Guessanym

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ratio

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Guessanym
Ratio

ratio

Depth
2
Use as Polynym Mark Unseen (✓)
Keyword:   two
Context:   Definition 4 makes this more rigorous. It states that a ratio of two quantities exists, when there is a multiple of each that exceeds the other.
Nodes:
    • quantities exists
    • when there is a multiple of each that exceeds the other
Full context:   Definition 3 describes what a ratio is in a general way. It is not rigorous in a mathematical sense and some have ascribed it to Euclid's editors rather than Euclid himself. Euclid defines a ratio as between two quantities of the same type, so by this definition the ratios of two lengths or of two areas are defined, but not the ratio of a length and an area. Definition 4 makes this more rigorous. It states that a ratio of two quantities exists, when there is a multiple of each that exceeds the other. In modern notation, a ratio exists between quantities p and q, if there exist integers m and n such that mp>q and nq>p. This condition is known as the Archimedes property.
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