Footnotes:
[1] “The fair things that Heaven holds.” Inferno XXXIV. 137, 138.
[2] Greek gnomon, an interpreter. A pole set up in order to show the length of shadow thrown by the sun.
[3] Greek planetes, a wanderer. This name was originally given to Mercury, Venus, Mars, Jupiter, Saturn, and also to sun and moon, for it indicated all the known heavenly bodies which changed their places among the stars. In modern usage it is not applied to the sun, but only to his satellites, of which many more are now known.
[4] Fractions omitted.
[5] Conv. IV., xxiii. 56, 57.
[6] Dr. C. Hose, in “Travel and Exploration,” for Feb. 1910, quoted in “Nature,” Feb. 17, 1910.
[7] Journal of the British Astronomical Association, June 24, 1909, report of a lecture on Chinese astronomy by E. B. Knobel, F.R.A.S.
[8] Acts, xvii. 28.
[9] The Phainomena of Aratos, done into English verse by Robert Brown, lines 1-13.
[10] Ibid., 373-382.
[11] Ptolemy says he made a few changes, as his predecessors had done. (Delambre, Histoire de l’Astronomie Ancienne, ii. 261).
[12] Origine de tous les cultes, ou Religion universelle, by C. F. Dupuis.
[13] Journal of the British Astronomical Association, “The Oldest Astronomy,” July 1898, June 1899, April 1904 May 1909; The Observatory, December 1898; Knowledge, October 1904; and elsewhere.
[14] The Phainomena of Aratos, by Robert Brown. See also his Eridanus, River and Constellation; Primitive Constellations, and other works.
[15] We are not sure what limits Aratus intended to set in the south to Centaur and Argo, and notably to the River Eridanus, which used to flow beneath the Sea-Monster (Cetus), joining the Water poured out by Aquarius. It changed its bed (like the Euphrates, of which it is perhaps the heavenly counterpart), and now has left the Sea-Monster high and dry, while on its ancient banks a chemist’s furnace and a sculptor’s workshop have been set up.
The Celestial Equator of Aratus fails to agree with the Equator of b.c. 2084, not only in passing over the head of Orion, instead of through his belt, as Brown himself points out, but also in running through the eye of the Bull, instead of his “crouching legs alone,” so this part is altogether too far north. The Equator some 1200 years later agreed better here, and equally well elsewhere, except in the opposite part of the sky where it was then too northerly for Aratus, leaving Corvus to the south of the line. Much the same may be said about the tropical circles. Either Aratus was careless, or the globe from which he took his descriptions was incorrect: in any case, there results an uncertainty of many centuries and many degrees in date and latitude.
[16] Epping and Strassmeier, Astronomisches aus Babylon, Kugler’s Babylonische Mondrechnung, and Babylonische Sternkunde. Schiaparelli’s two monographs on Babylonian Astronomy, from which much of the information here given is derived, are chiefly based on these works.
[17] King, History of Sumer and Akkad, p. 246.
[18] Schiaparelli, L’ Astronomia nell’ Antico Testamento, chap. vii.; Wellhausen, History of Israel, chap. iii.
[19] Sayce and Bosanquet identify Dilgan with Capella, not with part of Aries, and consider that a date of about b.c. 2000 is indicated—(Monthly Notices xxxix, 454). But in any case the method of calendar formation is the same.
[20] Sayce and Bosanquet understand Capella here also.
[21] If Taurus was originally considered the first constellation of the zodiac, instead of Aries, of which there are some indications, the change may well be explained by this change of method. It does not necessarily imply that the equinox was in Taurus when our zodiac was invented. It was near ω Arietis in b.c. 1000.
[22] A Babylonian treatise on astronomy recently published by the trustees of the British Museum supports Kugler’s view that truly scientific methods were not adopted before the sixth century b.c. This treatise formed the subject of a lecture given by Mr L. W. King before the Society of Biblical Archæology on Feb. 19, 1913.
[23] Gen. i. 6, 7; vii. 11.
[24] Ezek. xxxii. 18, 24.
[25] De Cœlo I. 3, and II. 1.
