The curious case of QP.6: the reception of Archimedes' mechanics by Federico Commandino and Guidobaldo dal Monte (Q2831664)

In his \textit{Quadrature of the parabola}, Archimedes stated in Proposition 6 (QP 6): ``Imagine that the supposed plane is perpendicular to the horizon and that all what is on the same side of \(\Delta\) compared to the line \(AB\) may be considered below, the rest above. Let the triangle \(B\Delta\Gamma\) be orthogonal, with a right angle at \(B\), and with side \(B\Gamma\) equal to the half of the beam of a balance. The triangle is to be suspended from the points \(B\) and \(\Gamma\). On the other side of the balance let there be fixed a certain figure \(Z\) at the point \(A\) so that \(Z\) at \(A\) `equiponderates' the triangle \(B\Delta\Gamma\) in the position where it was suspended. I claim that the figure \(Z\) is the third part of the triangle \(B\Delta\Gamma\).'' NEWLINENEWLINEFederico Commandino (1506--1575) and his disciple Guidobaldo dal Monte (1545--1607) of the Urbino school -- committed to restore Greek mathematics -- both interpreted QP 6, for the edition of Archimedes' works and for the \textit{Mechanicorum liber} (1577), respectively. The author points out that the interpretations differ substantially, and that these interpretations impact the understanding of the Archimedean theory of equilibrium. Reflections on central features of the so-called ``mathematical humanism'' of the Urbino school ensue.