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20 (76) Up to this point, then, having taken as hypothesis that the most southerly regions of India rise opposite the regions about Meroë — which many have stated and believed — I have pointed out the absurdities that result from this hypothesis. 77But since Hipparchus up to this point offers no objection to this hypothesis, and yet later on, in his Second Book, will not concede it, I must consider his argument on this matter, too. Well, then, he says: If only the regions that lie on the same parallel rise opposite each other, then, whenever the intervening distance is great, we cannot know this very thing, namely, that the regions in question are on the same parallel, without the comparison of the "climata"48 as observed at the other of the two places; now as for the "clima" at Meroë Philo, who wrote an account of his voyage to Ethiopia, reports that the sun is in the zenith fortyfive days before the summer solstice and tells also the relations of the gnomon to the shadows p291both in the solstices and the equinoxes, and Eratosthenes agrees very closely with Philo; whereas nobody reports the "clima" in India, not even Eratosthenes himself; however, if it is really true that in India the Bears set (both of them, as they think, relying on Nearchus and his followers), then it is impossible that Meroë and the capes of India lie on the same parallel. Now if Eratosthenes joins those who have already so stated in reporting that both Bears do set, how can it be that nobody reports about the "clima" in India, not even Eratosthenes himself? For this statement concerns the "clima." But if Eratosthenes does not join them in the report, let him be free from the accusation. No, he does not join them in the report; nay, because Deïmachus said that the Bears do not set and the shadows do not fall in the opposite direction anywhere in India (as Megasthenes assumed), Eratosthenes convicts him of inexperience, regarding as falsehood the combined statement, wherein by the acknowledgement of Hipparchus himself the false statement that the shadows do not fall in the opposite direction is combined with that about the Bears. For even if the southern capes of India do not rise opposite to Meroë, Hipparchus clearly concedes that they are at least farther south than Syene.49
21 In what follows, also, Hipparchus, in attempting proofs on the same questions, either states again the same things that I have already disproved, or employs additional false assumptions, or appends conclusions that do not follow. In the first place, take the statement p293of Eratosthenes that the distance from Babylon to Thapsacus is four thousand eight hundred stadia, and thence northwards to the Armenian Mountains two thousand one hundred: it does not follow from this that the distance from Babylon measured on the meridian through it to the northern mountains is more than six thousand stadia. Secondly, Eratosthenes does not say that the distance from Thapsacus to the mountains is two thousand one hundred stadia, 78but that there is a remainder of that distance which has not been measured; and hence the ensuing attack, made from an assumption not granted, could not result in a valid conclusion. And, thirdly, Eratosthenes has nowhere declared that Thapsacus lies north of Babylon more than four thousand five hundred stadia.
22 Next, still pleading for the early maps, Hipparchus does not produce the words of Eratosthenes in regard to the Third Section,50 but for his own gratification invented his statement,51 making it easy to overthrow. For Eratosthenes, pursuing his aforementioned thesis about the Taurus and the Mediterranean Sea, beginning at the Pillars,52 divides the inhabited world by means of this line into two divisions, and calls them respectively the Northern Division and the Southern Division, and then attempts to cut each of these divisions again into such sections as are possible; and he calls these sections "Sphragides."53 And so, after calling India Section First of the Southern Division, and Ariana Section Second, since they had contours easy to sketch, he was able to represent not only length and breadth of p297both sections, but, after a fashion, shape also, as would a geometrician. In the first place, India, he says, is rhomboidal,54 because, of its four sides, two are washed by seas (the southern and the eastern seas) which form shores without very deep gulfs; and because the remaining sides [are marked], one by the mountain55 and the other by the river,56 and because on these two sides, also, the rectilinear figure is fairly well preserved. Secondly, Ariana. Although he sees that it has at least three sides wellsuited to the formation of the figure of a parallelogram, and although he cannot mark off the western side by mathematical points, on account of the fact that the tribes there alternate with one another,57 yet he represents that side by a sort of line58 that begins at the Caspian Gates and ends at the capes of Carmania that are next to the Persian Gulf. Accordingly, he calls this side "western" and the side along the Indus "eastern," but he does not call them parallel; neither does he call the other two sides parallel, namely, the one marked by the mountain, and the one marked by the sea, but he merely calls them "the northern" and "the southern" sides.
