27. In the Third Section it is true he does make some mistakes, which we shall take into consideration; but they are nothing like the amount which Hipparchus attributes to him. However, we will examine his objections. [In the first place,] he would have the ancient charts left just as they are, and by no means India brought more to the south, as Eratosthenes thinks proper. Indeed, he asserts that the very arguments adduced by that writer only confirm him the more in his opinion. He says, “According to Eratosthenes, the northern side of the third section is bounded by a line of 10,000 stadia drawn from the Caspian Gates to the Euphrates, the southern side from Babylon to the confines of Carmania is a little more than 9000 stadia. On the western side, following the course of the Euphrates, from Thapsacus to Babylon there are 4800 stadia, and thence to the outlets of the river 3000 stadia more. Northward from Thapsacus [to the Gates of Armenia] is reckoned 1100 stadia; the rest has not been measured. Now since Eratosthenes says that the northern side of this Third Section is about 10,000 stadia, and that the right line parallel thereto drawn from Babylon to the eastern side is computed at just above 9000 stadia, it follows that Babylon is not much more than 1000 stadia east of the passage of [the Euphrates] near Thapsacus.”

28. We answer, that if the Caspian Gates and the boundary line of Carmania and Persia were exactly under the same meridian, and if right lines drawn in the direction of Thapsacus and Babylon would intersect such meridian at right angles, the inference would be just.[565] For then the line [from the common frontier of Carmania and Persia] to Babylon, if produced to the meridian of Thapsacus, would appear to the eye equal, or nearly equal, to that from the Caspian Gates to Thapsacus. Consequently, Babylon would only be east of Thapsacus in the same proportion as the line drawn from the Caspian Gates to Thapsacus exceeds the line drawn from the frontier of Carmania to Babylon.[566] Eratosthenes, however, does not tell us that the line which bounds the western coast of Ariana follows the direction of the meridian; nor yet that a line drawn from the Caspian Gates to Thapsacus would form right angles with the meridian of the Caspian Gates. But rather, that the line which would form right angles with the meridian, would be one which should follow the course of the Taurus, and with which the line drawn from the Caspian Gates to Thapsacus would form an acute angle. Nor, again, does he ever say that a line drawn from Carmania to Babylon would be parallel to that drawn [from the Caspian Gates] to Thapsacus; and even if it were parallel, this would prove nothing for the argument of Hipparchus, since it does not form right angles with the meridian of the Caspian Gates.

29. But taking this for granted, and proving, as he imagines, that, according to Eratosthenes, Babylon is east of Thapsacus rather more than 1000 stadia, he draws from this false hypothesis a new argument, which he uses to the following purpose; and says, If we suppose a right line drawn from Thapsacus towards the south, and another from Babylon perpendicular thereto, a right-angled triangle would be the result; whose sides should be, 1. A line drawn from Thapsacus to Babylon; 2. A perpendicular drawn from Babylon to the meridian of Thapsacus; 3. The meridian line of Thapsacus. The hypotenuse of this triangle would be a right line drawn from Thapsacus to Babylon, which he estimates at 4800 stadia. The perpendicular drawn from Babylon to the meridian of Thapsacus is scarcely more than 1000 stadia, the same amount by which the line drawn [from the Caspian Gates] to Thapsacus exceeds that [from the common frontier of Carmania and Persia] to Babylon. The two sides [of the triangle] being given, Hipparchus proceeds to find the third, which is much greater than the perpendicular[567] aforesaid. To this he adds the line drawn from Thapsacus northwards to the mountains of Armenia, one part of which, according to Eratosthenes, was measured, and found to be 1100 stadia; the other, or part unmeasured by Eratosthenes, Hipparchus estimates to be 1000 stadia at the least: so that the two together amount to 2100 stadia. Adding this to the [length of the] side upon which falls the perpendicular drawn from Babylon, Hipparchus estimated a distance of many thousand stadia from the mountains of Armenia and the parallel of Athens to this perpendicular, which falls on the parallel of Babylon.[568] From the parallel of Athens[569] to that of Babylon he shows that there cannot be a greater distance than 2400 stadia, even admitting the estimate supplied by Eratosthenes himself of the number of stadia which the entire meridian contains;[570] and that if this be so, the mountains of Armenia and the Taurus cannot be under the same parallel of latitude as Athens, (which is the opinion of Eratosthenes,) but many thousand stadia to the north, as the data supplied by that writer himself prove.

