Dean pointed to a small dot **midpoint** on the page.

Take a rod LMN bent at right angles at M, such that MN= AB; let the leg LM always pass through a fixed point 0 on AB produced such that OA = CA, where C is the middle point of AB, and cause N to travel along the line perpendicular to AB at C; then the **midpoint** of MN traces the cissoid.

By the **midpoint** of the twentieth century, America's dreamers were preoccupied with the future—and not just any old future, but the great and glorious future that seemed inevitable.