2359 And so, though he represents the Second Section merely by a rough outline, he represents the Third Section much more roughly than the Second — and for several reasons. First is the reason already mentioned, namely, because the side beginning at the Caspian Gates and running to Carmania (the side common to the Second and Third Sections) has not been determined distinctly; p299secondly, because the Persian Gulf breaks into the southern side, as Eratosthenes himself says, and therefore he has been forced to take the line beginning at Babylon as though it were a straight line running through Susa and Persepolis to the frontiers of Carmania and Persis, 79on which he was able to find a measured highway, which was slightly more than nine thousand stadia, all told. This side Eratosthenes calls "southern," but he does not call it parallel to the northern side. Again, it is clear that the Euphrates, by which he marks off the western side, is nowhere near a straight line; but after flowing from the mountains towards the south, it then turns eastward, and then southward again to the point where it empties into the sea. And Eratosthenes makes clear the river's lack of straightness when he indicates the shape of Mesopotamia, which results from the confluence of the Tigris and the Euphrates — "like a galley" as he says. And besides, as regards the stretch from Thapsacus to Armenia — Eratosthenes does not even know, as a distance that has been wholly measured, the western side that is marked off by the Euphrates; nay, he says he does not know how great is the stretch next to Armenia and the northern mountains, from the fact that it is unmeasured. For all these reasons, therefore, he says he represents the Third Section only in rough outline; indeed, he says that he collected even the distances from many writers who had worked out the itineraries — some of which he speaks of as actually p301without titles. So, then, Hipparchus would seem to be acting unfairly when he contradicts with geometrical accuracy a mere rough outline of this nature, instead of being grateful, as we should be, to all those who have reported to us in any way at all the physiography of the regions. But when Hipparchus does not even take his geometrical hypotheses from what Eratosthenes says, but fabricates on his own account, he betrays his spirit of jealousy still more obviously.
24 Now Eratosthenes says that it is only thus, "in a roughoutline way," that he has represented the Third Section, with its length of ten thousand stadia from the Caspian Gates to the Euphrates. And then, in making subdivisions of this length, he sets down the measurements just as he found them already assigned by others, after beginning in the inverse order at the Euphrates and its passage at Thapsacus. Accordingly, for the distance from the Euphrates to the Tigris, at the point where Alexander crossed it, he lays off two thousand four hundred stadia; thence to the several places in succession, through Gaugamela, the Lycus, Arbela, and Ecbatana (the route by which Darius fled from Gaugamela to the Caspian Gates) he fills out the ten thousand stadia, and has a surplus of only three hundred stadia. This, then, is the way he measures the northern side, not having first put it parallel with the mountains, or with the line that runs through the Pillars, Athens, and Rhodes. For Thapsacus lies at a considerable distance from the mountains, and the mountainrange and the highway from Thapsacus meet at the Caspian Gates. — And these are the northern portions of the boundary of the Third Section.
p303 25 80After having thus represented the northern side, Eratosthenes says it is not possible to take the southern side as along the sea, because the Persian Gulf breaks into it; but, says he, from Babylon to Susa and Persepolis to the frontiers of Persis and Carmania, it is nine thousand two hundred stadia — and this he calls "southern side," but he does not call the southern side parallel to the northern. As to the difference in the lengths of the estimated northern and southern sides, he says it results from the fact that the Euphrates, after having flowed southwards to a certain point, makes a considerable bend towards the east.
26 Of the two transverse sides Eratosthenes speaks of the western first; and what the nature of this side is, whether it is one line or two, is a matter open to consideration. For from the passage at Thapsacus, he says, along the Euphrates to Babylon, it is four thousand eight hundred stadia, and thence to the outlet of the Euphrates and the city of Teredon, three thousand; but as regards the distances from Thapsacus northward, the stadia have been measured up to the Armenian Gates and amount to about one thousand one hundred; whereas the stadia through Gordyene and Armenia are still unmeasured, and so for this reason he leaves them out of consideration. But of the side on the east, that part which runs through Persis lengthwise from the Red Sea, approximately toward Media and the north, is, he thinks, no less than eight thousand stadia (though, if reckoned from certain promontories, even above nine thousand stadia); and the remaining part, through Paraetacene60 and Media to the Caspian p305Gates, about three thousand stadia. The Tigris and the Euphrates, he says, flow from Armenia southwards; and then, as soon as they pass the mountains of Gordyene, they describe a great circle and enclose a considerable territory, Mesopotamia; and then they turn toward the winter rising of the sun61 and the south, but more so the Euphrates; and the Euphrates, after becoming ever nearer to the Tigris in the neighbourhood of the Wall of Semiramis and a village called Opis (from which village the Euphrates was distant only about two hundred stadia), and, after flowing through Babylon, empties into the Persian Gulf. "So it comes to pass," he says, "that the shape of Mesopotamia and Babylonia is like that of a galley." Such, then, are the statements which Eratosthenes has made.