But here, for the formation of his right-angled triangle, Hipparchus not only makes use of propositions already overturned, but assumes what was never granted, namely, that the hypotenuse subtending his right angle, which is the straight line from Thapsacus to Babylon, is 4800 stadia in length. What Eratosthenes says is, that this route follows the course of the Euphrates, and adds, that Mesopotamia and Babylon are encompassed as it were by a great circle formed by the Euphrates and Tigris, but principally by the former of these rivers. So that a straight line from Thapsacus to Babylon would neither follow the course of the Euphrates, nor yet be near so many stadia in length. Thus the argument [of Hipparchus] is overturned. We have stated before, that supposing two lines drawn from the Caspian Gates, one to Thapsacus, and the other to the mountains of Armenia opposite Thapsacus, and distant therefrom, according to Hipparchus’s own estimate, 2100 stadia at the very least, neither of them would be parallel to each other, nor yet to that line which, passing through Babylon, is styled by Eratosthenes the southern side [of the third section]. As he could not inform us of the exact length of the route by the mountains, Eratosthenes tells us the distance between Thapsacus and the Caspian Gates; in fact, to speak in a general way, he puts this distance in place of the other; besides, as he merely wanted to give the length of the territory between Ariana and the Euphrates, he was not particular to have the exact measure of either route. To pretend that he considered the lines to be parallel to each other, is evidently to accuse the man of more than childish ignorance, and we dismiss the insinuation as nonsense forthwith.

30. There, however, are some instances in which one may justly accuse Eratosthenes. There is a difference in dissecting limb by limb, or merely cutting off portions [indiscriminately], (for in the former you may only separate parts having a natural outline, and distinguished by a regular form; this the poet alludes to in the expression,

“Cutting them limb from limb;”[571]

whereas in regard to the latter this is not the case,) and we may adopt with propriety either one or other of these plans according to the time and necessity. So in Geography, if you enter into every detail, you may sometimes be compelled to divide your territories into portions, so to speak, but it is a more preferable way to separate them into limbs, than into such chance pieces; for thus only you can define accurately particular points and boundaries, a thing so necessary to the geographer. When it can be done, the best way to define a country is by the rivers, mountains, or sea; also, where possible, by the nation or nations [who inhabit it], and by its size and configuration. However, in default of a geometrical definition, a simple and general description may be said always to answer the purpose. In regard to size, it is sufficient to state the greatest length and breadth; for example, that the habitable earth is 70,000 stadia long, and that its breadth is scarcely half its length.[572] And as to form, to compare a country to any geometrical or other well-known figure. For example, Sicily to a triangle, Spain to an ox-hide, or the Peloponnesus to a plane-leaf.[573] The larger the territory to be divided, the more general also ought its divisions to be.

31. [In the system of Eratosthenes], the habitable earth has been admirably divided into two parts by the Taurus and the Mediterranean Sea, which reaches to the Pillars. On the southern side, the limits of India have been described by a variety of methods; by its mountains,[574] its river,[575] its seas,[576] and its name,[577] which seems to indicate that it is inhabited only by one people.[578] It is with justice too that he attributes to it the form of a quadrilateral or rhomboid. Ariana is not so accurately described, on account of its western side being interwoven with the adjacent land. Still it is pretty well distinguished by its three other sides, which are formed by three nearly straight lines, and also by its name, which shows it to be only one nation.[579] As to the Third Section of Eratosthenes, it cannot be considered to be defined or circumscribed at all; for that side of it which is common to Ariana is but ill defined, as before remarked. The southern side, too, is most negligently taken: it is, in fact, no boundary to the section at all, for it passes right through its centre, leaving entirely outside of it many of the southern portions. Nor yet does it represent the greatest length of the section, for the northern side is the longest.[580] Nor, lastly, can the Euphrates be its western boundary, not even if it flowed in a right line, since its two extremes[581] do not lie under the same meridian. How then is it the western rather than the southern boundary? Apart from this, the distance to the Seas of Cilicia and Syria is so inconsiderable, that there can be no reason why he should not have enlarged the third section, so as to include the kingdoms of Semiramis and Ninus, who are both of them known as Syrian monarchs; the first built Babylon, which he made his royal residence; the second Ninus,[582] the capital of Syria;[583] and the same dialect still exists on both sides of the Euphrates. The idea of thus dismembering so renowned a nation, and allotting its portions to strange nations with which it had no connexion, is as peculiarly unfortunate. Eratosthenes cannot plead that he was compelled to do this on account of its size, for had it extended as far as the sea and the frontiers of Arabia Felix and Egypt, even then it would not have been as large as India, or even Ariana. It would have therefore been much better to have enlarged the third section, making it comprehend the whole space as far as the Sea of Syria; but if this were done, the southern side would not be as he represents it, nor yet in a straight line, but starting from Carmania would follow the right side of the sea-shore from the Persian Gulf to the mouth of the Euphrates; it would then approach the limits of Mesene[584] and Babylon, where the Isthmus commences which separates Arabia Felix from the rest of the continent. Traversing the Isthmus, it would continue its course to the recess of the Arabian Gulf and Pelusium,[585] thence to the mouth of the Nile at Canopus.[586] Such would be the southern side. The west would be traced by the sea-shore from the [river’s] mouth at Canopus to Cilicia.[587]

32. The fourth section would consist of Arabia Felix, the Arabian Gulf, and the whole of Egypt and Ethiopia. Its length bounded by two meridians, one drawn through its most western point, the other through its most eastern; and its breadth by two parallels through its most northern and southern points. For this is the best way to describe the extent of irregular figures, whose length and breadth cannot be determined by their sides.

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.