The Carthiginians were lined up in a convex crescent opposed to the Roman forces, 40,000 infantry lined up in front, with 10,000 cavalry to the side next to the river.
http://en.wikipedia.org/wiki/Battle_of_Cannae MacDonald, John, Great Battlefields of the World, 1984, pg 10, MacMillan Publishing Company
The Romans under the consuls Lucius Aemilius Paullus and Gaius Terentius Varro began to line up in their legions, ready to march on the concave formation of Carthiginians. They outnumbered them almost 2 to 1.
The Roman cavalry attacked from the left flank against the Numidian horsemen. They would not be able to penetrate early on.
Menawhile, Hannibal ordered the cavalry on the left side to engage the opposing Roman cavalry on their flank. Eventually they were able to penetrate and send the Roman elite cavalry on this side scattering.
http://en.wikipedia.org/wiki/Battle_of_Cannae MacDonald, John, Great Battlefields of the World, 1984, pg 10-12, MacMillan Publishing Company
Roman infantry advances inward, supremely confident in victory despite the lack of progress on the cavalry flanks. However the conditions were bad thanks to winds from the southwest, choking dust blowing in the faces of the Romans as they rushed inward toward the front line.
What was once a concave formation now appeared exactly the opposite, as African soldiers lined up on the outer flanks of the Roman front and Hannibal kept the Spaniards and Gauls steadily retreating as the Romans rushed toward the center.
As the Roman cavalry on their right flank broke and ran, the heavy Carthaginian horses charged to the rear of the advancing Roman infantry, with some assisting their Numidian cavalry on the other side, the others getting ready to complete the encirclement of the Roman troops.
As the heavy cavalry from the right advanced to the rear of the Roman advance, the lighter Numidian horseman began to move into action against Varro's allied cavalry, mauling them and sending them fleeing into the hills.
The Romans began to box themselves into the center and race further inside, sure that the Carthaginian infantry in front of them were retreating and on the verge of defeat
The weaker Gaul and Spaniard columns began to further retreat and give the Romans the center. The veteran African infantry columns, however, stood their ground on the flanks, as the Romans slowly began to penetrate the weaker center, creating a U-shaped defensive front by the Carthaginians. They moved to encircle the Romans on their flanks and attack at the sides.
As the Romans advanced further, Hannibal ordered the African infantry on the flanks to advance on the Roman sides. The Carthaginian cavalry attacked the Roman rear.
The trapped Romans were enclosed in a pocket with no means of escape. The Carthaginians created a wall and began destroying the entrapped Romans as discussed earlier. Polybius claims that, "as their outer ranks were continually cut down, and the survivors forced to pull back and huddle together, they were finally all killed where they stood."
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