[27] His life was saved by his illustrious pupil, Pericles, of whom the story is told that on one occasion, just as his army was embarking for an expedition, the sun was eclipsed, and his pilot was terrified. Pericles snatched off his cloak, and held it so as to hide himself from the man’s eyes. “Is that terrible? is that an evil omen?” he cried. “Then do not fear the disappearance of the sun, for it is just the same, only the thing that hides it is larger than my cloak.”
[28] Some late followers said that Pythagoras, alone amongst men, could hear the music of the spheres.
[29] See Heath’s Aristarchus of Samos, pp. 187-189 and 251, 252. I very much regret that as Mr. Heath’s book was only published this year, I have been unable to make use of it while writing of early Greek astronomy. I can now only advise any readers who may be interested in my brief sketch of this period to read Mr. Heath’s history, where they will find the opinions of modern writers summarized and discussed, and also the full text (in English) of the most ancient and reliable sources of information. It is a great encouragement to find that my statements are in agreement with his in nearly all essential points, but readers will mark the following important differences:—
1. Anaximander’s heavens are said to have been spherical, not hemispherical, and this seems to be clearly proved by the evidence quoted from ancient writers.
2. Anaxagoras, not Thales, is said to have been the first to explain correctly the cause of solar eclipses and of the moon’s phases, viz. that the moon is an opaque body, shining only by reflected sunlight, and periodically hiding the sun from us when she passes in front of it. Mr. Heath regards the authorship of Anaxagoras as conclusively proved: readers will be able to judge of this from his quotations. Personally they seem to me to prove no more than that Anaxagoras agreed with others on this point, and was the first to express it clearly in writing. It is difficult to see why Mr. Heath denies that Parmenides held the same views before Anaxagoras: Parmenides’ own words seem to prove it, and his theory that the moon was composed of air and fire mingled is rather in favour of it than otherwise. He surely meant that the moon was not wholly bright, like the sun; yet that she had some light of her own must have seemed evident from the faint illumination we see during total lunar eclipses and on the part of her surface not lighted by the sun. (See Dante’s views, p. 402 of this book.)
The connection between her phases and her distance from the sun in the sky is so extremely obvious that I can hardly think the Greeks drew no inference from it until the fifth century b.c., and I cannot see why we should refuse to credit Thales with the discovery attributed to him that her light came in some way from the sun. Gruppe acutely observes that the reason why Thales’ pupil Anaximander did not accept the true explanation of lunar phases and solar eclipses may have been because he felt it necessary to have a theory which would apply equally well to eclipses of the moon; and as he believed in a flat earth he could not advocate the true explanation here. This was why he invented a new theory (viz. that both sun and moon were fire shining through holes in hollow rings, and that the occasional stopping up of these holes caused both lunar and solar eclipses, and also the lunar phases).
But Parmenides had learned the Pythagorean doctrine of Earth’s spherical form, hence he was able to accept the older theory that the moon obtains her light from the sun, and sometimes eclipses the sun by her opaque spherical body, for he could have added that the moon is eclipsed in like manner by the opaque spherical body of the earth.
[30] I follow the translation of Jowett.
[31] Compare Par. vii. 64-66.
[32] See his famous description of the eight spheres, on each of which stands a siren, singing, while the whole system turns upon a diamond spindle, the end of which rests upon the knees of Necessity. This book was not known in the Middle Ages.
[33] ειλλομενη.
[34] The period in which a planet is seen to revolve round the zodiac, and return to the same star, varies greatly, because complicated by its retrograde movements; but if the average of a sufficient number of periods be taken, it coincides for Mercury and Venus with the sidereal year; for Mars, Jupiter, and Saturn, with the period in which each is actually revolving round the sun (its “sidereal period”).
[35] Geminus.
[36] This varying velocity is due to the fact that all celestial orbits are not true circles, but ellipses, which was first discovered by Kepler (1609 a.d.).
[37] De Cœlo II. 10.
[38] Thus, (he adds) time also is threefold, for we have Beginning, Middle, and End. Therefore we apply three to Divine things, and also in common speech we call two “both,” and only say “all” when we reach three, following Nature’s law. The Pythagoreans say “The all and all things are bounded by the number three.”—De Cœlo I. 1.
[39] Par. iv. 1-3.
[41] Conv. II. iii. 59-65.
