What are the third and fourth ways in which William Charlton says "being" is used in Aristotle?

Question

I'm reading William Charlton's commentary on Aristotle's Physics I and II, and I am having trouble with the following:

Aristotle recognizes four main "ways in which a thing might be said" i.e. types of grounds in which the same expression might be applied to different things...

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First, different things might be called something on the same grounds, "in accordance with one thing "(Met, Z 1030b3) ...

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Second, things may be called something because they exceed or fall short of some norm (Phys. III 200b29)

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Third, things might be called something by analogy (E.N. I 1096b28, cf. Met. Omega, 1048a37)

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Finally, things may be called something on the ground that they "are related to a single thing" (Met, Γ 1003a33-4) in various ways.

I'm having trouble understanding the third and the fourth ways.

Answer 1

St. Thomas Aquinas gives the various senses of "being" in his commentary on Aristotle's Metaphysics 1003^a–1003^b22 [535.]:

He [Aristotle] accordingly says, first, that the term b̲e̲i̲n̲g̲,̲ ̲o̲r̲ ̲w̲h̲a̲t̲ ̲i̲s̲,̲ ̲h̲a̲s̲ ̲s̲e̲v̲e̲r̲a̲l̲ ̲m̲e̲a̲n̲i̲n̲g̲s. But it must be noted that a term is predicated of different things in various senses. Sometimes it is predicated of them according to a meaning which is entirely the same, and then it is said to be predicated of them univocally, as animal is predicated of a horse and of an ox. Sometimes it is predicated of them according to meanings which are entirely different, and then it is said to be predicated of them equivocally, as dog is predicated of a star and of an animal. And sometimes it is predicated of them according to meanings which are partly different and partly not (different inasmuch as they imply different relationships, and the same inasmuch as these different relationships are referred to one and the same thing), and then it is said “to be predicated analogously,” i.e., proportionally, according as each one by its own relationship is referred to that one same thing.