Paolo Ruffini (1765–1822) published his Riflessioni intorno alla soluzione delle equazioni algebraiche in 1813.
The first page of instruction:
The images above are provided courtesy of Columbia University Libraries, George Arthur Plimpton Collection.
Editor's note: For images from Ruffini's Teoria generale delle equazioni, containing his proof that polynomial equations of degree greater than four do not in general have algebraic solutions for their roots, see "Mathematical Treasure: Ruffini's Theory of Equations" here in Convergence.