In this work, Viviani reconstructed an ancient study of conic sections by Aristaeus the Elder (4th century B.C.E.). Viviani became Galileo’s student and assistant in 1639. In 1690, at the entrance to his residence in Florence, Viviani erected a public monument to Galileo which contributed to the rehabilitation of Galileo’s reputation. To the left and right of a bust of Galileo appear emblems of the satellites of Jupiter and the parabolic motion of projectiles. Two large cartouches on either side display inscriptions honoring Galileo, which are transcribed in this work.