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, an