27 Now, as regards the Third Section, although there are certain other errors which Eratosthenes makes — and I shall discuss these — still he does not err at all in the matters for which Hipparchus reproaches him. Let us see what Hipparchus says. In his desire to establish his initial statement, namely, that we must not shift India farther to the south, as Eratosthenes requires, he says it will be particularly obvious from Eratosthenes' own utterances 81that we must not do so; for after first saying that the Third Section is marked off on its northern side by the line drawn from the Caspian Gates to the Euphrates, a distance of ten thousand stadia, Eratosthenes adds, later on, that the southern side, which runs from Babylon to the frontiers of Carmania, is slightly more than nine thousand stadia in length, and the side on the west from Thapsacus along the p307Euphrates to Babylon is four thousand eight hundred stadia, and, next, from Babylon to the outlet of the Euphrates is three thousand stadia, and as for the distances north of Thapsacus, one of them has been measured off as far as one thousand one hundred stadia, while the remainder is still unmeasured. Then, says Hipparchus, since the northern side of the Third Section is about ten thousand stadia, and since the line parallel thereto, straight from Babylon to the eastern side, was reckoned by Eratosthenes at slightly more than nine thousand stadia, it is clear that Babylon is not much more than a thousand stadia farther east than the passage at Thapsacus.62
28 My reply will be: If, with geometrical precision, we took the Caspian Gates and the frontiers of Carmania and Persis as upon the same straight meridian, and if we drew the line to Thapsacus and the line to Babylon at right angles with the said straight meridian, then that conclusion of Hipparchus would be valid. Indeed, the line through Babylon,63 if further produced as far as the straight meridian through Thapsacus, would, to the eye, be equal — or at all events approximately equal — to the line from the Caspian Gates to Thapsacus; and hence Babylon would come to be farther east than Thapsacus by as much as the line from the Caspian Gates to Thapsacus exceeds the line from the Carmanian frontiers to Babylon! But, in the first p309place, Eratosthenes has not spoken of the line that bounds a western side of Ariana as lying on a meridian; nor yet of the line from the Caspian Gates to Thapsacus as at right angles with the meridian line through the Caspian Gates, but rather of the line marked by the mountainrange, with which line the line to Thapsacus forms an acute angle, since the latter has been drawn down64 from the same point as that from which the mountainline has been drawn. In the second place, Eratosthenes has not called the line drawn to Babylon from Carmania parallel to the line drawn to Thapsacus; and even if it were parallel, but not at right angles with the meridian line through the Caspian Gates, no advantage would accrue to the argument of Hipparchus.
29 But after making these assumptions offhand, and after showing, as he thinks, that Babylon, according to Eratosthenes, is farther east than Thapsacus by slightly more than a thousand stadia, 82Hipparchus again idly fabricates an assumption for use in his subsequent argument; and, he says, if we conceive a straight line drawn from Thapsacus towards the south and a line perpendicular to it from Babylon, we will have a rightangled triangle, composed of the side that extends from Thapsacus to Babylon, of the perpendicular drawn from Babylon to the meridian line through Thapsacus, and of the meridian itself through Thapsacus. Of this triangle he makes the line from Thapsacus to Babylon the hypotenuse, which he says is four thousand eight hundred stadia; and the perpendicular from Babylon to the meridian line through Thapsacus, slightly more than a thousand stadia — p311the amount by which the line to Thapsacus65 exceeded the line up to Babylon;66 and then from these sums he figures the other of the two lines which form the right angle to be many times longer than the said perpendicular. And he adds to that line the line produced northwards from Thapsacus up to the Armenian mountains, one part of which Eratosthenes said had been measured and was one thousand one hundred stadia, but the other part he leaves out of consideration as unmeasured. Hipparchus assumes for the latter part a thousand stadia at the least, so that the sum of the two parts amounts to two thousand one hundred stadia; and adding this sum to his straightline side67 of the triangle, which is drawn to meet its perpendicular from Babylon, Hipparchus computes a distance of several thousand stadia, namely, that from the Armenian Mountains, or the parallel that runs through Athens, to the perpendicular from Babylon — which perpendicular he lays on the parallel that runs through Babylon. At any rate, he points out that the distance from the parallel through Athens to that through Babylon is not more than two thousand four hundred stadia, if it be assumed that the whole meridian is the number of stadia in length that Eratosthenes says; and if this is so, then the mountains of Armenia and those of the Taurus could not lie on the parallel that runs through Athens, as Eratosthenes says they do, but many thousand stadia farther north, according to Eratosthenes' own statements. At this point, p313then, in addition to making further use of his now demolished assumptions for the construction of his rightangled triangle, he also assumes this point that is not granted, namely, that the hypotenuse — the straight line from Thapsacus to Babylon — is within four thousand eight hundred stadia. For Eratosthenes not only says that this route is along the Euphrates, but when he tells us that Mesopotamia, including Babylonia, is circumscribed by a great circle, by the Euphrates and the Tigris, he asserts that the greater part of the circumference is described by the Euphrates: consequently, the straight line from Thapsacus to Babylon 83could neither follow the course of the Euphrates, nor be, even approximately, so many stadia in length. So his argument is overthrown. And besides, I have already stated that, if we grant that two lines are drawn from the Caspian Gates, one to Thapsacus, the other to that part of the Armenian Mountains that corresponds in position to Thapsacus (which, according to Hipparchus himself, is distant from Thapsacus at the least two thousand one hundred stadia), it is impossible for both these lines to be parallel either to each other or to the line through Babylon, which Eratosthenes called "southern side." Now because Eratosthenes could not speak of the route along the mountainrange as measured, he spoke of only the route from Thapsacus to the Caspian Gates as measured, and he added the words "roughly speaking"; moreover, since he only wished to tell the length of the country between Ariana and the Euphrates, it did not make much difference whether he measured one route or the other. But Hipparchus, when he tacitly assumes p315that the lines are spoken of by Eratosthenes as parallel, would seem to charge the man with utterly childish ignorance. Therefore, I must dismiss these arguments of his as childish.
