Particularly of interest to Pascal was a work of Desargues on conic sections.
Following Desargues' thinking, the sixteen-year-old Pascal produced, as a means of proof, a short treatise on what was
called the "Mystic Hexagram", Essai pour les coniques ("Essay on Conics") and sent it—his first serious work of mathematics—to
Père Mersenne in Paris; it is known still today as Pascal's theorem.
It states that if a hexagon is inscribed in a circle (or conic) then the three intersection points of opposite sides lie on a line (called the Pascal line).
Pascal's work was so precocious that Descartes was convinced that Pascal's father had written it.
When assured by Mersenne that it was, indeed, the product of the son not the father, Descartes dismissed it with a sniff: "I do not find it strange that he has offered demonstrations about conics more appropriate than those of the ancients," adding
It states that if a hexagon is inscribed in a circle (or conic) then the three intersection points of opposite sides lie on a line (called the Pascal line).
Pascal's work was so precocious that Descartes was convinced that Pascal's father had written it.
When assured by Mersenne that it was, indeed, the product of the son not the father, Descartes dismissed it with a sniff: "I do not find it strange that he has offered demonstrations about conics more appropriate than those of the ancients," adding