Descartes's Mean Proportionals/Logarithm Machine
Use the checkboxes to show or hide aspects of the construction.
Turn on "Show construction lines" and "Show traced curves", then move point B to see the curves being traced.
In his Geometry (1637), Descartes described and illustrated this machine for solving the problem of finding any number of mean proportionals between two numbers. Later he used it to solve what would now be called a differential equation, resulting in a logarithmic function.
See Descartes's Logarithm Machine for a full explanation.
Related demonstration files at quadrivium.info:
Similar right triangles
Geometric means
Descartes's machine used to solve a "two mean proportionals" problem
Descartes's machine used to plot points on the graph of a logarithm function
Descartes's construction used to find the slope of a tangent to a logarithmic graph