Polybius, Book 15, Chapters 9-19
 
Note that I have placed these secions out of their original order, so that they correspond to the parallel text in Livy (which is your set text).

Livy, Book 30, Chapters 32-36

9.1. After this conversation, which held out no hopes of reconciliation, the two generals parted from each other.
2. On the following morning at daybreak they led out their armies and opened the battle, the Carthaginians fighting for their own safety and the dominion of Africa, and the Romans for the empire of the world.  3. Is there anyone who can remain unmoved in reading the narrative of such an encounter?  4. For it would be impossible to find more valiant soldiers, or generals who had been more successful and were more thoroughly exercised in the art of war, nor indeed had Fortune ever offered to contending armies a more splendid prize of victory, since the conquerors would not be masters of Africa and Europe alone, but of all those parts of the world which now hold a place in history; as indeed they very shortly were.

31.10. Peace negotiations had clearly broken down. They each returned to their own armies and reported that since words had failed, they must settle the matter with swords instead, and leave the fortunes of battle in the lap of the gods.  32.1. When they returned to camp, both generals ordered their soldiers to prepare for battle and stiffen their sinews for the final struggle. For if they won and the luck was with them, they would be victors not just for a day, but forever after.  32.2. Next day, before night fell, they would know whether Rome or Carthage would make laws for all the nations; the reward for victory was not just Italy or Africa, but all the world. But for those that lost the battle, the risk equalled the reward. 3 2.3. For the Romans, there would be no quick escape route home, here in an unfamiliar foreign land; for Carthage, with their last hope gone, immediate destruction loomed close at hand.
32.4. And so, next day, they reached the moment of decision.
The two most famous generals, the two most powerful armies of the two richest nations upon earth, came to do battle, destined either to double or destroy the countless battle honours they had previously won. 
32.5. Hope sometimes filled their hearts, and sometimes terror. They gazed at the battle lines, first their own and then the enemy’s, weighing by eye not number the strength of each, sometimes with hope, sometimes with growing fear, while their generals sought by advice and exhortation to supply whatever grounds for hope might not have naturally occurred to them already

11.6. Hannibal himself went the round of his own troops, begging and imploring them to remember their comradeship of seventeen years and the number of the battles they had previously fought against the Romans.  7. "In all these battles," he said, "you proved so invincible that you have not left the Romans the smallest hope of ever being able to defeat you.  8. Above all the rest, and apart from your success in innumerable smaller engagements, keep before your eyes the battle of the Trebia fought against the father of the present Roman general, bear in mind the battle of the Trasimene against Flaminius, and that of Cannae against Aemilius,  9. battles with which the action in which we are about to engage is not worthy of comparison either in respect to the numbers of the forces engaged or the courage of the soldiers."  10. He bade them, as he spoke thus, to cast their eyes on the ranks of the enemy. Not only were they fewer, but they were scarcely a fraction of the forces that had formerly faced them, and for courage they were not to be compared with those.  11. For then their adversaries were men whose strength was unbroken and who had never suffered defeat, but those of to‑day were some of them the children of the former and some the wretched remnant of the legions he had so often vanquished and put to flight in Italy.  12. Therefore he urged them not to destroy the glorious record of themselves and their general, but, fighting bravely, to confirm their reputation for invincibility.

32.6. The Carthaginian [Hannibal] reminded them of all they had achieved in Italy over those sixteen years, all the Roman generals they had slain, all the armies they had destroyed; and as he came to individual soldiers, heroes of particular battles, he would remind them of the honours each had won.

32.7. Scipio recalled the wars in the Spains and recent battles in Africa, and the enemy’s admission that their fear had given them no option but to sue for a peace, which their habitual treachery guaranteed they could not keep. 
32.8. In addition, since his negotiations with Hannibal were held in secret, he could make up anything he liked about them.  32.9. “I truly believe”, he said, “that as our enemies come out to battle, the gods are sending them the self same omens as those they sent to our ancestors before their final victory in the First Punic War, in the Aegatian Islands (241BC). 
32.10. This war is coming to an end; our toil is almost done; the wealth of Carthage lies within our grasp ; we are going back, my soldiers, to our parents, our children, our wives, and all the gods of home.” The author Celsus tells us that as he spoke his whole stance and demeanour were so uplifted, so transported with happiness that you might have thought that he had already won the day.