30 But the charges which one might bring against Eratosthenes are such as follow. Just as, in surgery, amputation at the joints differs from unnatural piecemeal amputation (because the former takes off only the parts that have a natural configuration, following some articulation of joints or a significant outline — the meaning in which Homer says, "and having cut him up limb by limb" — whereas the latter follows no such course), and just as it is proper for us to use each kind of operation if we have regard to the proper time and the proper use of each, just so, in the case of geography, we must indeed make sections of the parts when we go over them in detail, but we must imitate the limbby‑limb amputations rather than the haphazard amputations. For only thus it is possible to take off the member that is significant and welldefined, the only kind of member that the geographer has any use for. Now a country is welldefined when it is possible to define it by rivers or mountains or sea; and also by a tribe or tribes, by a size of such and such proportions, and by shape where this is possible. But in every case, in lieu of a geometrical definition, a simple and roughly outlined definition is sufficient. So, as regards a country's size, it is sufficient if you state its greatest length and breadth (of the inhabited world, for example, a length of perhaps seventy thousand stadia, a breadth slightly less than half the length); and as regards shape, if you liken a country to one of the geometrical figures (Sicily, for example, to a triangle), or to one of the p317other wellknown figures (for instance, Iberia to an oxhide, the Peloponnesus to a leaf of a planetree). 84And the greater the territory you cut into sections, the more rough may be the sections you make.
31 Now the inhabited world has been happily divided by Eratosthenes into two parts by means of the Taurus Range and the sea that stretched to the Pillars. And in the Southern Division: India, indeed, has been welldefined in many ways, by a mountain, a river, a sea, and by a single term, as of a single ethnical group — so that Eratosthenes rightly calls it foursided and rhomboidal. Ariana, however, has a contour that is less easy to trace because its western side is confused,68 but still it is defined by the three sides, which are approximately straight lines, and also by the term Ariana, as of a single ethnical group. But the Third Section is wholly untraceable, at all events as defined by Eratosthenes. For, in the first place, the side common to it and Ariana is confused, as I have previously stated. And the southern side has been taken very inaccurately; for neither does it trace a boundary of this section, since it runs through its very centre and leaves out many districts in the south, nor does it represent the section's greatest length (for the northern side is longer), nor does the Euphrates form its western side (it would not do so even if its course lay in a straight line), since its extremities do not lie on the same meridian. In fact, how can this side be called western rather than southern? And, quite apart from these objections, since the distance that remains between this line and the Cilician and Syrian Sea is slight, there is no convincing reason why the section should p319not be extended thereto, both because Semiramis and Ninus are called Syrians (Babylon was founded and made the royal residence by Semiramis, and Nineveh by Ninus, this showing that Nineveh was the capital of Syria) and because up to the present moment even the language of the people on both sides of the Euphrates is the same. However, to rend asunder so famous a nation by such a line of cleavage in this region, and to join the parts thus dissevered to the parts that belong to other tribes, would be wholly improper. Neither, indeed, could Eratosthenes allege that he was forced to do this by considerations of size; for the addition of the territory that extends up to the sea69 would still not make the size of the section equal to that of India, nor, for that matter, to that of Ariana, not even if it were increased by the territory that extends up to the confines of Arabia Felix and Egypt. Therefore it would have been much better to extend the Third Section to these limits, and thus, by adding so small a territory that extends to the Syrian Sea, to define the southern side of the Third Section as running, not as Eratosthenes defined it, nor yet as in a straight line, but as following the coastline that is on your right hand as you sail from Carmania into and along the Persian Gulf up to the mouth of the Euphrates, and then as following the frontiers of Mesene and Babylonia, which form the beginning of the Isthmus that separates Arabia Felix from the rest of the continent; 85then, next, as crossing this Isthmus itself, and as reaching to the recess of the Arabian Gulf and to Pelusium and even beyond to the Canobic mouth of the Nile. So much for the p321southern side; the remaining, or western, side would be the coastline from the Canobic mouth of the Nile up to Cilicia.
