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.


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 .


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




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

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