Evolutes

In this paper we summarize the results on the
cycloid appearing in Huygens' famous work
Horologium oscillatorium. In particular, we
look at how he constructed a tangent at an
arbitrary point on this curve and how, using
the evolute of a curve (envelope of normals),
he could calculate its length. In this way,
geometricallymanipulating second
derivatives (before the differential calculus of
Newton and Leibniz), he obtained the
curvature radius at every point of the cycloid
and of other curves, such as the parabola.