and we are obliged to accept the assertions of relatively late writers
as to the theories of the great Crotonian.

Perhaps we cannot do better than quote at length from an important
summary of the remaining doctrines of Pythagoras, which Diogenes himself
quoted from the work of a predecessor.(3) Despite its somewhat inchoate
character, this summary is a most remarkable one, as a brief analysis
of its contents will show. It should be explained that Alexander (whose
work is now lost) is said to have found these dogmas set down in the
commentaries of Pythagoras. If this assertion be accepted, we are
brought one step nearer the philosopher himself. The summary is as
follows:

"That the monad was the beginning of everything. From the monad proceeds
an indefinite duad, which is subordinate to the monad as to its cause.
That from the monad and the indefinite duad proceed numbers. And
from numbers signs. And from these last, lines of which plane figures
consist. And from plane figures are derived solid bodies. And from solid
bodies sensible bodies, of which last there are four elements--fire,
water, earth, and air. And that the world, which is indued with life and
intellect, and which is of a spherical figure, having the earth, which
is also spherical, and inhabited all over in its centre,(4) results from
a combination of these elements, and derives its motion from them; and
also that there are antipodes, and that what is below, as respects us,
is above in respect of them.

"He also taught that light and darkness, and cold and heat, and dryness
and moisture, were equally divided in the world; and that while heat was
predominant it was summer; while cold had the mastery, it was winter;
when dryness prevailed, it was spring; and when moisture preponderated,
winter. And while all these qualities were on a level, then was the
loveliest season of the year; of which the flourishing spring was the
wholesome period, and the season of autumn the most pernicious one. Of
the day, he said that the flourishing period was the morning, and the
fading one the evening; on which account that also was the least healthy
time.

"Another of his theories was that the air around the earth was immovable
and pregnant with disease, and that everything in it was mortal; but
that the upper air was in perpetual motion, and pure and salubrious, and
that everything in that was immortal, and on that account divine. And
that the sun and the moon and the