9.6. Scipio drew up his army in the following fashion.  7. In front he placed the hastati with certain intervals between the maniples and behind them the principes, not placing their maniples, as is the usual Roman custom, opposite to the intervals separating those of the first line, but directly behind these latter at a certain distance owing to the large number of the enemy's elephants.  8. Last of all he placed the triarii. On his left wing he posted Gaius Laelius with the Italian horse, and on the right wing Massanissa with the whole of his Numidians.  9. The intervals of the first maniples he filled up with the cohorts of velites, ordering them to open the action, 10 and if they were forced back by the charge of the elephants to retire, those who had time to do so by the straight passages as far as the rear of the whole army, and those who were overtaken to right or left along the intervals between the lines.

33.1. Scipio now marshalled his troops for battle: in front the spearmen (hastati), and behind them the second rankers (principes), and then the third row men (triarii), closing up the rear. He did not deploy his cohorts in conventional close order in front of their individual standards; instead he organised them by maniples , with wide passages in between each, so that the enemy’s elephants would not disrupt the battle lines as they charged.  33.2. He put Laelius in command of the Italian cavalry on the left wing. He had been his deputy commander (legatus), but for the current year was a special quaestor, appointed by senatorial decree instead of by lot. Masinissa and the Numidians were on the opposite wing, on the right.  33.3. He filled the open passages between the maniples with platoons of skirmishers (velites), who were lightly armed in those days, and gave them strict orders to retreat behind the front lines as soon as the elephants charged, or else to scatter to left and right and link up with the front line troops, thus opening up a route for the elephants to charge through and leave them vulnerable to fire from both quarters.

11.1. Hannibal placed in front of his whole force his elephants, of which he had over eighty, and behind them the mercenaries numbering about twelve thousand. They were composed of Ligurians, Celts, Balearic Islanders, and Moors.  2. Behind these he placed the native Libyans and Carthaginians, and last of all the troops he had brought over from Italy at a distance of more than a stade from the front lines.  3. He secured his wings by cavalry, placing the Numidian allies on the left and the Carthaginian horse on the right. 

33.4. Hannibal deployed his elephants in the front line, hoping to generate shock and awe among the Romans. There were eighty of them, more than had ever before been used in a battle line.  33.5. Behind them he placed his auxiliaries, Ligurians and Gauls, stiffened with additional Mauretanian troops and Balearic slingers. Behind them, in the second line, came the Carthaginians and Africans, together with a legion of Macedonian infantry.  33.6. A short distance behind all these he placed his reserves, Italian soldiers, mainly from Bruttium, of whom the majority had followed him in his retreat from Italy under compulsion, rather than of their own free will.  33.7. He too stationed his cavalry on the wings, Carthaginians on the right, Numidians on the left. 

4. He ordered each commanding officer of the mercenaries to address his own men, bidding them be sure of victory as they could rely on his own presence and that of the forces that he had brought back with him.  5. As for the Carthaginians, he ordered their commanders to set before their eyes all the sufferings that would befall their wives and children if the result of the battle were adverse. They did as they were ordered,

33.8. There was a confused roar, as his soldiers shouted encouragement to each other in a wide variety of languages: a vast army sharing neither language, culture, law, weaponry, clothes, nor appearance, and not even united in the reasons why they fought.  33.9. The auxiliaries were there for the money, and the prospect of increasing it by plunder; the Gauls had their own special and long standing hatred of the Romans; the Ligurians were drawn down from their savage mountain ranges by the hope of victory and the hope of new lands among the rich plains of northern Italy;  33.10. the Moors and Numidians were terrified by the prospect of a future tyranny under a Masinissa no longer powerless;  33.11. As for his Carthaginians, Hannibal reminded them of their city’s walls, the gods of their homes, the tombs of their ancestors, their parents and children and wives all cowering in terror. He played upon their hopes and fears, picturing for them the two dire alternatives, with no middle way between: either slavery and death, or else dominion over the whole wide world.

12.1. When all was ready for battle on both sides, the Numidian horse having been skirmishing with each other for some time, Hannibal ordered the drivers of the elephants to charge the enemy.  2. When the trumpets and bugles sounded shrilly from all sides, some of the animals took fright and at once turned tail and rushed back upon the Numidians who had come up to help the Carthaginians, and Massanissa attacking simultaneously, the Carthaginian left wing was soon left exposed.  3. The rest of the elephants falling on the Roman velites in the space between the two main armies,  4. both inflicted and suffered much loss, until finally in their terror some of them escaped through the gaps in the Roman line with Scipio's foresight had provided, so that the Romans suffered no injury, while others fled towards the right and, received by the cavalry with showers of javelins, at length escaped out of the field.  5. It was at this moment that Laelius, availing himself of the disturbance created by the elephants, charged the Carthaginian cavalry  6. and forced them to headlong flight. He pressed the pursuit closely, as likewise did Massanissa.

