In general it is to be observed, that length and breadth are to be understood in different ways, according as you speak of the whole or a part. Of a whole, the greater distance is called its length, and the lesser its breadth; of a part, that is to be considered the length which is parallel to the length of the whole, without any regard whether it, or that which is left for the breadth, be the greater distance. The length of the whole habitable earth is measured from east to west by a line drawn parallel to the equator, and its breadth from north to south in the direction of the meridian; consequently, the length of any of the parts ought to be portions of a line drawn parallel to the length of the whole, and their breadth to the breadth of the whole. For, in the first place, by this means the size of the whole habitable earth will be best described; and secondly, the disposition and configuration of its parts, and the manner in which one may be said to be greater or less than another, will be made manifest by thus comparing them.
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 Canopic588 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 stadia596 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