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The “Universal Information Society” of the XIX century?

From the inaugural lecture of J.J. Sylvester at Oxford, December 12, 1885, "On the method of reciprocants as containing an exhaustive theory of the singularities of curves", Collected Mathematical ...
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How exactly was the principle of conservation of energy discovered? [duplicate]

How did we come to know that, for example, the quantity Work=Force*distance is conserved?
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How did Galileo discover the law of inertia? [duplicate]

In the Feynman lectures, it is mentioned that [Vol 1; Gravitation]: Galileo discovered a very remarkable fact about motion, which was essential for understanding these laws. That is the principle ...