If God and creatures are radically different in being, then no word that applies to creatures can apply to God in the same sense — to say 'God is wise' would be equivocal, as meaningless as calling a bank account and a riverbank both 'bank.' But if words apply to God and creatures in exactly the same sense — univocally — then God is reduced to a very powerful version of a creature, and the divine transcendence is lost. Aquinas accepts neither horn of this dilemma.
Analogy occupies the middle ground. In the analogy of attribution, a term is applied primarily to one thing and secondarily to others in relation to it: 'healthy' applies primarily to a healthy organism, and derivatively to a healthy diet insofar as it promotes health. In the analogy of proper proportionality, a term applies to different things according to each thing's proper mode of being: wisdom in God is what wisdom is proportioned to divine being; wisdom in a human is what wisdom is proportioned to human nature. The relationship between the two is one of likeness without sameness.
The metaphysical basis of analogy is Aquinas's doctrine of participation: all creaturely perfections — goodness, wisdom, being, life — are participated forms of what God possesses eminently and without limit. Creatures do not merely resemble God from a distance; their real goodness, real wisdom, and real existence are effects of and participations in divine perfection. This is why the same terms apply, though not in the same measure or manner. Language ascends toward God by purifying its terms of creaturely limitation while affirming the genuine, if imperfect, likeness that runs from effect back to cause.
The doctrine of analogical predication is developed across multiple texts, including Summa Theologiae I, Q.13, and the Disputed Questions on the Power of God. The source lies in Aristotle's Categories, transformed by Aquinas's own metaphysics of participation.