33.12. While he was still speaking to his Carthaginians and the various tribal leaders addressing their troops (mainly through interpreters, because of their mixed nationalities), from the Roman line the horns and trumpets blared,  33.13. raising such a din that the elephants panicked and charged their own lines, especially on the left wing where the Moors and Numidians were stationed. Masinissa quickly added to the general panic and thus robbed that section of the line of its cavalry support.  33.14. A few of the elephants that had remained under control made a charge against the lines of light-armed skirmishers (velites) and wrought havoc among them, while suffering severe casualties themselves.  33.15. For by pulling back to the lines of regular infantry to avoid being crushed by the elephants, the skirmishers opened clear lanes between them and then caught them in cross fire by hurling spears against them from both sides. The javelins of the regular infantry kept up a hail of missiles from every quarter,  33.16. until the elephants were driven out of the Roman lines and turned against their own troops, putting to flight the Carthaginian cavalry on the right wing also. Laelius, with his cavalry on the Roman left, added to their panic as they fled.

12.7 In the meanwhile both phalanxes slowly and in imposing array advanced on each other, except the troops which Hannibal had brought back from Italy, who remained in their original position. 8 When the phalanxes were close to each other, Romans fell upon their foes, raising their war-cry and clashing their shields with their spears as is their practice,  9. while there was a strange confusion of shouts raised by the Carthaginian mercenaries, for, as Homer says, their voice was not one, but:

"Mixed was the murmur, and confused the sound,

Their names all various"

as appears from the list of them I gave above.

34.1. By the time the infantry battle was joined, the Carthaginian line had lost its cavalry support on both wings and was no longer a match for the Romans in morale or military strength. There were other factors involved, which may sound as if they were insignificant, but proved momentous in the actual event. The Romans’ battle-cry was uniform and for that reason all the louder and more terrible; the Carthaginians’ a cacophony of cries, as you would expect from a multitude of tribesmen, all with different languages. 

13.1. As the whole battle was a hand-to‑hand affair [ the men did not use either spears or swords],  2. the mercenaries at first prevailed by their courage and skill, wounding many of the Romans,  2. but the latter still continued to advance, relying on their admirable order and on the superiority of their arms.  3. The rear ranks of the Romans followed close on their comrades, cheering them on, but the Carthaginians behaved like cowards, never coming near their mercenaries nor attempting to back them up,  4. so that finally the barbarians gave way, and thinking that they had evidently been left in the lurch by their own side, fell upon those they encountered in their retreat and began to kill them.  5. This actually compelled many of the Carthaginians to die like men; for as they were being butchered by their own mercenaries they were obliged against their will to fight both against these and against the Romans,  6. and as when at bay they showed frantic and extraordinary courage, they killed a considerable number both of their mercenaries and of the enemy.  7. In this way they even threw the cohorts of the hastati into confusion, but the officers of the principes, seeing what was happening, brought up their ranks to assist,  8. and now the greater number of the Carthaginians and their mercenaries were cut to pieces where they stood, either by themselves or by the hastati. 

9. Hannibal did not allow the survivors in their flight to mix with his own men but, ordering the foremost ranks to level their spears against them, prevented them from being received into his force.  10. They were therefore obliged to retreat towards the wings and the open ground beyond.

34.2. The Roman assault held together, as their concentrated weight of numbers and heavy weaponry bore down upon the enemy, whose attack had speed but lacked force.  34.3. The result was that the Romans’ first charge destabilised the enemy line. They then shouldered their way forward, hammering the enemy with their shield bosses as they failed to hold position, and made considerable advances, almost as if there was no resistance.  34.4. As they saw the line begin to crack, the Roman rear started to push forward, adding weight to the pressure on the enemy. 
34.5. On their side, the Africans and Carthaginians in the second line could not hold back the weight of retreating auxiliaries, with the result that they too began to retreat, in case the enemy cut down the front lines, despite their obstinate resistance, and broke through to their own position.  34.6. As a result, the auxiliaries suddenly broke and turned tail. Some fled back to join the second line positions, and a number even attacked their own side, if they would not let them through, being angry that they had failed to support them and now would not even let them join their ranks. 

34.7. Two different battles now developed simultaneously: the first between the Romans and the Carthaginians, and another between the Carthaginians themselves. 34.8. They simply refused to allow their terrified and angry auxiliaries back into the line; instead they closed ranks and forced them out towards the wings and the open fields beyond the battle, to prevent the troops, who were wounded and in panic stricken flight, from disrupting their own unbroken ranks which were still holding their position.

