33. Eratosthenes, however, measures the length of the habitable earth by a line which he considers straight, drawn from the Pillars of Hercules, in the direction of the Caspian Gates and the Caucasus. The length of the third section, by a line drawn from the Caspian Gates to Thapsacus, and of the fourth, by one running from Thapsacus through Heroopolis to the country surrounded by the Nile: this must necessarily be deflected to Canopus and Alexandria, for there is the last mouth of the Nile, which goes by the name of the Canopic[588] or Heracleotic mouth. Whether therefore these two lengths be considered to form one straight line, or to make an angle with Thapsacus, certain it is that neither of them is parallel to the length of the habitable earth; this is evident from what Eratosthenes has himself said concerning them. According to him the length of the habitable earth is described by a right line running through the Taurus to the Pillars of Hercules, in the direction of the Caucasus, Rhodes, and Athens. From Rhodes to Alexandria, following the meridian of the two cities, he says there cannot be much less than 4000 stadia,[589] consequently there must be the same difference between the latitudes of Rhodes and Alexandria. Now the latitude of Heroopolis is about the same as Alexandria, or rather more south. So that a line, whether straight or broken, which intersects the parallel of Heroopolis, Rhodes, or the Gates of the Caspian, cannot be parallel to either of these. These lengths therefore are not properly indicated, nor are the northern sections any better. 34. 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,[590] 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.”[591]