So partly inspired by the other thread.... but...
Archimedes was interested in finding the area under the curves under polynomials. The method he used was similar to the Riemann sum (using rectangles to estimate area.) What if the Greeks realized that the rate of change was the answer to the problem. What if the Greeks were able to discover differentiation and in turn integration. The concept wouldn't be particularly hard. Honestly they would only have to deepen their understatement of the limit, in OTL they had all of the other tools needed.
Of course they probably wouldn't have the tools to examine trig functions and natural logarithmic problems (even though they could calculate e considering that f(x)=e^x f'(x)=e^x....)
But what would change if calculus was discovered nearly two thousand years early?
Archimedes was interested in finding the area under the curves under polynomials. The method he used was similar to the Riemann sum (using rectangles to estimate area.) What if the Greeks realized that the rate of change was the answer to the problem. What if the Greeks were able to discover differentiation and in turn integration. The concept wouldn't be particularly hard. Honestly they would only have to deepen their understatement of the limit, in OTL they had all of the other tools needed.
Of course they probably wouldn't have the tools to examine trig functions and natural logarithmic problems (even though they could calculate e considering that f(x)=e^x f'(x)=e^x....)
But what would change if calculus was discovered nearly two thousand years early?