All 4 Uses

prosperous
in
The Hobbit
(Edited)

By some curious chance one morning long ago in the quiet of the world, when there was less noise and more green, and the hobbits were still numerous and prosperous, and Bilbo Baggins was standing at his door after breakfast smoking an enormous long wooden pipe that reached nearly down to his woolly toes (neatly brushed) — Gandalf came by.
p. 5.4

prosperous = doing well
They did not hate dwarves especially, no more than they hated everybody and everything, and particularly the orderly and prosperous; in some parts wicked dwarves had even made alliances with them.
p. 59.8

prosperous = wealthy
They still throve on the trade that came up the great river from the South and was carted past the falls to their town; but in the great days of old, when Dale in the North was rich and prosperous, they had been wealthy and powerful, and there had been fleets of boats on the waters, and some were filled with gold and some with warriors in armour, and there had been wars and deeds which were now only a legend.
p. 176.7

prosperous = successful (doing well)
And Lake-town was refounded and was more prosperous than ever, and much wealth went up and down the Running River; and there was friendship in those parts between elves and dwarves and men.
p. 276.2 *

prosperous = financially successful

Definitions:

(1) (prosperous)
successful or good -- especially with regard to finances or wealth
(2) (meaning too rare to warrant focus)