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There is more difficulty in comprehending how he arrived at the

first term of the series, which is nowhere else mentioned, and

has no reference to any other part of his system. Nor indeed does

the relation of shadows to objects correspond to the relation of

numbers to ideas. Probably Plato has been led by the love of

analogy (Timaeus) to make four terms instead of three, although

the objects perceived in both divisions of the lower sphere are

equally objects of sense. He is also preparing the way, as his

manner is, for the shadows of images at the beginning of the

seventh book, and the imitation of an imitation in the tenth. The

line may be regarded as reaching from unity to infinity, and is

divided into two unequal parts, and subdivided into two more;

each lower sphere is the multiplication of the preceding. Of the

four faculties, faith in the lower division has an intermediate

position (cp.