The other doubles I've solved completely are 19, 21, 25 and 26dn - happy to help with the treated words in these, as follows: 19dn = CE and fluter (but the parsing of the latter mystifies me); 21dn = hairline and trebling; 25dn = commander and weigh; 26dn = sold and charmed.
What infuriates me about this puzzle is that I have the title, the quote and its alteration, part of the source and the systematic method (which incidentally appears to be randomly assigned to the clues, unless I've really fouled up - I took 'systematically' to mean 'related to the methods used by this branch of maths' as opposed to 'specifically' to each clue).
But, the infuriation: I *know* from the quote what all the letters are that give rise to the treatments, but *I still can't make sense of 16 of them*. Slogging away when all the PDMs have happened seems to me to be counter to the enjoyment of a puzzle. I know the Great Man is revered, but I feel he's broken a precept set by Ximenes, that the solver must always have a fair chance of defeating the setter.