their own heart and have seen nothing.

And this was, it must be said, the outcome of all the Ptolemaean
appliances.

In Physics they did little. In Art nothing. In Metaphysics less than
nothing.

We will first examine, as the more pleasant spectacle of the two, that
branch of thought in which some progress was really made, and in which
the Ptolemaic schools helped forward the development of men who have
become world-famous, and will remain so, I suppose, until the end of
time.

Four names at once attract us: Euclid, Aristarchus, Eratosthenes,
Hipparchus. Archimedes, also, should be included in the list, for he
was a pupil of the Alexandrian school, having studied (if Proclus is to
be trusted) in Egypt, under Conon the Samian, during the reigns of two
Ptolemies, Philadelphus and Euergetes.

Of Euclid, as the founder (according to Proclus) of the Alexandrian
Mathematical school, I must of course speak first. Those who wish to
attain to a juster conception of the man and his work than they can do
from any other source, will do well to read Professor De Morgan's
admirable article on him in "Smith's Classical Dictionary;" which
includes, also, a valuable little sketch of the rise of Geometric
science, from Pythagoras and Plato, of whose school Euclid was, to the
great master himself.

I shall confine myself to one observation on Euclid's genius, and on the