Apollonius of Perga is the first to…
225 BCE
Apollonius of Perga is the first to use coordinates to identify points on a conic.
Apollonius, who flourishes around 225 BCE, investigates the mathematical properties of conic sections in his “Conics,” in which the “Great Geometer” introduces the terms ellipse, hyperbola, and parabola.
Apollonius also performs fundamental work in Greek mathematical astronomy, applying geometrical models to planetary theory.
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Qin has by 221 BCE unified most of the states and occupied some lands south of the Yangtze River.
The conquered territories serve as the foundation of the Qin Dynasty.
Qin Shi Huang had conquered all opposing states and unified China in 221 BCE, establishing the Qin Dynasty.
Intending to impose centralized rule and prevent the resurgence of feudal lords, he orders the destruction of the wall sections that divide his empire along the former state borders.
To protect the empire against intrusions by the Xiongnu people from the north, he orders the building of a new wall to connect the remaining fortifications along the empire's new northern frontier.
Transporting the large quantity of materials required for construction is difficult, so builders always try to use local resources.
Stones from the mountains are used over mountain ranges, while rammed earth is used for construction in the plains.
There are no surviving historical records indicating the exact length and course of the Qin Dynasty walls.
Most of the ancient walls have eroded away over the centuries, and very few sections remain today.
The human cost of the construction is unknown, but it has been estimated by some authors that hundreds of thousands, if not up to a million, workers died building the Qin wall.
Qin armies, following a decade of conquest of neighboring states, now launch assaults to the east, and later the south as well; they take the Wei city of Daliang (now called Kaifeng) in 225 BCE and …
…force Chu to surrender by 223 BCE.
Shi Huangdi’s troops continue south as far as Guangdong and …
…Guangxi, and even into the Vietnamese border state of Tonkin.
Lastly, they depose the Zhou Dynasty's remnants in Luoyang and …
…conquer Qi, taking the city of Linzi in 221 BCE, and thus bringing to an end the Period of Warring States.
King Zheng—who had first assumed the throne of the Qin state at age thirteen—becomes the effective ruler of China when the conquests are complete in 221 BCE.
He solidifies his position as sole ruler with the abdication of his prime minister, Lü Buwei.
He then combines the titles of the earlier Three Sovereigns and Five Emperors into his new name: Shi Huangdi or "First Emperor".
The newly declared emperor orders all weapons not in the possession of the Qin to be confiscated and melted down.
The resulting metal is sufficient to build twelve large ornamental statues at the Qin's newly declared capital, Xianyang.
Shi Huangdi sets about applying to the wole empire the centralized administrative system that has been a source of Qin strength, dividing China into nonfeudal provinces with civil and military governors.
(The name “China” derives from the name of the dynasty.)
The emperor brooks no opposition, executing those who oppose his will.
The Qin ruling class subscribes to the Legalist authoritarian philosophy; Shi Huangdi’s chief minister, Li Si, is one of its exponents.
Li Si applies the tenets of the Legalist school as the basis for Shi Huangdi’s adroit consolidation of Qin rule, which also brings a new uniformity to weights and measures and coinage.
A six hundred thousand-strong Qin army led by Wang Ben conquers more than ten cities on the northern border of Chu in 225 BCE as a precautionary move to guard the flank from possible attacks from Chu while Qin is invading Wei.
Wang Ben then leads his forces north to attack and besiege Daliang (northwest of present-day Kaifeng, Henan), the capital of Wei.
As Daliang is situated at the confluence of the Sui and Ying rivers and the Hong Canal, its geographical location gives it a natural defensive advantage.
Besides, the moat around Daliang is very wide and all the five gates of the city have drawbridges, making it even more difficult for Qin forces to penetrate the city.
The Wei troops use the opportunity to strengthen their fortifications and defenses.
Wang Ben comes up with the idea of directing the waters from the Yellow River and the Hong Canal to flood Daliang.
Wang Ben's troops work for three months to redirect the water flow while maintaining the siege on Daliang, and succeed in their plan.
Daliang is heavily flooded and over one hundred thousand people die, including civilians.
King Jia of Wei surrenders and Wei comes under Qin's control.
Ying Zheng calls in 224 BCE for a meeting with his subjects to discuss his plans for the invasion of Chu.
