i. e. the flaming, a river in the lower world, is described as a son of Cocytus; but he is more commonly called Pyriphlegethon.
It flowed with fire that burned but did not consume fuel. In the Divine Comedy the river is made of boiling blood and is part of the seventh circle of hell, containing the shades of tyrants, murderers, robbers and those guilty of sins involving violence against others. Virgil mentions Phlegethon with the other infernal rivers in the Aeneid.
The Circles of Hell
Lo! to the secret shadows I retire,
To pay my penance till my years expire.
Proceed, auspicious prince, with glory crown'd,
And born to better fates than I have found."
He said; and, while he said, his steps he turn'd
To secret shadows, and in silence mourn'd.
The hero, looking on the left, espied
A lofty tow'r, and strong on ev'ry side
With treble walls, which Phlegethon surrounds
Whose fiery flood the burning empire bounds;
And, press'd betwixt the rocks, the bellowing noise resounds
Wide is the fronting gate, and, rais'd on high
With adamantine columns, threats the sky.
From The Aeneid By Virgil Book VI