Anaximenes of Miletus taught, like his predecessors, crude notions of the sun and stars, and speculated on the nature of the moon, but did nothing to advance his science on true grounds, except by the construction of sun-dials. The same may be said of Heraclitus, Xenophanes, Parmenides, and Anaxagoras: they were great men, but they gave to the world mere speculations, some of which are very puerile. They all held to the idea that the heavenly bodies revolved around the earth, and that the earth was a plain; but they explained eclipses, and supposed that the moon derived its light from the sun. Some of them knew the difference between the planets and the fixed stars. Anaxagoras scouted the notion that the sun was a god, and supposed it to be a mass of ignited stone,--for which he was called an atheist.
Socrates, who belonged to another school, avoided all barren speculations concerning the universe, and confined himself to human actions and interests. He looked even upon geometry in a very practical way, valuing it only so far as it could be made serviceable to land-measuring. As for the stars and planets, he supposed it was impossible to arrive at a true knowledge of them, and regarded speculations upon them as useless.
It must be admitted that the Greek astronomers, however barren were their general theories, laid the foundation of science. Pythagoras taught the obliquity of the ecliptic, probably learned in Egypt, and the identity of the morning and evening stars. It is supposed that he maintained that the sun was the centre of the universe, and that the earth revolved around it; but this he did not demonstrate, and his whole system was unscientific, assuming certain arbitrary principles, from which he reasoned deductively. "He assumed that fire is more worthy than earth; that the more worthy place must be given to the more worthy; that the extremity is more worthy than the intermediate parts,--and hence, as the centre is an extremity, the place of fire is at the centre of the universe, and that therefore the earth and other heavenly bodies move round the fiery centre." But this was no heliocentric system, since the sun moved, like the earth, in a circle around the central fire. This was merely the work of the imagination, utterly unscientific, though bold and original. Nor did this hypothesis gain credit, since it was the fixed opinion of philosophers that the earth was the centre of the universe, around which the sun, moon, and planets revolved. But the Pythagoreans were the first to teach that the motions of the sun, moon, and planets are circular and equable. Their idea that the celestial bodies emitted a sound, and were combined into a harmonious symphony, was exceedingly crude, however beautiful "The music of the spheres" belongs to poetry, as well as to the speculations of Plato.
Eudoxus, in the fifth century before Christ, contributed to science by making a descriptive map of the heavens, which was used as a manual of sidereal astronomy to the sixth century of our era.
The error of only one hundred and ninety days in the periodic time of Saturn shows that there had been for a long time close observations. Aristotle--whose comprehensive intellect, like that of Bacon, took in all forms of knowledge--condensed all that was known in his day into a treatise concerning the heavens. He regarded astronomy as more intimately connected with mathematics than any other branch of science. But even he did not soar far beyond the philosophers of his day, since he held to the immobility of the earth,--the grand error of the ancients. Some few speculators in science (like Heraclitus of Pontus, and Hicetas) conceived a motion of the earth itself upon its axis, so as to account for the apparent motion of the sun; but they also thought it was in the centre of the universe.
The introduction of the gnomon (time-pillar) and dial into Greece advanced astronomical knowledge, since they were used to determine the equinoxes and solstices, as well as parts of the day. Meton set up a sun-dial at Athens in the year 433 B.C., but the length of the hour varied with the time of the year, since the Greeks divided the day into twelve equal parts. Dials were common at Rome in the time of Plautus, 224 B.C.; but there was a difficulty in using them, since they failed at night and in cloudy weather, and could not be relied on. Hence the introduction of water-clocks instead.
Aristarchus is said to have combated (280 B.C.) the geocentric theory so generally received by philosophers, and to have promulgated the hypothesis "that the fixed stars and the sun are immovable; that the earth is carried round the sun in the circumference of a circle of which the sun is the centre; and that the sphere of the fixed stars, having the same centre as the sun, is of such magnitude that the orbit of the earth is to the distance of the fixed stars as the centre of the sphere of the fixed stars is to its surface." Aristarchus also, according to Plutarch, explained the apparent annual motion of the sun in the ecliptic by supposing the orbit of the earth to be inclined to its axis. There is no evidence that this great astronomer supported his heliocentric theory with any geometrical proof, although Plutarch maintains that he demonstrated it. This theory gave great offence, especially to the Stoics; and Cleanthes, the head of the school at that time, maintained that the author of such an impious doctrine should be punished. Aristarchus left a treatise "On the Magnitudes and Distances of the Sun and Moon;" and his methods to measure the apparent diameters of the sun and moon are considered theoretically sound by modern astronomers, but practically inexact owing to defective instruments. He estimated the diameter of the sun at the seven hundred and twentieth part of the circumference of the circle which it describes in its diurnal revolution, which is not far from the truth; but in this treatise he does not allude to his heliocentric theory.
