Two tan δ peaks related to MH4CLOn and PLA were observed in a dynamic mechanical curve of the semi-IPN.
A tabulation of these parameters permits reproduction of the mechanical curves.
It is treated in Book One, as Descartes explains his geometrical analysis, and then again in Book Two, where Descartes offers the synthesis, i.e., the geometrical demonstration, of his solution to the Pappus Problem in n-lines, a demonstration which relies on the famous distinction between "geometric" and "mechanical" curves that begins this part of the work.
Without a clear indication of why the pointwise construction of a Pappus curve is "geometric," Descartes would have to allow "mechanical" curves such as the spiral and quadratrix into the domain of geometrical curves, since these curves can also be pointwise constructed.
The geometric objects that were then of growing interest were precisely the mechanical curves that Descartes had wished to banish from mathematics.
This restriction excluded "mechanical" curves generated by kinematic processes.
Book Two of La Géométrie is entitled "On the Nature of Curved Lines" and commences with Descartes' famous distinction between "geometric" and "mechanical" curves.
One particular muscle strength/power training adaptation involves an increase in the force-velocity relationships and the mechanical parabolic curves of power vs. velocity after high-intensity training programs, both in isoinertial [14] and isokinetic [4] exercises.
This is an early example of a mechanical curve (a curve traced by a moving point) considered by a Greek mathematician.
