ent of the
magnitude of the earth,--being one of the first who brought
mathematical methods to the aid of astronomy, which in our day is almost
exclusively the province of the mathematician.

Apollonius of Perga, probably about forty years younger than Archimedes,
and his equal in mathematical genius, was the most fertile and profound
writer among the ancients who treated of geometry. He was called the
Great Geometer. His most important work is a treatise on conic sections,
which was regarded with unbounded admiration by contemporaries, and in
some respects is unsurpassed by any thing produced by modern
mathematicians. He however made use of the labors of his predecessors,
so that it is difficult to tell how far he is original. But all men of
science must necessarily be indebted to those who have preceded them.
Even Homer, in the field of poetry, made use of the bards who had sung
for a thousand years before him; and in the realms of philosophy the
great men of all ages have built up new systems on the foundations which
others have established. If Plato or Aristotle had been contemporaries
with Thales, would they have matured so wonderful a system of
dialectics? Yet if Thales had been contemporaneous with Plato, he might
have added to the great Athenian's sublime science even more than did
Aristotle. So of the great mathematicians of antiquity; they were all
wonderful men, and worthy to be classed with the Newtons and Keplers of
our times. Considering their means and the state of science, they made
as _great_ though not as _fortunate_ discoveries,--discoveries which
show patience, genius, and power of calculation. Apollonius was one of
these,--one of the master intellects of antiquity, like Euclid and
Archimedes; one of the master intellects of all ages, like Newton
himself. I might mention the subjects of his various works, but they
would not be understood except by those familiar with mathematics.

Other famous geometers could also be named, but such men as Euclid,
Archimedes, and Apollonius are enough to show that geometry was
cultivated to a great extent by the philosophers of antiquity. It
progressively advanced, like philosophy itself, from the time of Thales
until it had reached the perfection of which it was capable, when it
became merged into astronomical science. It was cultivated more
particularly by the disciples of Plato, who placed over his school this
inscription: "Let no one ignorant of geometry enter h