Wang Jian feels that they need at least six hundred thousand troops for the campaign, while Li Xin claims that less than two hundred thousand men will suffice.
Ying Zheng dismisses Wang Jian's idea and orders Li Xin and Meng Wu to lead an army of about two hundred thousand to attack Chu.
Wang Jian retires on the grounds of illness.
The Qin armies score initial victories as Li Xin's force conquers Pingyu (north of present-day Pingyu County, Zhumadian, Henan) while Meng Wu's capture Qinqiu (present-day Linquan County, Fuyang, Anhui).
After conquering Yan (present-day Yanling County, Xuchang, Henan), Li Xin leads his army west to rendezvous with Meng Wu at Chengfu (east of present-day Baofeng County, Pingdingshan, Henan).
The Chu army, led by Xiang Yan, has been avoiding using its main force to resist the Qin invaders while waiting for an opportunity to launch a counterattack.
During this time, Lord Changping, a relative of Ying Zheng who descends from the Chu royal family, incites a rebellion in a city previously conquered by Li Xin.
He also prepares for a surprise attack on Li Xin later.
The Chu army led by Xiang Yan secretly follows Li Xin at high speed for three days and three nights before launching a surprise attack.
Lord Changping's forces follow suit from behind and join Xiang Yan's army in attacking Li Xin.
Most of Li Xin's forces are destroyed in the battle.
Upon learning of Li Xin's defeat, Ying Zheng personally visits Wang Jian, who is in retirement, apologizes for not heeding Wang's advice earlier, and invites Wang back to serve in the court.
Per Wang Jian's request, Ying Zheng puts him in command of six hundred thousand troops and assigns Meng Wu to be Wang's deputy.
Wang Jian is aware that the king will doubt his loyalty because he wields too much military power, so he frequently sends messengers back to the king, requesting for rewards for his family so as to reduce the king's suspicions.
Wang Jian's army passes through the south of Chen (present-day Huaiyang County, Zhoukou, Henan) in 224 BCE, and makes camp at Pingyu.
The Chu forces, led by Xiang Yan, use their full strength to launch an offensive on the Qin camp but fail.
Wang Jian orders his troops to defend their positions firmly and avoid advancing further into Chu territory.
After failing to lure the Qin army to attack, Xiang Yan orders a retreat and Wang Jian seizes the opportunity to launch a surprise counterattack.
The Qin forces pursue the retreating Chu forces to Qinan (northwest of present-day Qichun County, Huanggang, Hubei), where Xiang Yan is killed in action[e] in the ensuing battle.
Qin launches another attack on Chu in 223 BCE and captures Shouchun (present-day Shou County, Lu'an, Anhui), the capital of Chu.
Fuchu, the king of Chu, is captured and Chu is annexed by Qin.
The following year, Wang Jian and Meng Wu lead the Qin army to attack the Wuyue region (covering present-day Zhejiang and Jiangsu), which is inhabited by the Baiyue, and capture the descendants of the royal family of Yue.
Prince Jia, the elder brother of King Qian of Zhao, had escaped from Handan and gone to Dai (present-day Yu County, Zhangjiakou, Hebei), where, with help from Zhao's remnants, he declares himself "King of Dai".
Dai is conquered in 222 BCE by the Qin army led by Wang Jian's son, Wang Ben.
Zhao Jia is taken captive.
Tian Jian had in 264 BCE ascended the throne of Qi, assisted by his mother, the queen dowager, in managing state affairs.
Qin has bribed Hou Sheng, the Qi chancellor, to dissuade King Jian from helping the other states while they were being attacked by Qin.
By 221 BCE, Qi is the only state in China that has yet to be conquered by Qin.
Qi hurriedly mobilizes its armies to its western borders as a safeguard against a possible Qin invasion, even though its military is not well equipped and morale is low.
In the same year, Ying Zheng uses Qi's rejection of a meeting with a Qin envoy as an excuse to attack Qi.
The Qin army, led by Wang Ben, avoids direct confrontation with enemy forces stationed on Qi's western borders, and advances into Qi's heartland via a southern detour from Yan.
The Qin forces meet with little resistance as they pass through Qi territory and eventually arrive at Linzi (north of present-day Zibo, Shandong), the capital of Qi.
King Jian is caught by surprise and, after being persuaded by Hou Sheng, he surrenders to Qin without putting up a fight.