home The Death of Distance: from Pythagoras to Galileo
An event at the Dome, November 29th, 2000

Ancient Greeks

thalesThales
Born: about 624 BC in Miletus, Asia Minor. Died: about 547 BC in Miletus

 Thales seems to be the first known Greek philosopher, scientist and mathematician although his occupation was that of an engineer. However, none of his writing survives so it is difficult to determine his views or to be certain about his mathematical discoveries. Indeed it is unclear whether he wrote any works at all and if he did they were certainly lost by the time of Aristotle who did not have access to any writings of Thales. On the other hand there are claims that he wrote a book on navigation but these are based on little evidence.
Proclus, the last major Greek philosopher, who lived around 450 AD, wrote:- Thales first went to Egypt and thence introduced this study geometry into Greece. He discovered many propositions himself, and instructed his successors in the principles underlying many others, his method of attacking problems had greater generality in some cases and was more in the nature of simple inspection and observation in other cases.





Heights of pyramids Thales measured the height of pyramids. He succeeded in measuring the pyramids by observation of the length of their shadow at the moment when our shadows are equal to our own height.
Please enable Java for an interactive construction (with Cinderella).

This is based on the idea of similar triangles, that at the instant when the length of the shadow of one object coincides with its height, then the same will be true for all other objects.






Elementary geometry In many textbooks on the history of mathematics Thales is credited with five theorems of elementary geometry:-
  • (i) A circle is bisected by any diameter.
  • (ii) The base angles of an isosceles triangle are equal.
  • (iii) The angles between two intersecting straight lines are equal.
  • (iv) Two triangles are congruent if they have two angles and one side equal.
  • (v) An angle in a semicircle is a right angle.
About 300 years later Euclid was to develop these ideas in hhis great work The Elements.
See link: Euclid's elements.
Distance from ship to shore Thales had an instrument consisting of two sticks nailed into a cross so that they could be rotated about the nail. An observer then went to the top of a tower, positioned one stick vertically (using say a plumb line) and then rotating the second stick about the nail until it point at the ship. Then the observer rotates the instrument, keeping it fixed and vertical, until the movable stick point at a suitable point on the land. The distance of this point from the base of the tower is equal to the distance to the ship.