Archimedes would not have approved of the legerdemain above. He arrived at the same result by a different route. He resorted to a subtle style of argumentation often described as double reductio ad absurdum, a double proof by contradiction. He proved that the area of the parabolic segment could not be less than 4/3 or greater than 4/3, so it must equal 4/3. As Sherlock Holmes later put it, “When you have eliminated the impossible, whatever remains, however improbable, must be the truth.”
