CHAP, i, 34. INTRODUCTION. 131 therefore these two lengths be considered to form one straight line, or to make an angle with Thapsacus, cer- tain 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 direc- tion 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, 1 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, 2 and perpendicular to the com- mon 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 hypo- tenuse less than one of the sides about the right angle ! Consequently Persia should be included in the second sec- tion." 3 1 It was a mistake common to Eratosthenes, Hipparchus, and Strabo, to fancy that Rhodes and Alexandria were under the same meridian. The longitude of the two cities differs by 2<> 22' 45". 2 Due east. 3 The following is a Resume 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 fron- tiers of Carmania is estimated by Eratosthenes at 9170, and that from the frontiers of Carmania to the Caspian Gates above 9000 stadia. K 2
