Astronomy was one of these. So far as mathematical genius is concerned, so far as astronomy taxed the reasoning powers, 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 accidental inventions, they might have earned a fame scarcely eclipsed by that of Kepler and Newton. The Ionic philosophers added but little to the realm of true philosophy, but they were pioneers of thought, and giants in their native powers. The old astronomers did as little as they to place science on a true foundation, but they showed great ingenuity, and discovered some great 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. [Footnote: Delambre, _Hist. d'Astr. Anc._, tom. 1, p. 184.] 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. [Footnote: Lewis, _Hist. of Astron._, p. 209.] We have settled, by physical geography, the exact form of the earth, but the ancients arrived at their knowledge by astronomical reasoning. "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 theory 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, [Footnote: Whewell, _Hist. Induc. Science_, v. i. p. 181.] and was equivalent to the most recent and improved processes by which modern astronomers deal with such motions." But I will not here enumerate the few discoveries which were made by the Alexandrian school. I only wish to show that there are a few names among the ancients which are inscribed on the roll of great astronomers, limited as were the triumphs of the science itself. But, until the time of Aristarchus, most of the speculations were crude and useless. Nothing can be more puerile than the notions of the ancients respecting the nature and motions of the heavenly bodies. [Sidenote: Astronomy born in Chaldea.]