"In Greek theoretical mathematics (as distinguished from practical or commercial arithmetic) a fraction that we would write as a/b was not regarded as a number, as a single entity, but as a relationship or a : b between the whole numbers a and b. Thus the ratio a : b was, in modern terms, simply an ordered pair, rather than a rational number. ... More formally, a : b = c : d provided [a/b and c/d are both integral multiples of some p/q, i.e.,] there exist integers p, q, m, n such that a = mp, b = mq, c = np, d = nq."
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C. H. Edwards, Jr., The Historical Development of the Calculus (1979)
https://en.wikiquote.org/wiki/History_of_mathematics
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History of mathematics
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