This remarkable theorem is not part of the history of mathematics.
Descartes' <i>Treatise</i> was never published, and lay hidden 
like a mathematical time capsule for over 200 years.<p>

In this column I will examine 
the statement quoted above (``Descartes'
Lost Theorem''), and the surrounding material. They
give us a look back into the mind of one of the
inventors of modern mathematics at the beginning of
his career, and they will give us a chance to
examine some of the more interesting discoveries of the next two
centuries, discoveries that are fundamental to 
geometry and topology as we know them today, and which Descartes' 
geometric intuition allowed him to anticipate.