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]
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,[592] [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,[593]] “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,[594] which lies more to the south than any other part of the coast, the side next the Indus must be the same.”
35. These arguments may be very geometrical, but they are not convincing. After having himself invented these various difficulties, he dismisses them, saying, “Had [Eratosthenes] been chargeable for small distances only, he might have been excused; but since his mistakes involve thousands of stadia, we cannot pardon him, more especially since he has laid it down that at a mere distance of 400 stadia,[595] such as that between the parallels of Athens and Rhodes, there is a sensible variation [of latitude].” But these sensible variations are not all of the same kind, the distance [involved therein] being in some instances greater, in others less; greater, when for our estimate of the climata we trust merely to the eye, or are guided by the vegetable productions and the temperature of the air; less, when we employ gnomons and dioptric instruments. Nothing is more likely than that if you measure the parallel of Athens, or that of Rhodes and Caria, by means of a gnomon, the difference resulting from so many stadia[596] will be sensible. But when a geographer, in order to trace a line from west to east, 3000 stadia broad, makes use of a chain of mountains 40,000 stadia long, and also of a sea which extends still farther 30,000 stadia, and farther wishing to point out the situation of the different parts of the habitable earth relative to this line, calls some southern, others northern, and finally lays out what he calls the sections, each section consisting of divers countries, then we ought carefully to examine in what acceptation he uses his terms; in what sense he says that such a side [of any section] is the north side, and what other is the south, or east, or west side. If he does not take pains to avoid great errors, he deserves to be blamed, but should he be guilty merely of trifling inaccuracies, he should be forgiven. But here nothing shows thoroughly that Eratosthenes has committed either serious or slight errors, for on one hand what he may have said concerning such great distances, can never be verified by a geometrical test, and on the other, his accuser, while endeavouring to reason like a geometrician, does not found his arguments on any real data, but on gratuitous suppositions.
36. The fourth section Hipparchus certainly manages better, though he still maintains the same censorious tone, and obstinacy in sticking to his first hypotheses, or others similar. He properly objects to Eratosthenes giving as the length of this section a line drawn from Thapsacus to Egypt, as being similar to the case of a man who should tell us that the diagonal of a parallelogram was its length. For Thapsacus and the coasts of Egypt are by no means under the same parallel of latitude, but under parallels considerably distant from each other,[597] and a line drawn from Thapsacus to Egypt would lie in a kind of diagonal or oblique direction between them. But he is wrong when he expresses his surprise that Eratosthenes should dare to state the distance between Pelusium and Thapsacus at 6000 stadia, when he says there are above 8000. In proof of this he advances that the parallel of Pelusium is south of that of Babylon by more than 2500 stadia, and that according to Eratosthenes (as he supposes) the latitude of Thapsacus is above 4800 stadia north of that of Babylon; from which Hipparchus tells us it results that [between Thapsacus and Pelusium] there are more than 8000 stadia. But I would inquire how he can prove that Eratosthenes supposed so great a distance between the parallels of Babylon and Thapsacus? He says, indeed, that such is the distance from Thapsacus to Babylon, but not that there is this distance between their parallels, nor yet that Thapsacus and Babylon are under the same meridian. So much the contrary, that Hipparchus has himself pointed out, that, according to Eratosthenes, Babylon ought to be east of Thapsacus more than 2000 stadia. We have before cited the statement of Eratosthenes, that Mesopotamia and Babylon are encircled by the Tigris and Euphrates, and that the greater portion of the Circle is formed by this latter river, which flowing north and south takes a turn to the east, and then, returning to a southerly direction, discharges itself [into the sea]. So long as it flows from north to south, it may be said to follow a southerly direction; but the turning towards the east and Babylon is a decided deviation from the southerly direction, and it never recovers a straight course, but forms the circuit we have mentioned above. When he tells us that the journey from Babylon to Thapsacus is 4800 stadia, he adds, following the course of the Euphrates, as if on purpose lest any one should understand such to be the distance in a direct line, or between the two parallels. If this be not granted, it is altogether a vain attempt to show that if a right-angled triangle were constructed by lines drawn from Pelusium and Thapsacus to the point where the parallel of Thapsacus intercepts the meridian of Pelusium, that one of the lines which form the right angle, and is in the direction of the meridian, would be longer than that forming the hypotenuse drawn from Thapsacus to Pelusium.[598] Worthless, too, is the argument in connexion with this, being the inference from a proposition not admitted; for Eratosthenes never asserts that from Babylon to the meridian of the Caspian Gates is a distance of 4800 stadia. We have shown that Hipparchus deduces this from data not admitted by Eratosthenes; but desirous to controvert every thing advanced by that writer, he assumes that from Babylon to the line drawn from the Caspian Gates to the mountains of Carmania, according to Eratosthenes’ description, there are above 9000 stadia, and from thence draws his conclusions.
