s, solstices, the
distribution of climates, etc. I cannot do more than merely allude to
the treatises on Conic Sections and on Maxima and Minima by Apollonius,
who is said to have been the first to introduce the words ellipse and
hyperbola. In like manner I must pass the astronomical observations
of Alistyllus and Timocharis. It was to those of the latter on Spica
Virginis that Hipparchus was indebted for his great discovery of the
precession of the eqninoxes. Hipparchus also determined the first
inequality of the moon, the equation of the centre. He adopted the
theory of epicycles and eccentrics, a geometrical conception for the
purpose of resolving the apparent motions of the heavenly bodies on the
principle of circular movement. He also undertook to make a catalogue
of the stars by the method of alineations--that is, by indicating those
that are in the same apparent straight line. The number of stars so
catalogued was 1,080. If he thus attempted to depict the aspect of
the sky, he endeavored to do the same for the surface of the earth, by
marking the position of towns and other places by lines of latitude and
longitude. He was the first to construct tables of the sun and moon.

THE SYNTAXIS OF PTOLEMY. In the midst of such a brilliant constellation
of geometers, astronomers, physicists, conspicuously shines forth
Ptolemy, the author of the great work, "Syntaxis," "a Treatise on the
Mathematical Construction of the Heavens." It maintained its ground
for nearly fifteen hundred years, and indeed was only displaced by the
immortal "Principia" of Newton. It commences with the doctrine that the
earth is globular and fixed in space, it describes the construction of a
table of chords, and instruments for observing the solstices, it deduces
the obliquity of the ecliptic, it finds terrestrial latitudes by the
gnomon, describes climates, shows how ordinary may be converted into
sidereal time, gives reasons for preferring the tropical to the sidereal
year, furnishes the solar theory on the principle of the sun's orbit
being a simple eccentric, explains the equation of time, advances to the
discussion of the motions of the moon, treats of the first inequality,
of her eclipses, and the motion of her nodes. It then gives Ptolemy's
own great discovery--that which has made his name immortal--the
discovery of the moon's evection or second inequality, reducing it to
the epicyclic theory. It attempts the determination of the distances of