MHB How Did Archimedes Achieve Quadrature of the Parabola Without Calculus?

minimoocha · May 10, 2020

How did Archimedes discover the Quadrature of the parabola without the use of calculus?

If someone could please explain, I would be eternally grateful.

HallsofIvy · May 11, 2020

I'm no expert but this: https://www.bing.com/search?q=Archi...s=n&sk=&cvid=d4e0b7d06ab74859b65f0e558ba281a5 has a pretty good description. Basically, he divides the parabola into many triangles, showing that their areas form a geometric sequence, then uses the formula for the sum of an infinite geometric sequence to get the formula for the area of a parabola.

Joppy · May 12, 2020

I recall an explanation of this in one of Apostle's Analysis books. Don't have it with me and can't remember how detailed it was, but could be useful. It's likely mentioned in any major book on calculus.

Also @HallsofIvy, Bing? :)

MHB How Did Archimedes Achieve Quadrature of the Parabola Without Calculus?

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