  It will be shown that Pascal's Theorem is equivalent to the associativity of
a natural binary operation on conic sections. A novel proof for Pascal's
Theorem will then be given by showing that this binary operation is associative
independent of Pascal's Theorem. Specifically, this operation is equivalent to
either addition of real numbers, multiplication of real numbers, or rotations
on the plane depending on the type of the conic. Since each of these is already
known to be associative, it will follow that the binary operation is
associative and this will prove Pascal's Theorem.
