“We see how many people incorrectly thought are what we call the power of an engine. When they hear about a steam engine, a water wheel of twenty horses for example, it contained only twenty horses harnessed together and acting both are driven by the engine. They thus confuse the effort exerted at a given time, and assumes no minimum time, with the mechanical work, which involves the idea of time. Archimedes said that with a lever and a fulcrum long enough, that it would raise the earth, he probably thought to have multiplied almost indefinitely the power of man, in reality, unconsciously perhaps He has made us very small. Lift the land means, in effect, use the engine working at our disposal, to raise to a height equal weight to that of Earth. But really, how long would it take a very vigorous man, working day and night, without rest, to lift such a weight to one millimeter in height? He would need two million of millions of centuries! Archimedes indeed, although we were humiliated.”
A depiction of Archimedes, who famously said "give me a lever long enough, and I will move the earth", moving the earth; thus Illustrating his "principle of the lever", supposedly one of the per-cursors to infinitesimals and hence to integral calculus. |
“Eudoxus first discovered the proof that the cone is one-third of the cylinder of equal height on the same base, and the pyramid one-third of the prism. No small share [of the discovery] should be assigned to Democritus, who first made the assertion about the above-mentioned figure without proof.”— Archimedes (c.220BC), Mathematical Theorems Addressed to Eratosthenes (see: Eratosthenes) [6]