structural:scholar_edition
Similar triangles

The story is told in Diogenes Laërtius, Pliny the Elder, and Plutarch, sourced from Hieronymus of Rhodes, that when Thales visited Egypt, he measured the height of the pyramids by their shadows at the moment when his own shadow was equal to his height. According to Plutarch, it pleased the pharoah Amasis. More practically, Thales was said to have the ability to measure the distances of ships at sea.

These stories indicate familiarity with the intercept theorem, and for this reason the 26th proposition in the first book of Euclid's Elements was attributed to Thales. They also indicate that he was familiar with the Egyptian seked, or seqed, the ratio of the run to the rise of a slope (cotangent). According to Kirk & Raven, all you need for this feat is three straight sticks pinned at one end and knowledge of your altitude. One stick goes vertically into the ground. A second is made level. With the third you sight the ship and calculate the seked from the height of the stick and its distance from the point of insertion to the line of sight.