32 The Fourth Section would be the one composed of Arabia Felix, the Arabian Gulf, all Egypt, and Ethiopia. Of this section, the length will be the space bounded by two meridian lines, of which lines the one is drawn through the most western point on the section and the other through the most eastern point. Its breadth will be the space between two parallels of latitude, of which the one is drawn through the most northern point, and the other through the most southern point; for in the case of irregular figures whose length and breadth it is impossible to determine by sides, we must in this way determine their size. And, in general, we must assume that "length" and "breadth" are not employed in the same sense of a whole as of a part. On the contrary, in case of a whole the greater distance is called "length," and the lesser, "breadth" but, in case of a part, we call "length" any section of a part that is parallel to the length of the whole — no matter which of the two dimensions is the greater, and no matter if the distance taken in the breadth be greater than the distance taken in the length. Therefore, since the inhabited world stretches lengthwise from east to west and breadthwise from north to south, and since its length is drawn on a line parallel to the equator and its breadth on a meridian line, we must also, in case of the parts, take as "lengths" all the sections that are parallel to the length of the inhabited world, and as "breadths" all the sections that are parallel to its breadth. For by this method we can better indicate, p323firstly, the size of the inhabited world as a whole, and, secondly, the position and the shape of its parts; because, by such comparison, it will be clear in what respects the parts are deficient and in what respects they are excessive in size.
33 Now Eratosthenes takes the length of the inhabited world on the line that runs through the Pillars, the Caspian Gates, and the Caucasus, as though on a straight line; and the length of his Third Section on the line that runs through the Caspian Gates and Thapsacus; and the length of his Fourth Section on the line that runs through Thapsacus and Heroönpolis to the region between the mouths of the Nile — a line which must needs come to an end in the regions near Canobus and Alexandria; for the last mouth of the Nile, called the Canobic or Heracleotic mouth, is situated at that point. Now whether he places these two lengths on a straight line with each other, or as though they formed an angle at Thapsacus, it is at any rate clear from his own words that he does not make either line parallel to the length of the inhabited world. 86For he draws the length of the inhabited world through the Taurus Range and the Mediterranean Sea straight to the Pillars on a line that passes through the Caucasus, Rhodes, and Athens; and he says that the distance from Rhodes to Alexandria on the meridian that passes through those places is not much less than four thousand stadia; so that also the parallels of latitude of Rhodes and Alexandria would be just this distance apart. But the parallel of latitude of Heroönpolis is approximately the same as that of Alexandria, or, at any rate, more to the south than the latter; and hence the line that intersects p325both the parallel of latitude of Heroönpolis and that of Rhodes and the Caspian Gates, whether it be a straight line or a broken line, cannot be parallel to either. Accordingly, the lengths are not well taken by Eratosthenes. And, for that matter, the sections that stretch through the north are not well taken by him.70
34 But let us first return to Hipparchus and see what he says next. Again fabricating assumptions on his own account he proceeds with geometrical precision to demolish what are merely the rough estimates of Eratosthenes. He says that Eratosthenes calls the distance from Babylon to the Caspian Gates six thousand seven hundred stadia, and to the frontiers of Carmania and Persis more than nine thousand stadia on a line drawn straight to the equinoctial east, and that this line comes to be perpendicular to the side that is common to the Second and the Third Sections, and that, therefore, according to Eratosthenes, a rightangled triangle is formed whose right angle lies on the frontiers of Carmania and whose hypotenuse is shorter than one of the sides that enclose the right angle;71 accordingly, adds Hipparchus, Eratosthenes has to make Persis a part of his Second Section! Now I have already stated in reply to this that Eratosthenes neither takes the distance from Babylon to Carmania on a parallel, nor has he spoken of the straight line that separates the two sections as a meridian line; and so in this argument Hipparchus has made no point against Eratosthenes. Neither is his subsequent conclusion p329correct. For, because Eratosthenes had given the distance from the Caspian Gates to Babylon as the said six thousand nine hundred stadia, and the distance from Babylon to Susa as three thousand four hundred stadia, Hipparchus, again starting from the same hypotheses, says that an obtuseangled triangle is formed, with its vertices at the Caspian Gates, Susa and Babylon, having its obtuse angle at Susa, and having as the lengths of it sides the distances set forth by Eratosthenes. Then he draws his conclusion, namely, that it will follow according to these hypotheses that the meridian line that runs through the Caspian Gates will intersect the parallel that runs through Babylon and Susa at a point further west than the intersection of the same parallel with the straight line that runs from the Caspian Gates to the frontiers of Carmania and Persis by more than four thousand four hundred stadia; 87and so the line that runs through the Caspian Gates and will lean in a direction midway between the south and the equinoctial east; and that the Indus River will be parallel to this line, and that consequently this river, also, does not flow south from the mountains as Eratosthenes says it does, but between the south and the equinoctial east, precisely as it is laid down on the early maps. Who, pray, will concede that the triangle now formed by Hipparchus is obtuseangled without also conceding that the triangle that p331comprehends it is rightangled?72 And who will concede that one of the sides which enclose the obtuse angle (the line from Babylon to Susa) lies on a parallel of latitude, without also conceding that the whole line on to Carmania does? And who will concede that the line drawn from the Caspian Gates to the frontiers of Carmania is parallel to the Indus? Yet without these concessions the argument of Hipparchus would be void. And it is without these concessions that Eratosthenes has made his statement that the shape of India is rhomboidal; and just as its eastern side has been stretched considerably eastwards (particularly at its extreme cape, which, as compared with the rest of the seaboard, is also thrown farther southwards, so, too, the side along the Indus has been stretched considerably eastwards.