[42] It is also mentioned in a compilation of philosophers’ opinions, probably made in the fifth century a.d. by Stobæus, who is very likely quoting Plutarch.
[44] Indian astronomers also refused to accept the doctrine of Aryabhata. Varâha Mihira (sixth century a.d.) says:—“Others maintain that the earth revolves and not the sphere: if that were the case, falcons and other birds could not return from the ether to their nests.”
[45] Spheres all centring in one point.
[46] Mahaffy, The Progress of Hellenism in Alexander’s Empire, p. 119.
[48] Almagest, Bk. viii.
[49] Greek peri near, apo away from, ge Earth.
[50] Syntaxis, book VII.; Delambre, Histoire de l’Astronomie Ancienne Vol. II. page 247 (1817 edition).
[51] Venus had passed her “inferior conjunction with the sun” on Sept. 15.
[52] It amounts to 5 degrees of longitude in 300 years.
[53] This is evident from the way he treats them, picking up an epicycle or a deferent just as best suits the purpose in hand and explaining sometimes that either would answer equally well.
[54] Taken from the Almagest catalogue, as given in Delambre’s History.
[55] Fifteen stars.
[56] Lockyer, Dawn of Astronomy, p. 196.
[57] The changing latitudes of the planets, for instance, which gave Ptolemy much trouble, are much more easily explained when it is granted that they partly depend upon Earth’s motion in an orbit whose plane is slightly inclined to the planes of their orbits.
[58] It therefore really approached more nearly the sidereal year, although the cycle was based on the tropical year.
[59] De Mon. II. vii., “Temple Classics” edition.
[60] De Senectute.
[61] The average year was the same, 365¼ days, in the old 8-year cycle of the Greeks, and also in the Calippic cycle, which did not come into practical use. The average year of the Metonic cycle was longer, and therefore departed further from the true tropical year.
[63] Ezekiel, v. 5.
[64] Arabic gib = Latin sinus, a fold; i.e. the chord folded in two.
[65] The Arabian mile was equal to 4000 “black cubits,” and if this is the Egyptian and Babylonian cubit, the values are rather too large, being in round numbers 26,500 and 8,500 English miles, instead of 25,000 and 8000.
[66] The Catalogue of Hipparchus is said to have contained 1080 stars, but Ptolemy’s has only 1022.
[67] Earth’s diameter, and even Earth’s distance from the sun, is too small a unit. Light, travelling 186,000 miles a second, takes 4¼ years to reach us from the nearest star.
[68] It is impossible to measure the diameter of any star, even with the help of the most powerful telescopes, but in the case of a double star at a known distance the movement of the components as they travel round their common centre of gravity enables us to determine the gravitational force they exercise on each other, and thus their combined mass; and their spectra give some idea of their density. For instance, the mass of the double star Alpha Centauri is nearly twice that of our sun; and as the components appear to be about equal to each other, and both show a spectrum resembling that of the sun, we may conclude that Alpha Centauri consists of two stars, each of which has about the same diameter as our sun. Arcturus has a diameter far greater, some say ten times, some not less than twenty-five times as great as the sun!
[69] The mean length of Earth’s shadow (which varies a little with her distance from the sun,) is 857,000 miles, or 216 times her semi-diameter.
[70] It was also translated from Arabic into Latin at Toledo, in 1175.
[71] Paradise Lost, II. 418
[72] Paradise Lost, VIII. 34-38.
[73] Paradise Lost, VIII. 77-84.
[74] All quotations from Salimbene’s Chronicle are taken from Coulton’s From Saint Francis to Dante.
[75] Croniche Fiorentine, Bk. VII. par. 80.
[76] Inf. xx. 118.
[77] V. E., I. xii. 20-35.
[78] Villani, Croniche Fiorentine, VI. 1 and 24.
[80] Boccaccio’s Vita di Dante; Translation from Toynbee’s Dante Alighieri (Oxford Biographies), pp. 92, 93.
[81] Inf. xv. 23 et seq.
[82] Inf. xv. 119.
[83] “If thou follow thy star,” Inf. xv. 55.
[84] “First refuge,” Par. xvii. 70.
[85] Par. xvii. 71, 72.
[86] Imbriani, Dante a Padova.
