Quadrature of the Parabola

work by Archimedes

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July 13, 2026

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The "Quadrature of the Parabola" is a treatise by Archimedes that demonstrates how to find the area of a parabolic segment. Archimedes proved that this area is exactly 4/3 the area of a triangle with the same base and height as the parabolic segment.1

He achieved this using two methods:
* Mechanical means: This involved using principles of balance and levers, as described in his work Method Concerning Mechanical Theorems.12
* Geometric methods: This employed the rigorous method of exhaustion, a technique for calculating areas and volumes by approximating them with known shapes.34

This work is a significant example of early calculus concepts, predating modern calculus by centuries.124

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Archimedes
His works
Quadrature of the Parabola demonstrates, first by “mechanical” means (as in Method, discussed below) and then by conventional geometric methods, that the area of any segment of a parabola is 4/3 of the area of the triangle having the same base and height as that…
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Quadrature of the Parabola demonstrates, first by “mechanical” means (as in Method, discussed below) and then by conventional geometric methods, that the area of any segment of a parabola is 4/3 of the area of the triangle having the same base and height as that…
Read More