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While a hand and a foot have many dissimilarities, the analogy focuses on their similarity in having an inner surface.
Medieval lawyers distinguished analogia legis and analogia iuris (see below).
Analogous objects did not share necessarily a relation, but also an idea, a pattern, a regularity, an attribute, an effect or a philosophy.
These authors also accepted that comparisons, metaphors and "images" (allegories) could be used as arguments, and sometimes they called them analogies.
In ancient Greek the word αναλογια (analogia) originally meant proportionality, in the mathematical sense, and it was indeed sometimes translated to Latin as proportio.
From there analogy was understood as identity of relation between any two ordered pairs, whether of mathematical nature or not. Kant argued that there can be exactly the same relation between two completely different objects.
Thomas Cajetan wrote an influential treatise on analogy.