The triangle inequality and Heron's problem | Euclid's Elements Book 1 Proposition 20

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euclid elements math maths mathematics greek greece ancient heron heron's problem heron's theorem

The correct Heron argument:

1. AE + EB' <= AP + PB' by the triangle inequality;
2. EB' = EB and PB' = PB by construction;
3. AE + EB <= AP + PB by substitution. QED.

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