35 In all these arguments Hipparchus speaks as a geometrician, though his test of Eratosthenes is not convincing. And though he prescribed the principles of geometry for himself, he absolves himself from them by saying that if the test showed errors amounting to only small distances, he could overlook them; but since Eratosthenes' errors clearly amount to thousands of stadia, they cannot be overlooked;73 and yet, continues Hipparchus, Eratosthenes himself declares that the differences of latitude are observable even within an extent of four hundred stadia; for example, between the parallels of Athens and Rhodes. Now the practice of observing differences of latitude is not confined to a single method, but one method is used where the difference is greater, another where it is lesser; where it is greater, if we rely on the evidence of the eye itself, or of the crops, p333or of the temperature of the atmosphere, in our judgment of the "climata"; but where it is lesser, we observe the difference by the aid of sundials and dioptrical instruments. Accordingly, the taking of the parallel of Athens and that of Rhodes and Caria with the sundial showed perceptibly (as is natural when the distance is so many stadia) the difference in latitude. But when the geographer, in dealing with a breadth of three thousand stadia and with a length of forty thousand stadia of mountain plus thirty thousand stadia of sea, takes his line from west to equinoctial east, 88and names the two divisions thus made the Southern Division and the Northern Division, and calls their parts "plinthia" or "sphragides,"74 we should bear in mind what he means by these terms, and also by the terms "sides that are northern" and "that are southern," and again, "sides that are western" and "that are eastern." And if he fails to notice that which amounts to a very great error, let him be called to account therefor (for that is just); but as regards that which amounts only to a slight error, even if he has failed to notice it, he is not to be condemned. Here, however, no case is made out against Eratosthenes on either ground. For no geometrical proof would be possible where the cases involve so great a breadth of latitude; nor does p335Hipparchus, even where he attempts geometrical proof, use admitted assumptions,75 but rather fabrications which he has made for his own use.
36 Hipparchus discusses Eratosthenes' Fourth Section better; though here, too, he displays his propensity for faultfinding and his persistent adherence to the same, or nearly the same, assumptions. He is correct in censuring Eratosthenes for this, namely, for calling the line from Thapsacus to Egypt the length of this section — which is as if one should call the diagonal of a parallelogram its length. For Thapsacus and the coastline of Egypt do not lie on the same parallel of latitude, but on parallels that are far part from each other; and between these two parallels the line from Thapsacus to Egypt is drawn somewhat diagonally and obliquely. But when he expresses surprise that Eratosthenes had the boldness to estimate the distance from Pelusium to Thapsacus at six thousand stadia, whereas the distance is more than eight thousand, he is incorrect. For having taken it as demonstrated that the parallel that runs through Pelusium is more than two hundred five hundred stadia farther south than the parallel that runs through Babylon,76 and then saying — on the authority of Eratosthenes, as he thinks — that the parallel through Thapsacus is four thousand eight hundred stadia farther north than the parallel through Babylon, he says that the distance between Pelusium and Thapsacus amounts p337to more than eight thousand stadia.77 I ask, then, how is it shown on the authority of Eratosthenes that the distance of the parallel through Babylon through the parallel through Thapsacus is as great as that? Eratosthenes has stated, indeed, that the distance from Thapsacus to Babylon is four thousand eight hundred stadia; but he has not further stated that this distance is measured from the parallel through the one place to the parallel through the other; neither indeed has he stated that Thapsacus and Babylon are on the same meridian. On the contrary, Hipparchus himself pointed out that, according to Eratosthenes, Babylon is more than two thousand stadia farther east than Thapsacus.78 And I have just cited the statements of Eratosthenes wherein he says that the Tigris and the Euphrates p339encircle Mesopotamia and Babylonia, and that the Euphrates does the greater part of the encircling, in that, 89after flowing from the north towards the south, it turns towards the east, and finally empties southwards. Now its southward course from the north lies approximately on some meridian, but its bend to the east and to Babylon is not only a deviation from the meridian but it is also not on a straight line, owing to the said encircling. It is true that Eratosthenes has stated the route to Babylon from Thapsacus to be four thousand eight hundred stadia long, though he added, as on purpose, "following the course of the Euphrates," in order that no one might interpret it as a straight line or as a measure of the distance between two parallels. If this assumption of Hipparchus be not granted, futile also is his subsequent proposition which has only the appearance of being proven, namely, that if a rightangled triangle be constructed with vertices at Pelusium, Thapsacus, and the point of