I have shown that in the field of artistic excellence, in literary composition, in the arts of government and legislation, and even in the realm of philosophical speculation, the ancients were our school-masters, and that among them were some men of most marvellous genius, who have had no superiors among us.  But we do not see among them the exhibition of genius in what we call science, at least in its application to practical life.  It would be difficult to show any department of science which the ancients carried to any considerable degree of perfection.  Nevertheless, there were departments in which they made noble attempts, and in which they showed large capacity, even if they were unsuccessful in great practical results.

Astronomy was one of these.  In this science such men as Eratosthenes, Aristarchus, Hipparchus, and Ptolemy were great lights of whom humanity may be proud; and had they been assisted by our modern inventions, they might have earned a fame scarcely eclipsed by that of Kepler and Newton.  The old astronomers did little to place this science on a true foundation, but they showed great ingenuity, and discovered some truths which no succeeding age has repudiated.  They determined the circumference of the earth by a method identical with that which would be employed by modern astronomers; they ascertained the position of the stars by right ascension and declination; they knew the obliquity of the ecliptic, and determined the place of the sun’s apogee as well as its mean motion.  Their calculations on the eccentricity of the moon prove that they had a rectilinear trigonometry and tables of chords.  They had an approximate knowledge of parallax; they could calculate eclipses of the moon, and use them for the correction of their lunar tables.  They understood spherical trigonometry, and determined the motions of the sun and moon, involving an accurate definition of the year and a method of predicting eclipses; they ascertained that the earth was a sphere, and reduced the phenomena of the heavenly bodies to uniform movements of circular orbits.  We have settled by physical geography the exact form of the earth, but the ancients arrived at their knowledge by astronomical reasoning.  Says Whewell:—­

“The reduction of the motions of the sun, moon, and five planets to circular orbits, as was done by Hipparchus, implies deep concentrated thought and scientific abstraction.  The theories of eccentrics and epicycles accomplished the end of explaining all the known phenomena.  The resolution of the apparent motions of the heavenly bodies into an assemblage of circular motions was a great triumph of genius, and was equivalent to the most recent and improved processes by which modern astronomers deal with such motions.”