Qing China reached its largest extent during the 18th century, when it ruled China proper (eighteen provinces) as well as the areas of present-day Northeast China, Inner Mongolia, Outer Mongolia, Xinjiang and Tibet, at approximately 13 million km2 in size. There were originally 18 provinces, all of which in China proper, but later this number was increased to 22, with Manchuria and Xinjiang being divided or turned into provinces. Taiwan, originally part of Fujian province, became a province of its own in the late 19th century, but was ceded to the Empire of Japan in 1895 following the First Sino-Japanese War. In addition, many surrounding countries, such as Korea (Joseon dynasty), Vietnam frequently paid tribute to China during much of this period. Khanate of Kokand were forced to submit as protectorate and pay tribute to the Qing dynasty in China between 1774 and 1798.
How did the Japanese win Taiwan?
First Sino-Japanese

The initial military maneuvers began in September 1806. In a notable letter to Marshal Soult detailing the plan for the campaign, Napoleon described the essential features of Napoleonic warfare and introduced the phrase le bataillon-carre ('square battalion'). In the bataillon-carre system, the various corps of the Grande Armee would march uniformly together in close supporting distance. If any single corps was attacked, the others could quickly spring into action and arrive to help. Napoleon invaded Prussia with 180,000 troops, rapidly marching on the right bank of the River Saale. As in previous campaigns, his fundamental objective was to destroy one opponent before reinforcements from another could tip the balance of the war. Upon learning the whereabouts of the Prussian army, the French swung westwards and crossed the Saale with overwhelming force. At the twin battles of Jena and Auerstedt, fought on 14 October, the French convincingly defeated the Prussians and inflicted heavy casualties. With several major commanders dead or incapacitated, the Prussian king proved incapable of effectively commanding the army, which began to quickly disintegrate. In a vaunted pursuit that epitomized the "peak of Napoleonic warfare," according to historian Richard Brooks, the French managed to capture 140,000 soldiers, over 2,000 cannons and hundreds of ammunition wagons, all in a single month. Historian David Chandler wrote of the Prussian forces: "Never has the morale of any army been more completely shattered." Despite their overwhelming defeat, the Prussians refused to negotiate with the French until the Russians had an opportunity to enter the fight.
To whom did Napoleon send a letter detailing his plans for the campaign with Prussia?
Marshal Soult

To Popper, who was an anti-justificationist, traditional philosophy is misled by the false principle of sufficient reason. He thinks that no assumption can ever be or needs ever to be justified, so a lack of justification is not a justification for doubt. Instead, theories should be tested and scrutinised. It is not the goal to bless theories with claims of certainty or justification, but to eliminate errors in them. He writes, "there are no such things as good positive reasons; nor do we need such things [...] But [philosophers] obviously cannot quite bring [themselves] to believe that this is my opinion, let alone that it is right" (The Philosophy of Karl Popper, p. 1043)
What don't we need to look for about theories in Popper's view?
good positive reasons