Answer
Assuming that the sun's rays are "practically parallel", and referring to Figure 1.1 on page 4, one may form two similar triangles.
$$\frac{Pillar \,shadow}{Pillar \,height} = \frac{Distance \,from \,Alexandria \,to \,Syene}{Earth's \,radius}$$
The two 1-to-8 ratios are equal.
Work Step by Step
See figure 1.1 on page 4, and the discussion on that page.
