ἀναλογία

Analogia (ἀναλογία) meant 'proportion' in Greek mathematics — ana ('according to') plus logos ('ratio, reason'). When Euclid wrote that 2:4 is analogous to 3:6, he meant the ratios were equal. The word was numerical before it was literary. It described a relationship between quantities, not ideas.

Aristotle stretched the word. In the Poetics, he argued that analogy was the basis of metaphor: 'old age is to life as evening is to day.' The proportional structure remained — A is to B as C is to D — but now the terms could be anything. Two things that shared no properties could be linked if they occupied the same structural position in their respective domains.

Latin took analogia directly from Greek. Renaissance scholars then developed it into a full theory of reasoning. Analogy became one of the primary ways humans learn: understanding the unfamiliar by mapping it onto the familiar. The heart is a pump. The atom is a solar system. The brain is a computer. Each analogy eventually breaks down, but not before doing real cognitive work.

English adopted analogy in the 1530s. It kept both meanings — the mathematical proportion and the rhetorical comparison. Scientists, lawyers, teachers, and children all reason by analogy, often without knowing it. When a four-year-old says 'my tummy is a washing machine,' that child is doing exactly what Aristotle described.