Plato has no belief in 'liberty of prophesying'; and having guarded against the dangers of lyric poetry, he remembers that there is an equal danger in other writings.

He cannot leave his old enemies, the Sophists, in possession of the field; and therefore he proposes that youth shall learn by heart, instead of the compositions of poets or prose writers, his own inspired work on laws.

These, and music and mathematics, are the chief parts of his education.
Mathematics are to be cultivated, not as in the Republic with a view to the science of the idea of good,--though the higher use of them is not altogether excluded,--but rather with a religious and political aim.
They are a sacred study which teaches men how to distribute the portions of a state, and which is to be pursued in order that they may learn not to blaspheme about astronomy.

Against three mathematical errors Plato is in profound earnest.

First, the error of supposing that the three dimensions of length, breadth, and height, are really commensurable with one another.