Qin King Zhuangxiang fled south of Longshan, defeated South Zheng, Chu Huai, and Ding Han.

  Here is the translation:

  Yesterday, King Huiwen of Qin arrived at Lueyang and rested for a night. His fear had just subsided when he got up early in the morning and said to Sima Cuo with a sigh: "I never expected that I would suffer such a great defeat as soon as I became king." Sima Cuo said, "It's not my fault that Your Majesty was frightened." King Huiwen of Qin said, "It's not your fault. I didn't expect King Huai of Chu to be so brave and the Chu army to be so strong."

  Just after King Huiwen and others finished their breakfast, a horseman came in a hurry to report: "Report to Your Majesty! King Huai of Chu has led his troops to Bao Han (Hanzhong City) and is marching towards us with a large army." Upon hearing the report, Sima Cuo said to King Huiwen, "Your Majesty should lead your troops to flee to Longnan (City). I will stay here to defend the city and fight a decisive battle against the Chu army."

  King Huiwen grasped Sima Cuo's hands and said, "Your arm injury has not healed yet, and you are not in good health. You are no match for King Huai of Chu. Don't sacrifice your life in vain here. I would rather give up this city than lose you, a famous general. Take the troops with you and follow me to Longnan." So Sima Cuo followed King Huiwen and abandoned the city to flee to Longnan.

  King Huai of Chu led his army to Lueyang and saw that King Huiwen had already fled to Longnan. He left 3,000 infantrymen and 2,000 cavalrymen to garrison Lueyang and led his main force back to Bao Han (Hanzhong City).

  Here is the translation:

  Furthermore, Zhao Yu led 40,000 cavalry and infantry to cross the Han River and attack Nanzheng. The Marquis of Shu heard the news and immediately ordered the city gates closed, personally leading 13,000 cavalry and infantry to defend the city walls, intending to fight to the end. Zhao Yu led 40,000 Chu soldiers across the Han River to Nanzheng, arrayed his troops, and called out for battle. The Shu army neither came out to fight nor surrendered. Zhao Yu had no choice but to order his soldiers to prepare battering rams and cloud ladders to attack the city.

  At this time, King Hui of Chu led his main force back to Bao Han (Hanzhong City) and ordered 20,000 infantry to cross the river and attack the city. The Marquis of Shu saw the situation and could only lead his army to escape from the rear mountain. However, the terrain behind Nanzheng was all steep mountains and cliffs, and while soldiers could climb over them, war horses could not. Over 10,000 war horses were unable to escape.

  The Marquis of Shu had wanted to order his soldiers to kill the war horses so as not to leave them for the Chu army, but it was already too late. The sound of killing shook the heavens as the Chu army attacked from both the west and east wings, with 50,000 Chu soldiers separately attacking the villages of Zhandou, Guo Jia Ying (west of Nanzheng County), Xia Jia An, and Xi Ma Xiang (east of Nanzheng County). The Marquis of Shu could only lead his Shu army in a frantic retreat over the rear mountain.

  Zhao Yu led the Chu army into Nanzheng and saw that the Shu army had already escaped over the rear mountain. He ordered his soldiers to cut off the ropes and block the roads behind the mountain, then dispatched 3,000 infantry and 2,000 cavalry to guard Nanzheng. He himself led the main force across the river back to Bao Han (Hanzhong City).

  Here is the translation:

  The ten-day Battle of Bo Han ended with a complete victory for the Chu army, while the Qin and Shu allied forces were defeated. The battle included Han Yin, Shi Quan, Cheng Gu, and Nan Zheng, among others. The decisive battle that determined the outcome was the initial Battle of Han Yin. In this battle, the Chu army killed 195,000 soldiers from the Qin and Shu allied forces, including 85,000 from the Qin army and 110,000 from the Shu army. They also captured 35,000 war horses, 190,000 sets of armor and weapons, and a large quantity of grain and carts. As a result of this battle, King Huai of Chu expanded his territory by over 400 miles from Ankang City to Lueyang County, gaining control of the ten cities (counties) of Bo Han (Hanzhong City), Han Yin, Zi Yang, Zhen Ba, Ning Shan, Shi Quan, Xi Xiang, Cheng Gu, Nan Zheng, Ning Qiang, and Lueyang. King Huiwen of Qin, who had just declared himself king at the beginning of the year with the intention of replacing King Hui of Wei as the dominant power in the Central Plains, was defeated by King Huai of Chu in the Battle of Bo Han and forced to flee in disarray, barely escaping capture by the Chu army. From then on, whenever King Huiwen of Qin heard the names "Hanzhong Prefecture" and "King Huai of Chu", he would be filled with dread.

  Afterwards, King Hui of Chu changed the name of Bao Han to Han Zhong Prefecture, with a jurisdiction spanning from Lüeyang County to Fang County, over 700 miles. He abolished Yong Prefecture and ordered its prefect to take office in Han Zhong, moving the original prefecture seat of Yong from Xunyang to An Kang as a subordinate county of Han Zhong. In Bao Han, he hosted a banquet to reward the three armies for three days.

  King Hui of Chu raised his wine goblet and said to all the generals: "The Han River is our auspicious place for the people of Chu. In ancient times, the Chu people went down along the Han River to reach Jinghan. Therefore, Chu is both Jing and Han. Today we have come to our ancestors' old land, and our ancestors' old land has returned to us today, which is a joyous occasion.

  This place is not Bao or Zheng, but Han. I want to establish a prefecture seat here and make our ancestors' hometown prosperous. This is the middle reaches of the Han River, so from now on, this place will be officially named Han Zhong Prefecture."

  The Chu army cheered with raised long spears: "Han Zhong Prefecture!" "Han Zhong Prefecture!"

  Three days later, King Huai of Chu appointed Liu Xiang (because of the same sound as Liu Liu, later changed to Liu Liu Yang's father and Liu Bang's great-grandfather) as the Grand General to lead 100,000 Chu troops (40,000 cavalry and 60,000 infantry) to garrison Hanzhong Prefecture and settle the wounded in Hanzhong for recuperation. Liu Xiang received the order and transmitted it: 20,000 cavalry and 30,000 infantry were stationed in Hanzhong, with 2,000 cavalry and 3,000 infantry each in Lüeyang, Ningqiang, Nanzheng, Xixiang, and Zhenba. The remaining 10,000 cavalry and 15,000 infantry were stationed in Hanzhong, distributed among Mianxian, Hanzhong, and Chenggu. 20,000 cavalry and 30,000 infantry were stationed in Ankang, with 2,000 cavalry and 3,000 infantry each in Zhen'an, Ziyang, Zhenping, Fangxian, and Yunxi. The remaining 10,000 cavalry and 15,000 infantry were stationed in Ankang, distributed among Hanyin, Ankang, and Xunyang. Liu Xiang ordered the soldiers to open up wasteland for farming and drill troops without slackening. King Huai of Chu had made all the arrangements and led his army of 150,000 (50,000 cavalry and 100,000 infantry) back to Jingzhou in a grand manner.