It is unnecessary to adduce the arguments relied upon by the Alexandrians to prove the globular form of the earth.  They had correct ideas respecting the doctrine of the sphere, its poles, axis, equator, arctic and antarctic circles, equinoctial points, 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 the sun and moon from the earth—­with, however, only partial success.  It considers the precession of the equinoxes, the discovery of Hipparchus, the full period of which is twenty-five thousand years.  It gives a catalogue of 1,022 stars, treats of the nature of the milky-way, and discusses in the most masterly manner the motions of the planets.  This point constitutes another of Ptolemy’s claims to scientific fame.  His determination of the planetary orbits was accomplished by comparing his own observations with those of former astronomers, among them the observations of Timocharis on the planet Venus.