intersection of the parallel of Thapsacus with the meridian of Pelusium, then one of the sides of the right angle, namely, that on the meridian, is greater than the hypotenuse, that is, the line from Thapsacus to Pelusium.79 Futile also is the proposition that he links with this proposition, because it is fabricated80 from something that is not conceded. For surely Eratosthenes has not granted the assumption that the distance from Babylon to the meridian that runs through the Caspian Gates is a matter of four thousand eight hundred stadia. I p341have proved that Hipparchus has fabricated this assumption from data that are not conceded by Eratosthenes; but in order to invalidate what Eratosthenes does grant, Hipparchus took as granted that the distance from Babylon to the line drawn from the Caspian Gates to the confines of Carmania just as Eratosthenes has proposed to draw it is more than nine thousand stadia, and then proceeded to show the same thing.81
37 That, therefore, is not the criticism that should be made against Eratosthenes,82 but rather the criticism that his roughlysketched magnitudes and figures require some standard of measure, and that more concession has to be made in one case, less in another. For example, if the breadth of the mountainrange that stretches toward the equinoctial east, and likewise the breadth of the sea that stretches up to the Pillars, be taken as three thousand stadia, one would more readily agree to regard as lying on a single line83 the parallels of that line drawn within the same breadth than he would the lines that intersect therein;84 and, of the intersecting lines, those that intersect within that said breadth than those that intersect without. p343Likewise, also, one would more readily agree to regard as lying on a single line those lines that extend within the limits of said breadth and do not reach beyond than those that reach beyond; and those lines that extend within greater lengths than those in lesser. 90For in such cases the inequality of the lengths and the dissimilarity of the figures would be more likely to escape notice; for instance, in the case of the breadth of the entire Taurus Range, and of the Sea up to the Pillars, if three thousand stadia be taken as hypothesis for the breadth, we can assume one single parallelogram which traces the boundary both of the entire Range and of the said Sea. Now if you divide a parallelogram lengthwise into several small parallelograms, and take the diagonal both of this whole and of its parts, then the diagonal of the whole might more easily be counted the same as (that is, both parallel and equal to) the long side than could the diagonal of any one of the small parallelograms as compared with the corresponding long side; and the smaller the parallelogram taken as a part, the more would this be true. For both the obliquity of the diagonal and the inequality of its length as compared with the long side are less easily detected in large parallelograms; so that you might not even hesitate in their case to call the diagonal the length of the figure. If, however, you make the diagonal more oblique, so that it falls exterior to both of the sides, p345or at least to one of them, this would no longer, in like manner, be the case.85 This is substantially what I mean by a standard of measurement for roughlysketched magnitudes. But when Eratosthenes, beginning at the Caspian Gates, takes not only the line which runs through the mountains themselves, but also the line which at once diverges considerably from the mountains into Thapsacus, as though both were drawn to the Pillars on the same parallel, and when, again, he still further produces his line, on from Thapsacus to Egypt, thus taking in all this additional breadth, and then measures the length of his figure by the length of this line, he would seem to be measuring the length of his rectangle by a diagonal of a rectangle. And whenever his line is not even a diagonal but a broken line, much more he would seem to err. In fact, it is a broken line that is drawn from the Caspian Gates through Thapsacus to the Nile. So much may be said against Eratosthenes.
48 See footnote 2, page 22.
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49 5,000 stadia directly north of Meroë. To one travelling north from the equator the Lesser Bear is first wholly visible at Meroë according to Hipparchus (2.5.35).
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50 See footnote, page 306.
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51 That is, which he charges to Eratosthenes.
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53 See paragraph 35 following and footnote.
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54 Strabo discusses this point again in 15.1.11.
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55 The Taurus.
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56 Indus.
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57 That is, they merge confusedly with one another across the imaginary line representing the common boundary between Section Second and Section Third.
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58 In mathematics, a dotted line.
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59 See figure and note on page 296.
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60 For the position of Paraetacene see 15.3.12.
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61 See footnote 2, page 105.
