Book:Archimedes/On the Quadrature of the Parabola

Archimedes: On the Quadrature of the Parabola

Published $\text {\text {c. $250$ BCE}}$.

Subject Matter

• Quadrature of Parabola

Contents

$24$ propositions:

Two proofs that the area of a parabolic segment is $\frac 4 3$ the area of a triangle with the same base and height.

A proof of the sum of the infinite series $1 + \frac 1 4 + \left({\frac 1 4}\right)^2 + \cdots$

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Critical View

It is apparent from this treatise that Archimedes was completely aware of the concept of a limit.

Sources

• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.5$: Archimedes (ca. $\text {287}$ – $\text {212}$ B.C.)
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.3$: Archimedes' Quadrature of the Parabola