In the book Lie algebra, Humphreys, during classification of Dynkin diagrams, arrives at the equation over positive integers: $$\frac{1}{p} + \frac{1}{q} +\frac{1}{r}>1$$ and makes a comment in bracket
(This inequality, by the way, has a long mathematical history)
I suddenly stopped at that classification, and wondered How long back the history goes for this inequality?