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62 Of course Hipparchus' argument is sound if his hypotheses be granted. Hipparchus assumes that Eratosthenes' figures refer to latitudinal and longitudinal distances; and by drawing a rectangle whose sides are formed by meridians through Thapsacus and the Caspian Gates, respectively, and by parallels of latitude through Thapsacus and the Caspian Gates, and though Babylon, he easily convicts Eratosthenes of inconsistency. That is, by a reductio ad absurdum, he forces Eratosthenes' Babylon much farther west than Eratosthenes meant it to be (cp. § 36 below on this point). Strabo proceeds to show the fallacy of Hipparchus' reasoning, and even to show that Hipparchus might have proved, on the same premises, still greater absurdity on the part of Eratosthenes.
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63 That is, the line drawn perpendicular to the meridian that passes though the Carmanian frontier.
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64 That is, with a divergence toward the south.
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65 From the Caspian Gates.
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66 From the Carmanian frontier.
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67 In § 26 Strabo indicates clearly that Eratosthenes did not say the western side was one straight line. But Hipparchus took this for granted.
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68 See § 22, above.
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69 The Mediterranean.
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70 That is, the sections that stretch north of the Taurus Range.
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71 See the figure and the note on page 328.
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72 If the line EB (p328) be produced to Eratosthenes' Susa (on his line drawn from A to Carmania), we shall then have a rightangle triangle AEB′ that comprehends the obtuseangled triangle AEB.
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73 Compare § 40, following.
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74 It was a common device of Eratosthenes and other ancient geographers to visualize countries and sections by comparing them to wellknown objects — for example, Spain to an ox‑hide, the Peloponnesus to a planeleaf, Sardinia to a human footprint. In this case the Greek words "plinthia" ("tiles") and "sphragides" ("seals", "gems") are used in a general sense as convenient terms for sections which presented, respectively, tileshaped and sealshaped appearances. (In 2.1.22, however, Strabo attributes only the latter word to Eratosthenes; and, furthermore, this is the word he himself often employs in the same sense.) Eratosthenes meant to convey by "sphragides" the notion of irregular quadrilaterals (as shows 15.1.11); but in his more specific description of a given section — India, for example — he refers to it as "rhomboidal," and, in the case of the Second Section, he refers to "three of its sides" as "fitting into a parallelogram" (see 2.1.22).
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75 "Lemma," the Greek word used, is, according to Proclus, a proposition previously proved, or hereafter to be proved; it is, therefore, for any proposition in hand, an assumption which requires confirmation.
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76 Both Eratosthenes and Strabo give Pelusium a higher latitude than Babylon.
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77 On the assumptions of Hipparchus, Eratosthenes' Thapsacus is made to lie at a latitude 7,300 stadia north of Pelusium (see figure, p337); and hence, computing the hypotenuse of the rightangled triangle for the distance between the two places, we get approximately 8,500 stadia. Hipparchus' argument is, as usual, a reductio ad absurdum, and his fallacy again lies, Strabo means, in his applying Eratosthenes' estimates to parallels of latitude and to meridians.
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78 Compare §§ 27‑29 (above), where Hipparchus, by his usual form of argument, forces Eratosthenes' Babylon to be 1,000 stadia farther west.
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79 In the figure on p337 draw a parallel of latitude through B (Thapsacus) and a meridian through A (Pelusium), and let them intersect at a point C′. Then AC′ (= BC = 4,800 stadia) becomes greater than AB (6,000 stadia) — that is, Eratosthenes' estimates lead to this result, says Hipparchus.
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80 The Greek verb here used corresponds to the noun which, in the formal divisions of a proposition, constitutes that division which, says Proclus, "adds what is wanting to the data for the purpose of finding out what is sought."
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81 Strabo refers to the false conclusion in § 34.
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82 Strabo had in the main accepted Eratosthenes' map together with his treatise thereof, inadequate though they were. He objected to Hipparchus' criticism based upon false assumptions and geometrical tests applied to specific cases. He argues in this paragraph that the map requires a "metron," or standard of measure, by means of which, as a sort of sliding scale, we may make proportional concessions or allowances in the matter of linear directions and geometrical magnitudes. Practically applied, this "metron" would save us from such a mistake as placing the Caspian Gates and the mouth of the Nile on the same parallel of latitude, and again from such a mistake as estimating the actual distance between these two points to be the same as the longitudinal distance. Furthermore, Strabo shows by parallelograms that the actual distance between any two points, A and B, does not grow less in the same proportion as does their difference of longitude.
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83 That is, an assumed line drawn east and west through the length of the strip — a strip approximately 70,000 stadia in length.
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84 See the figure and the note on pages 342 and 343.
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85 A′O represents a line which falls exterior to BG and AH, and AO a line which falls exterior to BG. Let ABCD be the large parallelogram; then the small parallelograms are ABGH, HGCD, FECD, JICD — and so on indefinitely.
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