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Hence a curve has a unique evolute but infinitely many involutes.
He gives propositions determining the centre of curvature which lead immediately to the Cartesian equation of the evolute .
Of course the evolute of an involute of a circle is a circle.
On 22 January 1769 Monge wrote to Bossut explaining that he was writing a work on the evolutes of curves of double curvature.
He defines evolutes and involutes of curves and, after giving some elementary properties, finds the evolutes of the cycloid and of the parabola.
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