the Egyptian seked, or seqed, the ratio of the run to the rise of a slope (cotangent). The seked is at the base of problems 56, 57, 58, 59 and 60 of the Rhind papyrus — an ancient Egyptian mathematical document. More practically Thales used the same method to measure the distances of ships at sea, said Eudemus as reported by Proclus ("in Euclidem"). 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 (Proclus, In Euclidem, 352). Thales' theorems There are two theorems of Thales in elementary geometry, one known as Thales' theorem having to do with a triangle inscribed in a circle and having the circle's diameter as one leg, the other theorem being also called the intercept theorem. In addition Eudemus attributed to him the discovery that a circle is bisected by its diameter, that the base angles of an isosceles triangle are equal and that vertical angles are equal. According to a historical Note, when Thales visited Egypt, he observed that whenever the Egyptians drew two intersecting lines, they would measure the vertical angles to make sure that they were equal. Thales concluded that one could prove that all vertical angles are equal if one accepted some general notions such as: all straight angles are equal, equals added to equals are equal, and equals subtracted from equals are equal. The evidence for the primacy of Thales comes to us from a book by Proclus who wrote a thousand years after Thales but is believed to have had a copy of Eudemus' book. Proclus wrote "Thales was the first to go to Egypt and bring back to Greece this study." He goes on to tell us that in addition to applying the knowledge he gained in Egypt "He himself discovered many propositions and disclosed the underlying principles of many others to his successors, in some case his method being more general, in others more empirical." Other quotes from Proclus list more of Thales' mathematical achievements: In addition to Proclus, Hieronymus of Rhodes also cites Thales as the first Greek mathematician. Hieronymus