Practice question · True or false
The two middle segments of Plato’s divided line are equal whatever ratio is used to divide it.
Hints
- Work through the algebra for an arbitrary ratio.
- Both middle segments come out proportional to the same product, so they are equal regardless.
Show the answer
True
Why
True, it holds for every ratio, which is a genuinely elegant fact. Plato exploits the equality to mark belief and reasoning as the two intermediate cognitive states, neither highest nor lowest.
Practise The Minor Socratics and Plato
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