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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.

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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.

In this diagram you can see many similar right triangles and many geometric means.

See Descartes's Logarithm Machine for a full explanation.

Related demonstration files:

Similar right triangles

Geometric means

Descartes's mean proportionals/logarithm machine

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

Susan Addington, Created with GeoGebra


Mathematical Intentions
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Last updated December 26, 2009

Copyright 2009-10 David Dennis and Susan Addington. All rights reserved.