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Triangular Relationships and Most Beautiful Bodies: On the Significance of απειρα at Timaeus 57d5, and on the Number of Plato's Elementary Triangles

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image of Mnemosyne

According to an interpretation first proposed by Cornford (1937), Plato intends that the many different triangles or squares required for the construction of 'elements' in the Timaeus are all built up using multiples of two elemental triangles, the στοιχεια. An alternative view, which also has wide acceptance, is that there are many elemental triangles, of different sizes; in an extreme form of this there is an unlimited or even infinite variety of the triangles. These views are analysed, and it is concluded that Cornford's interpretation, despite some problems, is still the best currently available.

Affiliations: 1: Trinity College, Chemistry Department, Dublin 2, Ireland;, Email:


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