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These entities he called Ideas,I have translated ἰδέα by Idea and εἶδος by Form wherever Aristotle uses the words with reference to the Platonic theory. Plato apparently uses them indifferently, and so does Aristotle in this particular connection, but he also uses εἶδος in the sense of form in general. For a discussion of the two words see Taylor, Varia Socratica, 178-267, and Gillespie, Classical Quarterly, 6.179-203. and held that all sensible things are named afterFor this interpretation of παρὰ ταῦτα see Ross’s note ad loc. them sensible and in virtue of their relation to them; for the plurality of things which bear the same name as the Forms exist by participation in them. (With regard to the participation, it was only the term that he changed; for whereas the Pythagoreans say that things exist by imitation of numbers, Plato says that they exist by participation—merely a change of term.
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As to what this participation or imitation may be, they left this an open question.)
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Further, he states that besides sensible things and the Forms there exists an intermediate class, the objects of mathematics,i.e. arithmetical numbers and geometrical figures. which differ from sensible things in being eternal and immutable, and from the Forms in that there are many similar objects of mathematics, whereas each Form is itself unique.
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Now since the Forms are the causes of everything else, he supposed that their elements are the elements of all things. Accordingly the material principle is the Great and Small, and the essence 〈or formal principle〉 is the One, since the numbers are derived from the Great and Small by participation in the the One.