14.1. The space which separated the two armies still on the field was now covered with blood, slaughter, and dead bodies, and the Roman general was placed in great difficulty by this obstacle to his completing the rout of the enemy.  2. For he saw that it would be very difficult to pass over the ground without breaking his ranks owing to the quantity of slippery corpses which were still soaked in blood and had fallen in heaps and the number of arms thrown away at haphazard.  3. However, after conveying the wounded to the rear and recalling by bugle those of the hastati who were still pursuing the enemy, he stationed the latter in the fore part of the field of battle, opposite the enemy's centre, and making the principes and triarii close up on both wings ordered them to advance over the dead.  5. When these troops had surmounted the obstacles and found themselves in a line with the hastati the two phalanxes closed with the greatest eagerness and ardour.  6. As they were nearly equal in numbers as well as in spirit and bravery, and were equally well armed, the contest was for long doubtful, the men falling where they stood out of determination,  7. and Massanissa and Laelius, returning from the pursuit of the cavalry, arrived providentially at the proper moment.  8. When they fell on Hannibal's army from the rear, most of the men were cut down in their ranks, while of those who took to flight only quite a few escaped, as the cavalry were close on them and the country was level.  9. More than fifteen hundred Romans fell, the Carthaginian loss amounting to twenty thousand killed and nearly the same number of prisoners.

34.9. A problem now arose: the piles of slaughtered soldiers and their weapons, which filled the area recently occupied by the auxiliaries, were so vast that it became almost more difficult for the Romans to advance through them than it had been to break through the enemy line.  34.10. And so the front rank troops (hastati) lost formation and contact with their standards, as they followed up the enemy in hot pursuit as best they could through the heaps of corpses and weaponry. Seeing the line in front of them gradually disintegrating, the second rank troops (principes) began to lose formation also.  34.11. As soon as Scipio became aware of it, he ordered the recall to be sounded for the front rankers (hastati) to re-group, pulled out the wounded and sent them to the rear, and led the second and third rankers (principes and triarii) out to the wings, so that the front rank (hastati) could consolidate and secure the line. 

34.12. That was the beginning of a completely new battle. The Romans now faced their real enemies, a match for them in quality of equipment, military experience, famed for their deeds, and with fears and expectation just as great as their own.  34.13. But now the Romans had the advantage both in numbers and morale, since they had already routed the elephants, and having broken the enemy front were now challenging their second line.  35.1. At this critical moment, Laelius and Masinissa returned from a fairly long pursuit of the defeated cavalry, and charged the Carthaginian rear. This attack by the cavalry finally broke the Carthaginians.  35.2. Many were surrounded and slaughtered where they stood, many others scattered across the open fields in flight but died at the hands of the cavalry, who held all the escape routes.  35.3. 20,000 Carthaginians and their allies died that day; a similar number were taken prisoner, along with 132 military standards, and 11 elephants. The victorious Romans lost some 1500 men.

15.1. Such was the result of the final battle between Scipio and Hannibal, the battle which decided the war in favour of Rome...  3. Hannibal accompanied by a few horsemen never stopped until he was in safety in Adrumetum. He had done in the battle and before it all that could be done by a good general of long experience.  4. For, in the first place, he had by his conference with Scipio attempted to terminate the dispute by himself alone;  5. showing thus that while conscious of his former successes he mistrusted Fortune and was fully aware of the part that the unexpected plays in war. 6. In the next place, when he offered battle he so managed matters that it was impossible for any commander with the same arms at his disposal to make better dispositions for a contest against the Romans than Hannibal did on that occasion.  7. The order of a Roman force in battle makes it very difficult to break through, for without any change it enables every man individually and in common with his fellows to present a front in any direction, the maniples which are nearest to the danger turning themselves by a single movement to face it.  8. Their arms also give the men both protection and confidence owing to the size of the shield and owing to the sword being strong enough to endure repeated blows. So that for these reasons they are formidable antagonists very difficult to overcome.  16.1. But nevertheless to meet each of these advantages Hannibal had shown incomparable skill in adopting at the critical moment all such measures as were in his power and could reasonably be expected to succeed.  2. For he had hastily collected that large number of elephants and had placed them in front on the day of battle in order to throw the enemy into confusion and break his ranks.  3. He had placed the mercenaries in advance with the Carthaginians behind them in order that the Romans before the final engagement might be fatigued by their exertions and that their swords might lose their edge owing to the great slaughter, and also in order to compel the Carthaginians thus hemmed in on both sides to stand fast and fight, in the words of Homer "That e'en the unwilling might be forced to fight".  4. The most efficient and steadiest of his troops he had placed behind at a certain distance in order that, anticipating and witnessing from afar what took place, they might with undiminished strength and spirit make use of their qualities at the proper time.  5. If he, who had never as yet suffered defeat, after taking every possible step to insure victory, yet failed to do so, we must pardon him.  6. For there are times when Fortune counteracts the plans of valiant men, and again at times, as the proverb says, "A brave man meets another braver yet," as we may say happened in the case of Hannibal.

