English example sentences with "ratios"

During Europe's Renaissance, artists like Leonardo da Vinci recognized math's importance in painting and the ancient Greeks investigated musical scales in terms of numerical ratios.
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The utility of a thing grows less as the quantity of it increases, and it is the utility of the last increment of supply, or the marginal utility, that determines the subjective value of the whole supply, and it is the ratios between these subjective values that determine exchange values.
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