Quadrature of the Parabola (Greek: Τετραγωνισμὸς παραβολῆς) is a treatise on geometry, written by Archimedes in the 3rd century BC and addressed to his Alexandrian acquaintance Dositheus. It contains 24 propositions regarding parabolas, culminating in two proofs showing that the area of a parabolic segment (the region enclosed by a parabola and a line) is that of a certain inscribed triangle.
It is one of the best-known works of Archimedes, in particular for its ingenious use of the method of exhaustion and in the second part of a geometric series. Archimedes dissects the area into infinitely many triangles whose areas form a geometric progression.[1] He then computes the sum of the resulting geometric series, and proves that this is the area of the parabolic segment. This represents the most sophisticated use of a reductio ad absurdum argument in ancient Greek mathematics, and Archimedes' solution remained unsurpassed until the development of integral calculus in the 17th century, being succeeded by Cavalieri's quadrature formula.[2]
^Swain, Gordon; Dence, Thomas (1998). "Archimedes' Quadrature of the Parabola Revisited". Mathematics Magazine. 71 (2): 123–130. doi:10.2307/2691014. ISSN 0025-570X. JSTOR 2691014.
^Cusick, Larry W. (2008). "Archimedean Quadrature Redux". Mathematics Magazine. 81 (2): 83–95. doi:10.1080/0025570X.2008.11953535. ISSN 0025-570X. JSTOR 27643090. S2CID 126360876.
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QuadratureoftheParabola (Greek: Τετραγωνισμὸς παραβολῆς) is a treatise on geometry, written by Archimedes in the 3rd century BC and addressed to his...
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the Sphere and Cylinder Measurement of a Circle On Conoids and Spheroids On Spirals On the Equilibrium of Planes The Sand Reckoner TheQuadratureof the...
times the area of a triangle with equal base and height (QuadratureoftheParabola). The most characteristic product of Hellenistic mathematics was the theory...
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