no doubt
instrumental later on in determining that theory of the mechanics of
the heavens which we shall see elaborated presently. To have made such
a discovery argues again for the practicality of the mind of Pythagoras.
His, indeed, would seem to have been a mind in which practical
common-sense was strangely blended with the capacity for wide and
imaginative generalization. As further evidence of his practicality,
it is asserted that he was the first person who introduced measures and
weights among the Greeks, this assertion being made on the authority of
Aristoxenus. It will be observed that he is said to have introduced,
not to have invented, weights and measures, a statement which suggests
a knowledge on the part of the Greeks that weights and measures were
previously employed in Egypt and Babylonia.

The mind that could conceive the world as a sphere and that interested
itself in weights and measures was, obviously, a mind of the visualizing
type. It is characteristic of this type of mind to be interested in the
tangibilities of geometry, hence it is not surprising to be told
that Pythagoras "carried that science to perfection." The most famous
discovery of Pythagoras in this field was that the square of the
hypotenuse of a right-angled triangle is equal to the squares of the
other sides of the triangle. We have already noted the fable that
his enthusiasm over this discovery led him to sacrifice a hecatomb.
Doubtless the story is apocryphal, but doubtless, also, it expresses
the truth as to the fervid joy with which the philosopher must have
contemplated the results of his creative imagination.

No line alleged to have been written by Pythagoras has come down to us.
We are told that he refrained from publishing his doctrines, except by
word of mouth. "The Lucanians and the Peucetians, and the Messapians and
the Romans," we are assured, "flocked around him, coming with eagerness
to hear his discourses; no fewer than six hundred came to him every
night; and if any one of them had ever been permitted to see the master,
they wrote of it to their friends as if they had gained some great
advantage." Nevertheless, we are assured that until the time of
Philolaus no doctrines of Pythagoras were ever published, to which
statement it is added that "when the three celebrated books were
published, Plato wrote to have them purchased for him for a hundred
minas."(2) But if such books existed, they are lost to the modern world,