The Folium of Descartes
____________ Descartes' Tangent Find the line tangent to a given curve
by constructing a circle tangent to the curve at
point
P.
The radius of the circle is perpendicular to the tangent of both the circle and the curve at point P. 
Biographical Sketch René Descartes ( 1596  1650 ): Gentleman, Soldier, Philosopher, and Mathematician Modern mathematics began with two great advances, analytic geometry and the calculus. The man who finally crystallized the method of wedding algebra to geometrical proof was René Descartes. Moreover, his persistent rational skepticism, his questioning of how one could ever know truth, has led to what we generally today call "the scientific method," i.e., controlled experiments based on the application of rigid mathematical reasoning. His life spanned one of the greatest intellectual periods in the history of all civilization. To mention only a few of the giants, Fermat and Pascal were his contemporaries in mathematics. Shakespeare died when Descartes was twenty; Descartes outlived Galileo by eight years; and Newton was eight when Descartes died. Descartes was twelve when Milton was born and Harvey outlived Descartes by seven years. Father Mersenne, the famous amateur of science and mathematics, was Descartes' older chum, schoolmate, and lifelong friend. Cardinal Richelieu was his supporter. The concept of analytic geometry came to Descartes in a dream on November 10, 1619; thus, this day marks the official birthday of modern mathematics. Its formal debut to his contemporaries came on June 8, 1637, with the publication of La Géométrie as an appendix to his now famous Discours de la Méthode. Descartes was then fortyone years old. As a soldier, he joined armies and survived fierce battles. As a gentleman and traveler, he visited most of the major sites of late Renaissance Europe. As a teacher, he enjoyed the companionship of royalty. He died in Stockholm of complications  some say poisoning, others say lung disorders  acquired while delivering 5 AM instruction to Queen Christina of Sweden, the daughter of Gustavus Adolphus. He is now buried in the Pantheon in Paris. May we encourage you to read further. Such an interesting, varied, and accomplished life deserves depth of investigation. The small town where Descartes was born has been renamed in his honor.


