Squeeze enough juice from 3 oranges to measure 1 cup.
Cook sugar in a 1 1/2-quart heavy saucepan over medium-high, stirring occasionally with a fork, until the sugar begins to turn golden brown, about 10 minutes. Tilt pan and carefully add orange juice (caramel will harden and vigorously steam). Simmer, stirring, until caramel is completely dissolved, about 2 minutes.
Cut peel, including all white pith, from remaining 6 oranges with a sharp paring knife and cut each orange crosswise into thirds.
Heat 1/3 of butter (1 teaspoon) in a 12-inch nonstick skillet over moderately high heat until hot but not smoking, then saute 6 orange slices until golden, 2 to 3 minutes on each side. Transfer to a plate. Saute remaining orange slices in butter in same manner, wiping out skillet between batches if necessary. Return all orange slices to skillet along with caramel sauce and cook over moderate heat until heated through, about 1 minute. Sprinkle the slices with cinnamon.