Mars

   ... conveniasi a quella pietra scema
che guarda il ponte, che Fiorenza fesse
vittima nella sua pace postrema.

(Paradiso XVI.145-47)

   ... it was established that Florence,
at the close of her peace, should make a sacrifice
to the broken stone that guards the bridge.

These philosophical musings come from Cacciaguida, whose words are somewhat opaque. In short, Dante’s ancestor is referring to the murder of Buondelmonte de’ Buondelmonti who died here on this spot at the foot of the statue of Mars in 1215. The history of this statue was explained by Boccaccio:

“In order to understand these words, one must know that, according to the opinion of some people, Mars was the lord of the ascendant when the city of Florence was first founded. Consequently, those who founded it, being pagans, took the god Mars as their protector and patron. They had a sandstone sculpture of him, armed and on horseback, made and placed on top of a column in the temple [the Baptistry] that we nowadays call San Giovanni. There he was honored with reverence and sacrifices for as long as paganism lasted in the city. Then, once the truth of the Gospels was sown here and the citizens, having become Christians, abandoned this pagan error, the statue of Mars was removed from the said temple. But since they still felt a little something from this former error, they did not want to have the statue destroyed or thrown away. Instead, they had a pillar set up on the parapet of Ponte Vecchio and had it placed there. [...] This they did because they feared certain prophecies of their ancestors, which were interpreted to mean that the statue had been made in accordance with the stars in such a way that, should it ever be kept in a less than honorable location or be subjected to any act of violence, great harm would befall the city. It remained upon that tower until the time when the city was destroyed by Attila [really Totila]. Then, either because the tower on which it rested collapsed or because it was pushed off by some other cause, the statue of Mars fell into the Arno, where it remained until the city had been rebuilt. Once the city had been restored, during the time of Charlemagne’s empire, it was found and fished out, though no longer wholly intact. From the waist up, Mars’s figure was broken off and the upper part was never recovered. They say that the remaining portion was placed, as written above, upon a pillar on top of Ponte Vecchio. In the year of our Lord 1333, a flood larger than any other in memory (not because of any great rains, but for some other reason) caused the Arno to rise so much that it inundated the whole city and carried away the two bridges downstream along with Ponte Vecchio, the pillar, and the statue, which they afterward neither looked for nor recovered.” (Expositions on Dante’s Comedy 13.lit.98-101)

During one of the Dante lessons in the Badia, according to Benvenuto da Imola (another famous Dante scholar), Boccaccio recalled how, as a child, he had heard old people warn children not to throw stones or mud at the statue.

According to art historians, the ill-omened statue that washed into the Arno probably inspired the portrayal of Mars as a knight on horseback on the Duomo’s bell tower. The original panel is in the Museum of the Duomo, but you can see its substitute on the west side of Giotto’s campanile on the row dedicated to the planets, which is flanked by lion heads.