War with Alba Longa
Livy recounts this tale in the first book of his History of Rome. During the roman king Tullus Hostilius' war with the neighboring city of Alba Longa, it was agreed that rather than fighting a costly war between their armies, the conflict would be settled by a fight to the death between the Horatii and the Curiatii: male triplets from Alba Longa. The combatants met on the field between the lines of the two armies and, with the attention of both armies and their cities upon them, the contest began.
As the fight progressed, all three Curiatii, were wounded, but they had killed two of the Horatii in the process. The lone survivor for Rome, Publius was uninjured, but surrounded by the Curiatii. Realizing that he could not defeat them alone against all three together, he begins to run across the field hoping that they'll follow. They do so, as fast their individual injuries permit. This plays perfectly into Publius' plan. After running a fair distance, he turns and sees that his opponents are far separated from one another. He launches a furious attack on the closest Curiatius and slays him.
The Roman spectators, who had been sure of defeat a moment ago, were now cheering wildly as the Albans were shouting at the Curatii to regroup in the face of Publius' oncoming assault. Despite nearly reaching one another, The Horatius strikes down the second Curiatius while he and his brother are still separated. The final Curiatius is physically spent from his wounds and exhausted from the chase. His hope has been crushed by watching both of his brothers die. He manages to unsteadily stand his ground and faces the Horatius, who is heartened by his wildly successful strategy and confident of his imminent victory. Publius declares that the first two Curiatii were killed to avenge his fallen brothers and the last would be "offered to the shades" for the Roman cause and their rule over the Albans. He thrusts his sword down the Alban's throat and leaves him naked after stripping his armor.
Mettus, the leader of the Albans honors the treaty and accepts Roman rule.
The Horatius' return to Rome
The victorious Horatius returned to Rome with the spoils of his victory. His sister, who had been engaged to one of the Curiatii, cried out in grief when she learned he had fallen. Proclaiming: "So perish any Roman woman who mourns the enemy", Publius killed his sister. For his crime, he was condemned to death. On the advice of a jurist named Tullus, Publius appealed to one of the popular assemblies. In defense of his son, the Horatius' father, also Publius, spoke of the recent victory and entreated them to spare his last surviving son (his fourth son, a brother of the Horatii had also passed). The assembly was persuaded and Publius' sentence was commuted. This may be the source of the Roman tradition of allowing the condemned to appeal their sentences to the populace. Publius the elder was required to offer a sacrifice to atone for his son's crime and from that time forward, the the Horatia family made it a tradition to offer the same. The spoils of the victory were hung in a place that became known as Pila Horatia.
Instead of executing Publius, a wooden beam was erected on the slope of the Oppian Hill, which was called the Sororium Tigillum (Sister's Beam). It symbolized a yoke, under which Publius the younger was made to pass. It remained standing long after his death.