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Wellsprings
mathematics

Ratio & Proportion

λόγος καὶ ἀναλογία

A theory of when four magnitudes share 'the same ratio' — rigorous enough to handle even quantities no number could express.

Greek mathematics built a careful theory of ratio and proportion, one that defined when four magnitudes stand 'in the same ratio' — and did so even for incommensurable quantities, without leaning on numbers at all. Its rigorous form is the achievement of Eudoxus of Cnidus (4th century BCE), preserved in Book V of Euclid's Elements. This definition of equal ratios underpins all proportional reasoning in Greek geometry and anticipated the modern rigorous treatment of the real numbers.

Where this idea shows up

30 Greek sources

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