How Did Archimedes Achieve Quadrature of the Parabola Without Calculus?

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SUMMARY

Archimedes achieved the quadrature of the parabola by dividing it into a series of triangles, demonstrating that their areas form a geometric sequence. He utilized the formula for the sum of an infinite geometric series to derive the area of the parabola. This method predates calculus and showcases Archimedes' innovative approach to geometry. Relevant resources include Apostle's Analysis books, which provide detailed explanations of these concepts.

PREREQUISITES
  • Understanding of geometric sequences
  • Familiarity with the concept of area in geometry
  • Knowledge of Archimedes' work in mathematics
  • Basic principles of infinite series
NEXT STEPS
  • Research Archimedes' method of exhaustion
  • Study the properties of geometric sequences and series
  • Explore the historical context of Archimedes' mathematical contributions
  • Read Apostle's Analysis for insights on the quadrature of the parabola
USEFUL FOR

Mathematicians, educators, students of geometry, and anyone interested in the historical development of mathematical concepts prior to calculus.

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

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

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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? :)
 

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