worth nothing ‘Eratosthenes himself also states,’ [continues Hipparchus,4] ‘that the form of India is rhomboidal; and since the whole eastern border of that country has a decided tendency towards the east, but more particularly the extremest cape,5 which lies more to the south than any other part of the coast, the side next the Indus must be the same.’
1 Due east.
2 The following is a Resumé of the argument of Hipparchus, ‘The hypotenuse of the supposed triangle, or the line drawn from Babylon to the Caspian Gates being only 6700 stadia, would be necessarily shorter than either of the other sides, since the line from Babylon to the frontiers of Carmania is estimated by Eratosthenes at 9170, and that from the frontiers of Carmania to the Caspian Gates above 9000 stadia. The frontiers of Carmania would thus be east of the Caspian Gates, and Persia would consequently be comprised, not in the third, but in the second section of Eratosthenes, being east of the meridian of the Caspian Gates, which was the boundary of the two sections.’ Strabo, in the text, points out the falsity of this argument.
3 Viz. 6700 stadia.
4 These two words, continues Hipparchus, are not in the text, but the argument is undoubtedly his.
5 Cape Comorin.
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