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In the late 17th century, Gottfried Leibniz proposed the idea of the Latin: vis viva, or living force, which defined as the product of the mass of an object and its velocity squared; he believed that total vis viva was conserved. To account for slowing due to friction, Leibniz theorized that thermal energy consisted of the random motion of the constituent parts of matter, a view shared by Isaac Newton, although it would be more than a century until this was generally accepted. The modern analog of this property, kinetic energy, differs from vis viva only by a factor of two.

In what century did Leibniz propose the idea of Latin: vis viva?
Answer: late 17th century
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By August, the KPA had pushed back the ROK Army and the Eighth United States Army to the vicinity of Pusan in southeast Korea. In their southward advance, the KPA purged the Republic of Korea's intelligentsia by killing civil servants and intellectuals. On 20 August, General MacArthur warned North Korean leader Kim Il-sung that he was responsible for the KPA's atrocities. By September, the UN Command controlled the Pusan perimeter, enclosing about 10% of Korea, in a line partially defined by the Nakdong River.

Where did the Eighth United States and ROK get pushed back to?
Answer: southeast Korea
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The Antikythera mechanism is believed to be the earliest mechanical analog "computer", according to Derek J. de Solla Price. It was designed to calculate astronomical positions. It was discovered in 1901 in the Antikythera wreck off the Greek island of Antikythera, between Kythera and Crete, and has been dated to circa 100 BC. Devices of a level of complexity comparable to that of the Antikythera mechanism would not reappear until a thousand years later.

What is thought to be the first mechanical analog computer?
Answer:
The Antikythera mechanism