Book:Archimedes/On the Quadrature of the Parabola

Archimedes: On the Quadrature of the Parabola

Published $\text {c. 250 BCE}$

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 $1 + \frac 1 4 + \paren {\frac 1 4}^2 + \cdots$

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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
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Archimedes of Syracuse (c. 287-212 bc)
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Archimedes, axiom of
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Archimedes of Syracuse (c.287-212 bc)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Archimedes, axiom of