Archimedean Metronomy

Spiral Bridge of Rectification

Archimedes thinks of the spiral in terms of the combined mechanical motion of a point undergoing two distinct uniform motions: A uniform motion in a fixed linear direction with constant velocity, and a uniform motion in a circle with constant velocity as well. Both uniform motions start at the same point, which is considered as the pole of the non-uniform combined motion traced by the emerging spiral. The spiral is depicted together with its tangent attached to each point of the motion it traces. After a complete turn, the area of the circle is rectified, through the spiral bridge, in terms of the area of the adjacent to the spiral triangle emerging by means of the attached tangent, and thus the quadrature of the circle follows. The perimeter of the circle is metronomically unrolled to the side of the orthogonal triangle opposite to the angle of the tangent, whose other side is the radius of the circle.








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