**Thales** was the first known Greek philosopher, scientist and mathematician. He is credited with five theorems of elementary geometry.

- His parents are said by some to be from Miletus but others report that they were Phoenicians.
- Thales seems to be the first known Greek philosopher, scientist and mathematician although his occupation was that of an engineer.
- He is believed to have been the teacher of Anaximander (611 BC - 545 BC) and he was the first natural philosopher in the Milesian School.
- However, none of his writing survives so it is difficult to determine his views or to be certain about his mathematical discoveries.
- Even if the book is fictitious, it is quite probable that Thales did indeed define the constellation Ursa Minor.
- 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.
- There is a difficulty in writing about Thales and others from a similar period.
- Although there are numerous references to Thales which would enable us to reconstruct quite a number of details, the sources must be treated with care since it was the habit of the time to credit famous men with discoveries they did not make.
- Partly this was as a result of the legendary status that men like Thales achieved, and partly it was the result of scientists with relatively little history behind their subjects trying to increase the status of their topic with giving it an historical background.
- Certainly Thales was a figure of enormous prestige, being the only philosopher before Socrates to be among the Seven Sages.
- He persuaded the separate states of Ionia to form a federation with a capital at Teos.
- It is reported that Thales predicted an eclipse of the Sun in 585 BC.
- The cycle of about 19 years for eclipses of the Moon was well known at this time but the cycle for eclipses of the Sun was harder to spot since eclipses were visible at different places on Earth.
- Thales's prediction of the 585 BC eclipse was probably a guess based on the knowledge that an eclipse around that time was possible.
- No Babylonian theory for predicting a solar eclipse existed at 600 BC, as one can see from the very unsatisfactory situation 400 years later, nor did the Babylonians ever develop any theory which took the influence of geographical latitude into account.
- day was all of a sudden changed into night.
- This event had been foretold by Thales, the Milesian, who forewarned the Ionians of it, fixing for it the very year in which it took place.
- The Medes and Lydians, when they observed the change, ceased fighting, and were alike anxious to have terms of peace agreed on.
- a more likely explanation seems to be simply that Thales happened to be the savant around at the time when this striking astronomical phenomenon occurred and the assumption was made that as a savant he must have been able to predict it.
- There are several accounts of how Thales measured the height of pyramids.
- This appears to contain no subtle geometrical knowledge, merely an empirical observation 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.
- What Egyptians knew of geometry was mainly rules of thumb, and there is no reason to believe that Thales arrived at deductive proofs, such as later Greeks discovered.
- However, although there is much evidence to suggest that Thales made some fundamental contributions to geometry, it is easy to interpret his contributions in the light of our own knowledge, thereby believing that Thales had a fuller appreciation of geometry than he could possibly have achieved.
- The base angles of an isosceles triangle are equal.
- Proclus, writing around 450 AD, is the basis for the first four of these claims, in the third and fourth cases quoting the work History of Geometry by Eudemus of Rhodes, who was a pupil of Aristotle, as his source.
- The History of Geometry by Eudemus is now lost but there is no reason to doubt Proclus.
- A deeper examination of the sources, however, shows that, even if they are accurate, we may be crediting Thales with too much.
- It is quite likely that Thales did not even have a way of measuring angles so 'equal- angles would have not been a concept he would have understood precisely.
- He may have claimed no more than "The base angles of an isosceles triangle look similar".
- The theorem (iv) was attributed to Thales by Eudemus for less than completely convincing reasons.
- The method which he thinks it most likely that Thales used was to have 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 points at the ship.
- The distance of this point from the base of the tower is equal to the distance to the ship.
- Although theorem (iv) underlies this application, it would have been quite possible for Thales to devise such a method without appreciating anything of 'congruent triangles'.
- Also even Pamphile cannot be taken as an authority since she lived in the first century AD, long after the time of Thales.
- Others have attributed the story about the sacrifice of an ox to Pythagoras on discovering Pythagoras's theorem.
- Thales believed that the Earth floats on water and all things come to be from water.
- It has also been claimed that Thales explained earthquakes from the fact that the Earth floats on water.
- Again the importance of Thales' idea is that he is the first recorded person who tried to explain such phenomena by rational rather than by supernatural means.
- It is interesting that Thales has both stories told about his great practical skills and also about him being an unworldly dreamer.
- On the other hand Plato tells a story of how one night Thales was gazing at the sky as he walked and fell into a ditch.

Born about 624 BC, Miletus, Asia Minor (now Turkey). Died about 547 BC, Miletus, Asia Minor (now Turkey).

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**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive