Arc, amplitude, and curvature sustain a similar relation to each other as time, motion, and velocity, or as volume, mass, and density.
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"Gauss's Abstract of the Disquisitiones Generales circa Superficies Curvas presented to the Royal Society of Gottingen" (1827) Tr. James Caddall Morehead & Adam Miller Hiltebeitel in General Investigations of Curved Surfaces of 1827 and 1825 (1902)