In a proportion written as a:b = c:d, the means are the middle terms (b and c) and the extremes are the outer terms (a and d). A fundamental property states that the product of the means equals the product of the extremes.
From Latin 'medius' meaning 'middle' and 'extremus' meaning 'outermost'. This terminology was established in classical Greek mathematics, particularly in Euclid's Elements, where proportions were studied extensively in geometric contexts.
The means-extremes property is like a mathematical balance scale - it reveals that proportions have a hidden symmetry where the 'inside' and 'outside' products must be equal! This ancient principle, discovered by the Greeks, still powers modern proportion-solving techniques.
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