Meaning of "on the wax" from an article in Stanford Encyclopedia of Philosophy

This is obviously a reference to the wax tablets that were used for drafts and note-taking before the invention of paper; after you had made a fair copy onto a roll of papyrus, you could simply smooth over the wax tablet and re-use it. Nowadays we would probably say 'in manuscript', but in ancient times, of course, all writing was in manuscript, so apparently the Stanford author thought this would be a clever alternative.

For the benefit of others looking for the definition of "on the wax", although TimLymington's answer fit's the usage in the question this phrase can also mean "on the rise" (as SomethingDark notes in their comment on the question).

The usage comes from the idiom "wax and wane". The etymology on Wiktionary has further info.

The reference in the Stanford article is to a statement made in Diogenes' Lives...

After doing a CTRL+F on the PDF from Project Gutenberg, this passage, located in book 3 (as per the Stanford ref) reads: XXV. Aristotle says, that the treatises of Plato are something between poems and prose; and Phavorinus says, when Plato read his treatise on the Soul, Aristotle was the only person who sat it out, and that all the rest rose up and went away. And some say that Philip the Opuntian copied out the whole of his books upon Laws, which were written on waxen tablets only. Some people also attribute the Epinomis to him. Euphorion and Panætius have stated that the beginning of the treatise on the Republic was often altered and re-written; and that very treatise, Aristoxenus affirms, was found almost entire in the Contradictions of Protagoras; and that the first book he wrote at all was the Phædrus; and indeed that composition has a good many indications of a young composer. But Dicæarchus blames the whole style of that work as vulgar.