The phrase "set down on paper" is correct and usable in written English.
You can use it when you want to indicate that an idea has been written down. For example, "I decided to set down my thoughts on paper before I presented them to the group."
Whereas the First's soundworld is in no way extraordinary, here Gergiev and his players could revel in some of the most luscious orchestration ever set down on paper, working as one to press the piece steadily towards its vertiginous climax.
Hamlet is one of the most dangerous things ever set down on paper.
Flowers knew the silent girl read voraciously but, as she told her over tea and cookies one afternoon, words "mean more than what is set down on paper.
Set down on paper, they are astonishing, laughable.
This confession was set down on paper the next day, and petitioner signed it after he had been committed by a magistrate.
In secret, he set down on paper as many poems as he could recall — about 400 — which took three days of continuous writing.
It comes two ways: to stay (sliced in half through wax-paper wrapper and set down on a small plastic plate, with a moist towelette and two chocolate mints) or to go (in a paper bag with all the aforementioned except the plate and the slicing).
It's the story of an entire parish, set down not on paper or in stone, but on wood.
As I set down my papers on the living room table for our interview, Yeni Gomez apologized while she cleared the space.
Set down a large sheet of waxed paper or a pastry cloth with some flour on it.
So on the first day of camp, when Pettey, who had never coached a position before in the N.F.L., met his tight ends, he told them to set down their goals on paper.
