Now, said I, my dear Apollonides, you mathematiciansThis is implied by the second person plural addressed to Apollonides, cf. 925 B s.v. and 920 F, 921 C supra. say that the sun is an immense distance from the upper circumference and that above the sun Venus and Mercury and the other planetsFor the order of the planets cf. Dreyer, , pp. 168-170, and Boyancè, , pp. 59-65; the order here given is not the one adopted by most of the astronomers of Plutarch’s time, by the later Stoics, or in all probability by Posidonius. revolve lower than the fixed stars and at great intervals from one another; but you think that in the cosmos there is provided no scope and extension for heavy and earthy objects. You see that it is ridiculous for us to deny that the moon is earth because she stands apart from the nether region and yet to call her a star although we see her removed so many thousands of miles from the upper circumference as if plunged [into] a pit. So far beneath the stars is she that the distance cannot be expressed, but you mathematicians in trying to calculate it run short of numbers; she practically grazes the earth and revolving close to it Whirls like a chariot’s axle-box about, Empedocles says,Empedocles, frag. B 46 (i, p. 331 [Diels-Kranz]).That skims [the post in passing].

Frequently she does not even surmount the earth’s shadow, though it extends but a little way because the illuminating body is very large; but she seems to revolve so close, almost within arm’s reach of the earth, as to be screened by it from the sun unless she rises above this shadowy, terrestrial, and nocturnal place which is earth’s estate. Therefore we must boldly declare, I think, that the moon is within the confines of [the] earth inasmuch as she is occulted by its extremities.

Dismiss the fixed stars and the other planets and consider the demonstrations of Aristarchus in his treatise, , that the distance of the sun is more than 18 times and less than 20 times the distance of the moon, that is its distance from us.This is Proposition 7 of Aristarchus’s treatise, the full title of which is . The treatise is edited and translated by Sir Thomas Heath in his , pp. 352 ff. According to the highest estimate, however, the moon’s distance from us is said to be 56 times the radius of the earth.This was not the highest estimate hitherto given, nor have I been able to identify its author. cf. on this matter and the subsequent calculations in this passage xlvi (1951), pp. 140-141. No attempt is made to give equivalents for stades in calculations, for it is uncertain what stade is meant in any one place. Schiaparelli assumes everywhere the Olympic stade of 185 metres (, i, p. 333, n. 3 and p. 342, n. 1); Heath argues that Eratosthenes used a stade of 157.5 metres and Ptolemy the royal stade of 210 metres (, pp. 339 and 346); and Raingeard (p. 83 on 925 D 6) assumes without argument that Plutarch used the Attic stade of 177.6 metres. Even according to the mean calculations this radius is 40,000 stades; and, if we reckon from this, the sun is more than 40,300,000 stades distant from the moon. She has migrated so far from the sun on account of her weight and has moved so close to the earth that, if propertiesThere is a play on the meaning of τὰs οὐσίας, substances, as property or estates and as the real nature of things. are to be determined by locations, the lot, I mean the position, of earth lays an action against the moon and she is legally assignable by right of propinquity and kinship to the chattels real and personal of earth. We do not err at all, I think, if granting such altitude and extension to the things called upper we leave what is down below also some room to move about in and so much latitude as there is from earth to moon. For as he is immoderate who calls only the outermost surface of the heaven up and all else down, so is he intolerable who restricts down to the earth or rather to the centre; but both there and here some extension must be granted since the magnitude of the universe permits it. The claim that everything away from the earth is ipso facto up and on high answered by a counter-claim that what is away from the circuit of the fixed stars is ipso facto down.

After all, in what sense is earth situated in the middle and in the middle of what? The sum of things is infinite; and the infinite, having neither beginning nor limit, cannot properly have a middle, for the middle is a kind of limit too but infinity is a negation of limits. He who asserts that the earth is in the middle not of the sum of things but of the cosmos is naive if he supposes that the cosmos itself is not also involved in the very same difficulties.cf., 424 D, where καθ’ ὅυς δ’ ἔστιν (scil, τὸ κενόν) refers to the Stoics (for whose distinction between the pa=n and the κόσμος see note c on 924 E supra), and , 1054 B - D, where as here Plutarch uses against the Stoics a weapon taken from their own arsenal. In fact, in the sum of things no middle has been left for the cosmos either, but it is without hearth and habitation,cf., ix. 5. 828 D: ἄοικοι καὶ ἀνίδρυτοι. moving in infinite void to nothing of its own; [or], if it has come to rest because it has found some other reason for abiding, not because of the nature of its location,cf. ii, pp. 174-175, frags. 552 and 553; , 1054 F 1055 B. similar inferences are permissible in the cases of both earth and moon, that the former is stationary here and the latter is in motion there by reason of a different soul or nature rather [than] a difference [of location]. Besides this, consider whether theyThe Stoics. have not overlooked an important point. If anything in any way at all off the centre of the earth is up, no part of the cosmos is down; but it turns out that the earth and the things on the earth and absolutely all body surrounding or enclosing the centre are up and only one thing is down, that incorporeal pointcf. ii, p. 169. 9-11, frag. 527: τῆς γῆς περὶ τὸ μέσον σημεῖον τoῦ κόσμου κειμένης, ὅ δὴ τοῦ παντός ἐστι κάτω, ἄνω δὲ τὸ ἀπ’ αὐτοῦ εἰς τὸ κύκλῳ πάντῃ. which must be in opposition to the entire nature of the cosmos, if in fact down and up are natural opposites.cf. ii, p. 176, frag. 556: τὸ ἄνω καὶ τὸ κάτω οὐ κατὰ σχέσιν φύσει γὰρ διάφορα ταῦτα. This, moreover, does not exhaust the absurdity. The cause of the descent of heavy objects and of their motion to this region is also abolished, for there is no body that is down towards which they are in motion and it is neither likely nor in accordance with the intention of these men that the incorporeal should have so much influence as to attract all these objects and keep them together around itself.See note d on 924 B supra, and cf. , 424 E against Aristotle. On the contrary, it proves to be entirely unreasonable and inconsistent with the facts for the whole cosmos to be up and nothing but an incorporeal and unextended limit to be down; but that statement of ours is reasonable, that ample space and broad has been divided between up and down.