PHYSICAL SCIENCES IX ANCIENT GREECE. 400 



which the Regular Solids are assigned as the forms of the Elements of 

 which the Universe is composed. This curious branch of mathematics, 

 Solid Geometry, had been pursued with great zeal by Plato and his 

 friends, and with remarkable success. The five Regular Solids, the 

 Tetrahedron or regular Triangular Pyramid, the Cube, the Octahedron, 

 the Dodecahedron, and the Icosahedron, had been discovered; and 

 the remarkable theorem, that of regular solids there can be just so 

 many, these and no others, was known. And in the Timceus it is as- 

 serted that the particles of the various elements have the forms of these 

 solids. Fire has the Pyramid ; Earth has the Cube ; Water the Octa- 

 hedron ; Air the Icosahedron ; and the Dodecahedron is the plan of 

 the Universe itself. It was natural that when Plato had learnt that 

 other mathematical properties had a bearing upon the constitution of 

 the Universe, he should suppose that the singular property of space, 

 which the existence of this limited and varied class of solids implied, 

 should have some corresponding property in the Universe, which exists 

 in space. 



We find afterwards, in Kepler and others, a recurrence to this as- 

 sumption ; and we may say perhaps that Crystallography shows us 

 that there are properties of bodies, of the most intimate kind, which 

 involve such spatial relations as are exhibited in the Regular Solids. 

 If the distinctions of Crystalline System in bodies were hereafter to be 

 found to depend upon the chemical elements which predominate in 

 their composition, the admirers of Plato might point to his doctrine, 

 of the different form of the particles of the different elements of the 

 Universe, as a remote Prelude to such a discovery. 



But the mathematical doctrines concerning the parts and elements 

 of the Universe are put forwards by Plato, not so much as assertions 

 concerning physical facts, of which the truth or falsehood is to be de- 

 termined by a reference to nature herself. They are rather propounded 

 as examples of a truth of a higher kind than any reference to observa- 

 tion can give or can test, and as revelations of principles such as must 

 have prevailed in the mind of the Creator of the Universe ; or else as 

 contemplations by which the mind of man is to be raised above the 

 region of sense, and brought nearer to the Divine Mind. In the Ti- 

 mceus these doctrines appear rather in the former of the two lights ; as 

 an exposition of the necessary scheme of creation, so far as its leading 

 features are concerned. In the seventh Book of the Polity, the same 

 doctrines are regarded more as a mental discipline ; as the necessary 

 study of the true philosopher. But in both places these mathematical 



