Treatise on the Barycentre of Curvature of Plane Curves

Résumé du livre

This is a translation of 'Del baricentro di curvatura' by Jacob Steiner (available from www.e-rara.ch).This book is generally about cycloids and related matters, but is not limited to circles rolling upon straight lines, but rather convex curves or arcs rolling upon other convex curves or arcs, and the areas of curves described by points fixed relative to the rolling arc or curve. The author finds that there is a unique point, which he calls the barycentre of curvature of the curve (or arc), which describes a curve of minimum area with respect to the base upon which it rolls. He uses the term barycentre in analogy to the centre of gravity of a system of weights, but here the curvatures of the successive points of the arc or curve are what determine the location of the barycentre. The areas descibed by points other than the barycentre are found to be given by relatively simple formulae dependent upon the distance from the barycentre of the curve. Although not an easy treatise to comprehend, the level of mathematical ability required is not much more than basic analytic geometry.