nce the
conclusion, as PLATO put it, that "this (the regular dodecahedron) the
Deity employed in tracing the plan of the Universe."(2b) Hence also
the high esteem in which the pentagon was held by the Pythagoreans. By
producing each side of this latter figure the five-pointed star (fig.
9), known as the pentagram, is obtained. This was adopted by the
Pythagoreans as the badge of their Society, and for many ages was held
as a symbol possessed of magic powers. The mediaeval magicians made use
of it in their evocations, and as a talisman it was held in the highest
esteem.

(2a) _Cf_. PLATO: The Timaeus, SESE xxviii--xxx.

(1) In reference to this matter FRANKLAND remarks: "In those early days
the innermost secrets of nature lay in the lap of geometry, and the
extraordinary inference follows that Euclid's _Elements_, which are
devoted to the investigation of the regular solids, are therefore in
reality and at bottom an attempt to 'solve the universe.' Euclid,
in fact, made this goal of the Pythagoreans the aim of his
_Elements_."--_Op. cit_., p. 35.

(2b) _Op. cit_., SE xxix.

Music played an important part in the curriculum of the Pythagorean
Brotherhood, and the important discovery that the relations between
the notes of musical scales can be expressed by means of numbers is a
Pythagorean one. It must have seemed to its discoverer--as, in a sense,
it indeed is--a striking confirmation of the numerical theory of the
Cosmos. The Pythagoreans held that the positions of the heavenly bodies
were governed by similar numerical relations, and that in consequence
their motion was productive of celestial music. This concept of "the
harmony of the spheres" is among the most celebrated of the Pythagorean
doctrines, and has found ready acceptance in many mystically-speculative
minds. "Look how the floor of heaven," says Lorenzo in SHAKESPEARE'S
_The Merchant of Venice_--

"... Look how the floor of heaven
Is thick inlaid with patines of bright gold:
There's not the smallest orb which thou behold's"
But in his motion like an angel sings,
Still quiring to the young-eyed cherubins;
Such harmony is in immortal souls;
But whilst this muddy vesture of decay
Doth grossly close it in, we cannot hear it."(1)

(1) Act v. scene i.

Or, as KINGSLEY writes in one of his letters, "When I walk the fields I
am oppressed every now and then with an innate feeling that everything
I see has a meaning, if I could but understand i