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Equality of a Segment and an Arc in Archimedes's Spiral

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This Demonstration illustrates Proposition 20 of Archimedes's work On Spirals.

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Let be any point on the first turn of the spiral, and let be the intersection of the tangent to the spiral at , with the perpendicular to at . Then .

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Contributed by: Izidor Hafner (November 2012)
Open content licensed under CC BY-NC-SA

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Reference

[1] T. L. Heath (ed.), The Works of Archimedes, New York: Dover Publications, 2002.

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