In the other direction, Cavalieri's principle grew out of the ancient Greek method of exhaustion, which used limits but did not use infinitesimals.
12.
He used the method of exhaustion to calculate the area under the arc of a parabola with the surfaces of revolution and an ingenious system for expressing very large numbers.
13.
Concerns about the soundness of arguments involving infinitesimals date back to ancient Greek mathematics, with Archimedes replacing such proofs with ones using other techniques such as the method of exhaustion.
14.
The development of analytical geometry and rigorous integral calculus in the 17th-19th centuries subsumed the method of exhaustion so that it is no longer explicitly used to solve problems.
15.
In his other works, Archimedes often proves the equality of two areas or volumes with Eudoxus'method of exhaustion, an ancient Greek counterpart of the modern method of limits.
16.
Archimedes used the method of exhaustion as a way to compute the area inside a circle by filling the circle with a polygon of a greater area and greater number of sides.
17.
This passive method of exhaustion of karmic matter around the soul, after enjoyment of its fruits, is compared with emptying of a pond through evaporation, while water channels are still pouring in.
18.
Had been known to Euclid, but all proofs of it involve some form of limiting process or calculus, notably the method of exhaustion or, in more modern form, Cavalieri's principle.
19.
*PM : derivation of a definite integral formula using the method of exhaustion, id = 6634-- WP guess : derivation of a definite integral formula using the method of exhaustion-- Status:
20.
*PM : derivation of a definite integral formula using the method of exhaustion, id = 6634-- WP guess : derivation of a definite integral formula using the method of exhaustion-- Status:
