assertions, says Eratosthenes, arise from the ignorance of Deimachus. For it is nothing else than ignorance to suppose that the autumnal equinox is not equally distant from the tropics with the vernal; since in both equinoxes the sun rises at the same point, and performs a similar revolution. Further, [he continues,] the distance from the terrestrial tropic to the equator, between which, according to Deimachus himself, India is situated, has been proved by measurement to be much less than 20,000 stadia, consequently his own statements prove that my assertion is correct, and not his. For supposing India to be twenty or thirty thousand stadia [in breadth] it could not be contained in the given space, but if my estimate be taken it is simple enough. It is another evidence of his want of information, to say that the two Bears are not seen to set, or the shadows to fall both ways, in any part of India, since 5000 stadia south of Alexandria542 both of these phenomena are observable. Thus reasons Eratosthenes; whom Hipparchus again criticises in the same mistaken way. First he substitutes [in the text of Deimachus] the summer in place of the winter tropic; then he says that the evidence of a man ignorant of astronomy ought not to be received in a mathematical question; as if Eratosthenes in the main had actually been guided by the authority of Deimachus. Could he not see that Eratosthenes had followed the general custom in regard to idle reasoners, one means of refuting whom is to show that their arguments, whatever they may be, go only to confirm our views.
20. It is by assuming as a fact that the southern extremity of India is under the same parallel as Meroe, a thing affirmed and believed by most writers, that we shall be best able to show the absurdities of the system of Hipparchus. In the first book of his Commentaries he does not object to this hypothesis, but in the second book he no longer admits it; we must examine his reasons for this. He says, “when two countries are situated under the same parallel, but separated by a great distance, you cannot be certain that they are exactly under the same parallel, unless the climata543 of both the places are found to be similar. Now Philo, in his account of a voyage by sea to Ethiopia, has given us the clima of Meroe. He says that at that place the sun is vertical forty-five days before the summer solstice,544 he also informs us of the proportion of shadow thrown by the gnomon both at the equinoxes and solstices. Eratosthenes agrees almost exactly with Philo. But not a single writer, not even Eratosthenes, has informed us of the clima of India; but if it is the case, as many are inclined to believe on the authority of Nearchus,545 that the two Bears are seen to set in that country, then certainly Meroe and the southern extremity of India cannot be under the same parallel.”546 [Such is the reasoning of Hipparchus, but we reply,] If Eratosthenes confirms the statement of those authors who tell us that in India the two Bears are observed to set, how can it be said that not a single person, not even Eratosthenes, has informed us of any thing concerning the clima of India? This is itself information on that point. If, however, he has not confirmed this statement, let him be exonerated from the error. Certain it is he never did confirm the statement. Only when Deimachus affirmed that there was no place in India from which the two Bears might be seen to set, or the shadows fall both ways, as Megasthenes had asserted, Eratosthenes thereupon taxed him with ignorance, regarding as absolutely false this two-fold assertion, one half of which, namely, that concerning the shadows not falling both ways, Hipparchus himself acknowledged to be false; for if the southern extremity of India were not under the same parallel as Meroe, still Hipparchus appears to have considered it south of Syene.
21. In the instances which follow, Hipparchus, treating of these subjects, either asserts things similar to those which we have already refuted, or takes for granted matters which are not so, or draws improper sequences. For instance, from the computation [of Eratosthenes] that the distance from Babylon to Thapsacus547 is 4800 stadia, and thence northward to the mountains of Armenia548 2100 stadia more, it does not follow that, starting from the meridian of that city, the distance to the northern mountains is above 6000 stadia. Besides, Eratosthenes never says that the distance from Thapsacus to these mountains is 2100 stadia, but that a part thereof has never yet been measured; so that this argument [of Hipparchus], founded on a false hypothesis, amounts to nothing. Nor did Eratosthenes ever assert that Thapsacus lies more than 4500 stadia north of Babylon.
22. Again, Hipparchus, ever anxious to defend the [accuracy of the] ancient charts, instead of fairly stating the words of Eratosthenes concerning his third section of the habitable earth, wilfully makes him the author of an assertion easy of disproof. For Eratosthenes, following the opinion we before mentioned, that a line drawn from the Pillars of Hercules across the Mediterranean, and the length of the Taurus, would run due west and east,549 divides, by means of this line, the habitable earth into two portions, which he calls the northern and southern divisions; each of these he again essays to subdivide into as many smaller partitions as practicable, which he denominates sections.550 He makes India the first section of the southern part, and Ariana551 the second; these two countries possessing a good outline, he has been able not only to give us an accurate statement of their length and breadth, but an almost geometrically exact description of their figure. He tells us that the form of India is rhomboidal, being washed on two of its sides by the southern and eastern oceans [respectively], which do not deeply indent its shores. The two remaining sides are contained by its mountains and the river [Indus], so that it presents a kind of rectilinear figure.552 As to Ariana, he considered three of its sides well fitted to form a parallelogram; but of the western side he could give no regular definition, as it was inhabited by various nations; nevertheless he attempts an idea of it by a line drawn from the Caspian Gates553 to the limits of Carmania, which border on the Persian Gulf. This side he calls western, and that next the Indus eastern, but he does not tell us they are parallel to each other; neither does he say this of the other sides, one bounded by the mountains, and the other by the sea; he simply calls them north and south.
23. Having in this manner but imperfectly traced the outlines of his second section, the third section, for various reasons, is still less exact. The first cause has been already explained, viz. that the line from the Caspian Gates to Carmania is not clearly defined, as the side of the section is common both to the third and second sections. Secondly, on account of the Persian Gulf interrupting the continuity of the southern side, as he himself tells us, he has been obliged to take the measured road running through Susa and Persepolis to the boundaries of Carmania and Persia, and suppose it straight.554 This road, which he calls the southern side, is a little more than 9000 stadia. He does not, however, tell us, that it runs parallel to the northern side. It is also clear that the Euphrates, which he makes the western boundary, is any thing but a straight line. On leaving the mountains it flows south, but soon shifts its course to the east; it then again pursues a southerly direction till it reaches the sea. In fact, Eratosthenes himself acknowledges the indirect course of this river, when he compares the shape of Mesopotamia, which is formed by the junction of the Tigris and Euphrates, to the cushion on a rower’s bench. The western side bounded by the Euphrates is not entirely measured; for he tells us that he does not know the extent of the portion between Armenia and the northern mountains,555 as it has not been measured. By reason of these hinderances he states that he has been only able to give a very superficial view of the third section, and that his estimate of the distances is borrowed from various Itineraries, some of them, according to his own description, anonymous. Hipparchus therefore must be considered guilty of unfairness, for criticising with geometrical precision a work of this general nature. We ought rather to be grateful to a person who gives us any description at all of the character of such [unknown] places. But when he urges his geometrical objections not against any real statement of Eratosthenes, but merely against imaginary hypotheses of his own creation, he shows too plainly the contradictory bent of his mind.
24. It is