37. Eratosthenes[599] cannot, therefore, be found fault with on these grounds; what may be objected against him is as follows. When you wish to give a general outline of size and configuration, you should devise for yourself some rule which may be adhered to more or less. After having laid down that the breadth of the space occupied by the mountains which run in a direction due east, as well as by the sea which reaches to the Pillars of Hercules, is 3000 stadia, would you pretend to estimate different lines, which you may draw within the breadth of that space, as one and the same line? We should be more willing to grant you the power of doing so with respect to the lines which run parallel to that space than with those which fall upon it; and among these latter, rather with respect to those which fall within it than to those which extend without it; and also rather for those which, in regard to the shortness of their extent, would not pass out of the said space than for those which would. And again, rather for lines of some considerable length than for any thing very short, for the inequality of lengths is less perceptible in great extents than the difference of configuration. For example, if you give 3000 stadia for the breadth at the Taurus, as well as for the sea which extends to the Pillars of Hercules, you will form a parallelogram entirely enclosing both the mountains of the Taurus and the sea; if you divide it in its length into several other parallelograms, and draw first the diagonal of the great parallelogram, and next that of each smaller parallelogram, surely the diagonal of the great parallelogram will be regarded as a line more nearly parallel and equal to the side forming the length of that figure than the diagonal of any of the smaller parallelograms: and the more your lesser parallelograms should be multiplied, the more will this become evident. Certainly, it is in great figures that the obliquity of the diagonal and its difference from the side forming the length are the less perceptible, so that you would have but little scruple in taking the diagonal as the length of the figure. But if you draw the diagonal more inclined, so that it falls beyond both sides, or at least beyond one of the sides, then will this no longer be the case; and this is the sense in which we have observed, that when you attempted to draw even in a very general way the extents of the figures, you ought to adopt some rule. But Eratosthenes takes a line from the Caspian Gates along the mountains, running as it were in the same parallel as far as the Pillars, and then a second line, starting directly from the mountains to touch Thapsacus; and again a third line from Thapsacus to the frontiers of Egypt, occupying so great a breadth. If then in proceeding you give the length of the two last lines [taken together] as the measure of the length of the district, you will appear to measure the length of one of your parallelograms by its diagonal. And if, farther, this diagonal should consist of a broken line, as that would be which stretches from the Caspian Gates to the embouchure of the Nile, passing by Thapsacus, your error will appear much greater. This is the sum of what may be alleged against Eratosthenes.
38. In another respect also we have to complain of Hipparchus, because, as he had given a category of the statements of Eratosthenes, he ought to have corrected his mistakes, in the same way that we have done; but whenever he has any thing particular to remark, he tells us to follow the ancient charts, which, to say the least, need correction infinitely more than the map of Eratosthenes.
The argument which follows is equally objectionable, being founded on the consequences of a proposition which, as we have shown, is inadmissible, namely, that Babylon was not more than 1000 stadia east of Thapsacus; when it was quite clear, from Eratosthenes’ own words, that Babylon was above 2400 stadia east of that place; since from Thapsacus to the passage of the Euphrates where it was crossed by Alexander, the shortest route is 2400 stadia, and the Tigris and Euphrates, having encompassed Mesopotamia, flow towards the east, and afterwards take a southerly direction and approach nearer to each other and to Babylon at the same time: nothing appears absurd in this statement of Eratosthenes.
39. The next objection of Hipparchus is likewise false. He attempts to prove that Eratosthenes, in his statement that the route from Thapsacus to the Caspian Gates is 10,000 stadia, gives this as the distance taken in a straight line; such not being the case, as in that instance the distance would be much shorter. His mode of reasoning is after this fashion. He says, “According to Eratosthenes, the mouth of the Nile at Canopus,[600] and the Cyaneæ,[601] are under the same meridian, which is distant from that of Thapsacus 6300 stadia. Now from the Cyaneæ to Mount Caspius, which is situated close to the defile[602] leading from Colchis to the Caspian Sea, there are 6600 stadia,[603] so that, with the exception of about 300 stadia, the distance from the meridian of the Cyaneæ to that of Thapsacus, or to that of Mount Caspius, is the same: and both Thapsacus and Mount Caspius are, so to speak, under the same meridian.[604] It follows from this that the Caspian Gates are about equi-distant between Thapsacus and Mount Caspius, but that the distance between them and Thapsacus is much less than the 10,000 stadia mentioned by Eratosthenes. Consequently, as the distance in a right line is much less than 10,000 stadia, this route, which he considered to be in a straight course from the Caspian Gates to Thapsacus, must have been a circumbendibus.”