Answer
A projectile at a given height can "fall around the Earth" if it has the correct tangential speed v. After an elapsed time t, it will have moved a horizontal distance vt and fallen a vertical distance $\frac{1}{2}gt^{2}$ below the horizontal. If the Earth's surface curves downward by exactly that distance, the projectile will be at the same height above the surface.
This is discussed on page 190.
