Blaise Pascal (1623-1662) did fundamental work in many areas of science and mathematics, including the physics of hydrostatics, the geometry of conic sections, and the foundations of probability and philosophy. He is also credited with inventing the first digital calculator. The following result is due to Pascal. Given ?ABC, construct a line DE, intersecting sides AB and AC at D,E, and parallel to BC. Pick any point F on BD and construct FE. Then, construct BG parallel to FE, intersecting side AC at G. Then, FC must be parallel to DG. Prove Pascal's Theorem. [Hint: Use the theorems in this section on parallels and similar triangles to show that AD = AF .] Hilbert [21, page 46] used Pascal's Theorem extensively to develop his "arithmetic of segments," by which he connected segment length with ordinary real numbers