Archimedes of Syracuse, born 287 B.C., is stated to have measured the distance of the sun, moon, and planets, and he constructed an orrery in which he exhibited their motions. But it was not in the Grecian colony of Syracuse, but of Alexandria, that the greatest light was shed on astronomical science. Here Aristarchus resided, and also Eratosthenes, who lived between the years 276 and 196 B.C. The latter was a native of Athens, but was invited by Ptolemy Euergetes to Alexandria, and placed at the head of the library. His great achievement was the determination of the circumference of the earth. This was done by measuring on the ground the distance between Syene, a city exactly under the tropic, and Alexandria, situated on the same meridian. The distance was found to be five thousand stadia. The meridional distance of the sun from the zenith of Alexandria he estimated to be 7° 12', or a fiftieth part of the circumference of the meridian. Hence the circumference of the earth was fixed at two hundred and fifty thousand stadia,--which is not very different from our modern computation. The circumference being known, the diameter of the earth was easily determined. The moderns have added nothing to this method. He also calculated the diameter of the sun to be twenty-seven times greater than that of the earth, and the distance of the sun from the earth to be eight hundred and four million stadia, and that of the moon seven hundred and eighty thousand stadia,--a close approximation to the truth.
Astronomical science received a great impulse from the school of Alexandria, the greatest light of which was Hipparchus, who flourished early in the second century before Christ. He laid the foundation of astronomy upon a scientific basis. "He determined," says Delambre, "the position of the stars by right ascensions and declinations, and was acquainted with the obliquity of the ecliptic. He determined the inequality of the sun and the place of its apogee, as well as its mean motion; the mean motion of the moon, of its nodes and apogee; the equation of the moon's centre, and the inclination of its orbit. He calculated eclipses of the moon, and used them for the correction of his lunar tables, and he had an approximate knowledge of parallax." His determination of the motions of the sun and moon, and his method of predicting eclipses evince great mathematical genius. But he combined with this determination a theory of epicycles and eccentrics which modern astronomy discards. It was however a great thing to conceive of the earth as a solid sphere, and to reduce the phenomena of the heavenly bodies to uniform motions in circular orbits. "That Hipparchus should have succeeded in the first great steps of the resolution of the heavenly bodies into circular motions is a circumstance," says Whewell, "which gives him one of the most distinguished places in the roll of great astronomers." But he did even more than this: he discovered that apparent motion of the fixed stars round the axis of the ecliptic, which is called the Precession of the Equinoxes,--one of the greatest discoveries in astronomy. He maintained that the precession was not greater than fifty-nine seconds, and not less than thirty-six seconds. Hipparchus also framed a catalogue of the stars, and determined their places with reference to the ecliptic by their latitudes and longitudes. Altogether he seems to have been one of the greatest geniuses of antiquity, and his works imply a prodigious amount of calculation.
Astronomy made no progress for three hundred years, although it was expounded by improved methods. Posidonius constructed an orrery, which exhibited the diurnal motions of the sun, moon, and five planets. Posidonius calculated the circumference of the earth to be two hundred and forty thousand stadia, by a different method from Eratosthenes. The barrenness of discovery from Hipparchus to Ptolemy,--the Alexandrian mathematician, astronomer, and geographer in the second century of the Christian era,--in spite of the patronage of the royal Ptolemies of Egypt, was owing to the want of instruments for the accurate measure of time (like our clocks), to the imperfection of astronomical tables, and to the want of telescopes. Hence the great Greek astronomers were unable to realize their theories. Their theories however were magnificent, and evinced great power of mathematical combination; but what could they do without that wondrous instrument by which the human eye indefinitely multiplies its power? Moreover, the ancients had no accurate almanacs, since the care of the calendar belonged not so much to the astronomers as to the priests, who tampered with the computation of time for sacerdotal objects. The calendars of different communities differed. Hence Julius Caesar rendered a great service to science by the reform of the Roman calendar, which was exclusively under the control of the college of pontiffs, or general religious overseers. The Roman year consisted of three hundred and fifty-five days; and in the time of Caesar the calendar was in great confusion, being ninety days in advance, so that January was an autumn month. He inserted the regular intercalary month of twenty-three days, and two additional ones of sixty-seven days. These, together with ninety days, were added to three hundred and sixty-five days, making a year of transition of four hundred and forty-five days, by which January was brought back to the first month in the year after the winter solstice; and to prevent the repetition of the error, he directed that in future the year should consist of three hundred and sixty-five and one-quarter days, which he effected by adding one day to the months of April, June, September, and November, and two days to the months of January, Sextilis, and December, making an addition of ten days to the old year of three hundred and fifty-five. And he provided for a uniform intercalation of one day in every fourth year, which accounted for the remaining quarter of a day.