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PYTHAGOREAN GEOMETRY 
may be described thus. The universe is spherical in shape 
and finite in size. Outside it is infinite void which enables 
the universe to breathe, as it were. At the centre is the 
central fire, the Hearth of the Universe, called by various 
names, the Tower or Watch-tower of Zeus, the Throne of 
Zeus, the House of Zeus, the Mother of the Gods, the Altar, 
Bond and Measure of Nature. In this central fire is located 
the governing principle, the force which directs the movement 
and activity of the universe. In the universe there revolve 
in circles about the central fire the following bodies. Nearest 
to the central fire revolves the counter-earth, which always 
accompanies the earth, the orbit of the earth coming next to 
that of the counter-earth; next to the earth, reckoning in 
order from the centre outwards, comes the moon, next to the 
moon the sun, next to the sun the five planets, and last of 
all, outside the orbits of the five planets, the sphere of the 
fixed stars. The counter-earth, which accompanies the earth 
and revolves in a smaller orbit, is not seen by us because 
the hemisphere of the earth on which we live is turned away 
from the counter-earth (the analogy of the moon which 
always turns one side towards us may have suggested this); 
this involves, incidentally, a rotation of the earth about its 
axis completed in the same time as it takes the earth to 
complete a revolution about the central fire. As the latter 
revolution of the earth was held to produce day and night, 
it is a natural inference that the earth was supposed to 
complete one revolution round the central fire in a day and 
a night, or in twenty-four hours. This motion on the part of 
the earth with our hemisphere always turned outwards would, 
of course, be equivalent, as an explanation of phenomena, 
to a rotation of the earth about a fixed axis, but for the 
parallax consequent on the earth describing a circle in space 
with radius greater than its own radius; this parallax, if we 
may trust Aristotle, 1 the Pythagoreans boldly asserted to be 
negligible. The superfluous thing in this system is the 
introduction of the counter-earth. Aristotle says in one 
place that its object was to bring up the number of the 
moving bodies to ten, the perfect number according to 
1 Arist. T)e caelo, ii. 18, 298 b 25-30.