35.4. In the general confusion, Hannibal managed to escape with a band of cavalry, and fled to Hadrumetum. Before escaping from the battle, he had tried everything both in his preparations and his tactical decisions;  35.5. indeed, both Scipio and all the military experts agree that his tactical deployment of his troops on the day of battle was masterly.  35.6. He had placed his elephants in the front line, so that their random attacks and irresistible force would prevent the Romans from following their standards and holding their formations, which was for them one of their most important military principles.  35.7. His auxiliaries were drawn from the dregs of every tribe under the sun, lacked loyalty to any cause, and were driven only by their desire for pay.  35.8. So he had wisely placed them in front of his own Carthaginians, so as to ensure that they had no obvious means of escape, but would bear the brunt of the Romans’ first assault, and dull the force and impetus of their charge - or at least blunt their opponents’ swords with their own wounds.  35.9. Finally, his Carthaginians and Africans, in whom he placed his highest hopes and who were a match for any eventuality, had been stationed behind his auxiliaries, to give them the added advantage of fighting against soldiers already wounded and exhausted, while they themselves were fresh. The Italians were unreliable allies, and might turn traitor, so he had placed them in the rear, well separated from the main lines of battle. 
35.10. It was the final demonstration of Hannibal’s brilliance as a military commander.

[19.2. It is said that when one of the senators was about to oppose the acceptance of the terms of peace and was beginning to speak Hannibal came forward and pulled him down from the tribune.  3. The other members were indignant with him for such a violation of the usage of the house, and Hannibal then rose again and said that he confessed he had been in error, but they must pardon him if he acted contrary to their usage, as they knew that he had left Carthage at the age of nine, and was, now that he had returned, over five and forty.] 

Having escaped to Hadrumetum, he was summoned back to Carthage, returning there in the thirty sixth year since he had left it as a boy.  35.11. In their senate he acknowledged that he had lost not just the battle but the war, and that their only hope was to sue for peace .

15.2. The action over, Scipio after following up the enemy and plundering their camp returned to his own.

36.1. Immediately after the battle, Scipio stormed and destroyed the enemy camp, before returning to the coast and his fleet with a huge collection of booty.  36.2. There news reached him that Publius Lentulus had reached Utica, just north of Carthage, with 50 warships and 100 transports, filled with all sorts of necessary supplies.  36.3. Scipio decided that he should inflict still further terrors from every direction on an already shattered Carthage. So he despatched Laelius back to Rome with the news of victory, ordered Gnaeus Octavius to lead his legions to Carthage by the overland route, and he himself united his existing fleet with that of Lentulus. He then set out from Utica for the port of Carthage. 

[Polybius says no more about Scipio's actions, and goes straight into a discussion of the peace treaty.]

36.4. He had nearly got there when a Carthaginian ship came out to meet him, bedecked with symbols of surrender, woollen fillets and olive branches. On board were ten ambassadors, leading citizens, sent to beg for peace at Hannibal’s suggestion.  36.5. They approached the stern of Scipio’s flagship, holding out their olive branches with woollen fillets, tokens of supplication, begging and beseeching him for magnanimity and mercy.  36.6. Scipio made no reply, stating simply that he planned to move his camp to Tunis, and that they should meet him there. He himself sailed on in order to reconnoitre the site of Carthage, but entered the harbour with no real intention of exploring it for the moment; his aim was simply to demoralise the enemy. He then returned to Utica and told Octavius to join him there.

36.9. They then re-established their camp at Tunis, in the same location as before, and there a delegation of thirty envoys came to Scipio from Carthage. They pleaded their cause in far more heart-rending terms than they had before. Fortune had forced such woes upon them; but the memory of their recent treachery won them proportionately less pity from the Romans.  36.10. They held a council of war, at which initially righteous anger and indignation encouraged them to wipe out the whole city. But then they began to calculate the sheer size of Carthage, and how long it would take them to besiege and capture somewhere so strong and formidably fortified.  36.11. In Scipio’s mind was also the anxious thought that his successor would soon be on his way, and that he would enjoy the fruits of a victory, which had already been won by the efforts and dangers of his predecessor. In the end there was a consensus for peace.
A