Tales of Miletus, the philosopher who asserted logical thinking as an explanation for the origin of the universe

In the year 624 BC, the philosopher, mathematician, astronomer, geometer, physicist and great Greek thinker Thales of Miletus, considered the first Western philosopher, for his insistent search for a rational response to different natural phenomena.

Miletus was the founder of the Milesian philosophical school, where he taught Anaximander and Anaximenes, who was a student of the latter. His days ended in Miletus in 543 BC, during the gymnastics games at the Olympics.

The theorem of Thales of Miletus

By means of two theorems linked to geometry, Thales of Miletus compared the similarity between triangles, and determined that two triangles are equal if they have identical corresponding angles and identical sides. they are proportional to each other.

There are two theorems that make up the Thales theorem or Thales theorem , which are presumed to have been discovered by him when he was studying the existence of parallelism between two straight lines .

The first theorem considered the foundation of descriptive geometry, provides that if a parallel line is drawn to any of the sides of a triangle, the result is two proportional triangles.

The fraction A'C' is drawn to triangle ABC, giving rise to a new triangle identified A'BC', identical to the first. Consequently, the three angles of the triangle are similar and their sides are equal.

This first Thales theorem was very useful for measuring tall structures, because at the time, there were no other measuring devices.

As a consequence of the first theorem, another variant arises: if two parallel lines are cut by two other lines, the segments derived from both lines are proportional.

The second theorem of Tales is about geometry, linked to right triangles, inscribed in each angle of a circumference.

According to this theorem, in a circle with center O and diameter AC, each point B of the circle (different from A and C) determines a right triangle ABC, with right angle

Application of the Thales Theorem

The Thales theorem influences many of the activities we do every day, for example, to calculate the height of an object by means of the projection of the shadow, with the support of a stake or rod

Now then, taking into account the relationship of equal triangles, the link I establish with my shadow is similar to the one that the pyramid establishes with its own.

The story goes that Plutarch maintained that Thales of Miletus discovered the height of the pyramids of Giza, based on his first theorem, with the support of shadow measure.

The two theorems of Tales are also applied in the solution of other cases, as well as for the analysis of transformations.

In this sense, it is applied to divide a segment into equal parts, calculate the fourth and third proportional of two given segments, the proportional mean, the graphical calculation of products and ratios of given segments.

Likewise, they are used in the similarity and study of scales, the golden segmentation, the fourth proportional of three given segments, as well as to calculate simple, double and quaternary harmonic ratios.

Thales' contribution to the sciences

The knowledge of Thales of Miletus was under the influence of the Egyptian and Babylonian sages.Historically considered one of the seven wise men of Greece. He was the forerunner of Greek mathematics and geometry.

One of the purposes of his research was to study the origin of the physical cosmos, from a logical, rational point of view, and thus break with the myths on which it was based.

He believed that there was a common principle from which all things emanated and developed. He asserted that all things were intrinsically equal to one another. He emphatically maintained that this common element, intrinsic to everything, was water, recognizing it as the arche or first creative principle of everything.

Tales refuted the disparity between cause and effect, stating that if reality is physical, its cause is also physical.

He established during the beginning of his proofs of geometric theorems by means of logical reasoning, that every diameter bisects the circumference, the angles opposite the vertex are equal, and that the base angles of an isosceles triangle are also equal .

He determined that two triangles that have two equal angles and one equal side are similar, that every angle inscribed in a semicircle is right. He found the constellation Ursa Minor and concluded that the moon was seven hundred times smaller than the sun.

Likewise, he studied and spoke about solar and lunar eclipses. He established the number of days in the year. He was a pioneer in the investigation of the magnetic phenomenon.

It is believed that Thales of Miletus wrote three works, Astrology, On the Solstice and On the Equinox, although there was a record of it. It is also believed that part of his mathematical works were embodied in the Elements of Euclid : the definition I. 17 and the propositions I. 5, I. 15, I. 26 and III. 31.

According to Aristotle, Tales affirmed that the earth is a kind of island that “floats” on the water, being the reason why sometimes it trembles, since it is not attached to no fixed base, causing it to wobble.

Among other important aspects in favor of Tales of Miletus, is that the lunar crater Thales, located northeast of the moon, east of Strabo -which is the largest crater-, southeast of walled plain De La Rue, was named in honor of this great philosopher.

It also highlights the story represented by Thales of Miletus, known as The astrologer who fell into a well, which was cited for the first time in the platonic dialogue Theaetetus (174a).

This story narrates that Tales was looking towards the firmament, inquiring about the origin of the universe. As he walked so lost in his thoughts, he fell into a well.

Meanwhile, a woman from Thrace who was near him, laughed at the event and asked him why he was so interested in knowing the things that existed in the universe, while what he had in front of him escaped him. .