[87] “Torno a Ravenna e de lì non mi parto (I am going back to Ravenna, and shall not leave it again), is a line in the Acerba which Cecco d’ Ascoli puts into the mouth of Dante, as though from a letter written to himself from the divine poet at the time” (about the year 1319). Dante and Giovanni del Virgilio, by Wicksteed and Gardner, p. 84.
[88] Inf. xxxi. 136-141.
[89] Conv. II. xiii. 22-26.
[90] Conv. III. ix. 146-157.
[91] Conv. II. xv. 73-77.
[92] Conv. II. iii. 36-52, V. N. xxx.
[93] Averroës, in his commentary on Aristotle’s De Cœlo, says that the ancients believed the eighth, or starry, heaven, to be the outermost, but that Ptolemy assumed a ninth, “because he said that he had discovered a slow motion along the signs of the zodiac in the fixed stars.” Albertus Magnus, in his De Cœlo et Mundo, Book II., says also that the ancients, including Aristotle, believed that there were only eight heavens, but that Ptolemy, so far as he can understand, believed in ten, on philosophical not mathematical grounds (compare Conv. II. iii. 40, 41). Albertus accepted the theory of “trepidation,” and thought this was the only movement which ought to be assigned to the star sphere; there remained, therefore, two motions, which affect all the planetary spheres and the star sphere, for which two more spheres must be assumed, a ninth sphere for precession, and a tenth, the primum mobile, for the diurnal motion. Outside all was the Empyrean. Dante never mentions trepidation, and evidently did not believe in it: he needed only nine moving spheres, therefore, but counts the Empyrean as a tenth heaven.
[94] Conv. II. xiv. 198-202. Ibid. 249-253.
[95] “Ptolemy says in the book above cited.”
[96] Par. xiii. 1-13.
[97] See Schiaparelli’s letter in Lubin’s Dante e gli Astronomi Italiani. The name is, however, also used as a sub-title in the printed edition of Christmann, Frankfort, 1590, which was based not on the translation of Gerard but of Johannes Hispalensis of Seville; and Toynbee thinks that this Frankfort edition represents most nearly the version of Alfraganus used by Dante. It is the only one of the five printed editions which gives the same figure for the diameter of Mercury as that quoted by Dante. See Toynbee, “Dante’s Obligations to Alfraganus” in Romania xxiv. 95, and Moore, Studies in Dante iii. p. 3, note.
[98] “That glorious philosopher to whom Nature most fully revealed her secrets,” Conv. III. v. 54-56; “almost divine,” Conv. IV. vi. 133; “supreme and highest authority,” Ibid. 52.
[99] Moore, Studies in Dante I. (Scripture and Classical Authors in Dante), from which much of the information in this chapter has been taken.
[100] Conv. II. iii. 19-21.
[101] Conv. III. v. 62-65.
[102] “My master.”
[103] Conv. III. v. 32.
[104] Inf. ii. 76-78; Par. xxii. 134-138.
[105] Conv. ii. xiv. 174-176.
[106] Phaëthon, Conv. II. xv. 53-55, Purg. xxix. 118-120; Latona, Purg. xx. 130-132; the Horses of the Sun, Conv. IV. xxiii. 134-139, etc., etc.
[107] Conv. III. v. 115-117.
[108] “A man of supreme excellence.” Conv. II. v. 21, 22.
[109] Conv. III. xiv. 76-79.
[110] Par. iv. 22-24, 49-60.
[111] Conv. III. xi. 39; Inf. iv. 137.
[112] Conv. III. xi. 22-33; II. xiv. 144-147; III. v. 29-44; III. xi. 41-47.
[113] Conv. II. xiv. 34, 35.
[114] Conv. II. xv. 56.
[115] Qu. xviii. 38, 39.
[116] Conv. III. ii. 37.
[117] Conv. II. xv. 77, II. xiv. 32.
[118] Conv. II. xiv. 170-174.
[119] Inf. iv. 80, 81, 90, 131-144.
[120] “The advocate of the Christian centuries.” (Par. x. 199). Orosius is also mentioned by name in Conv. III. xi. 27; V. E. II. vi. 84; and De Mon. II. ix. 26.
[122] Toynbee, Dante Dictionary; the source also of many other details given in this chapter.