Selection from St. Thomas Aquinas, On the Principles of Nature
Trans. R. A. Kocourek, cc. 46-49.
Something is predicated of many things in three ways: univocally, equivocally and analogically. Something is predicated univocally according to the same name and the same nature, i.e., definition, as animal is predicated of man and of ass, because each is called animal and each is a sensible, animated substance, which is the definition of animal. That is predicated equivocally which is predicated of some things according to the same name but according to a different nature, as dog is said of the thing that barks and of the star in the heavens, which two agree in the name but not in the definition or in signification, because that which is signified by the name is the definition, as is said in the fourth book of the Metaphysics. That is said to be predicated analogically which is predicated of many whose natures are diverse but which are attributed to one same thing, as health is said of the animal body, or urine and of food, but it does not signify entirely the same thing in all three; it is said of urine as a sign of health, of body as of a subject and of food as of a cause. But all these natures are attributed to one end, namely to health.
Sometimes those things which agree according to analogy, i.e., in proportion, comparison or agreement, are attributed to one end, as was plain in the preceding example of health. Sometimes they are attributed to one agent, as medical is said of one who acts with art, of one who acts without art, as a midwife, and even of the instruments; but it is said of all by attribution to one agent which is medicine. Sometimes it is said by attribution to one subject, as "being" is said of substance, quantity, quality and the other predicaments, because it is not entirely for the same reason that substance is being, and quantity and the others. Rather, all are called being in so far as they are attributed to substance which is the subject of the others.
Therefore being is said primarily of substance and secondarily of the others. Therefore "being" is not a genus of substance and quantity because no genus is predicated of its species according to prior and posterior; rather, "being" is predicated analogically. This is what we mean when we say that substance and quantity differ generically but are the same analogically.
Therefore the form and matter of those things which are numerically the same are themselves likewise numerically the same, as are the form and matter of Tullius and Cicero. The matter and form of those things which are specifically the same and numerically diverse are not the same numerically, but specifically, as the matter and form of Socrates and Plato. Likewise, the matter and form of those things which are generically the same, as the soul and body of an ass and a horse differ specifically but are the same generically; likewise, the principles of those things which agree only analogically or proportionally are the same only analogically or proportionally, because matter, form and privation or potency and act are the principles of substance and of the other genera. However, the matter, form and privation of substance and of quantity differ generically, but they agree according to proportion only, in so far as the matter of substance is to substance, in the nature of matter, as the matter of quantity is to quantity; still, just as substance is the cause of the others, so the principles of substance are the principles of all the others.