Thales the Milesian works. Milesian School: Thales, Anaximander and Anaximenes

2. Milesian school: Thales, Anaximander and Anaximenes Thales of Miletus (c. 625–547 BC) - the founder of European science and philosophy; in addition, he is a mathematician, astronomer and politician, enjoyed great respect from his fellow citizens. Thales came from a noble family

In the pre-scientific period, the people who came closest to science were cosmogonist poets and representatives of practical professions. However, the former were content with exclusively mythological positions, and the latter with exclusively technical ones and had not yet applied science. But during this period the Greeks experienced a transition from myths and practical skills to science. It seems to us that this happened in the 6th century. Later Greek authors pointed to Thales as the philosopher who accomplished this transition.

Personality of Thales. This semi-legendary Greek lived at the turn of the 7th and 6th centuries. (624–547) BC e., that is, during the time of Solon and Croesus. He was an outstanding representative of craftsmen and sages. Even the meager information about him allows us to judge that he combined a politician (his political merits brought him the fame of a sage), a technician, an engineer, a merchant and a traveler, who brought not only goods, but also various practical skills and abilities from different countries. In addition, he was a scientist.

1. Transition from skills and abilities to science. Thales knew a way to measure the height of the pyramids and distances at sea. It seems that he was a geometric scientist. He predicted a solar eclipse on May 26, 585, surprising his countrymen, and this gives the impression that he was an astronomer. However, the calculations that he performed were carried out in a technical rather than a scientific way: he calculated and predicted phenomena, without being able to justify his calculations, without knowing the causes of the phenomena. Measurements were carried out in a similar way in Egypt, and astronomical predictions were made in Babylon. It is quite possible that it was from there that Thales brought his skills. He cannot, however, be considered the creator of the mathematical and astronomical sciences, since their emergence dates back to later times. Thales had remarkable skills and abilities in these areas, but not scientific knowledge.

How is science different from skill? Firstly, a single successful observation and a single true statement do not constitute science. There were many such observations and statements before Thales. To become science, they must be related to other observations and statements and ordered. Secondly, the general awareness that things should be this way and not different does not create science. This awareness must be analyzed and expressed in the form of statements using concepts. Finally, it is not enough to know something; it is also necessary to justify or prove that this is exactly the case. Even before the appearance of the first mathematician, everyone who built himself a hut from two identical sticks knew that they should be inclined equally, but this knowledge did not yet give him the opportunity to conceptually formulate theorems about isosceles triangles and, moreover, of course, did not give him the opportunity to prove these theorems. Consequently, in order for the achieved knowledge to be recognized as scientific, it must be organized, analyzed and proven. Without this, even the most complex skills are not science. To summarize, we can say that science requires not only skill, but also understanding.

Science is also different from skills. The goal of science is to achieve truths that are interesting in themselves. As for skills, we are talking only about practically valuable truths. Skills and abilities were developed for practical purposes and for these purposes they were quite sufficient. And when they began to be interested in truths in themselves, then a new goal and a new way of comprehending it, inherent in science, appeared. Thales studied mathematics and astronomy for practical purposes and in practical ways. But after that, if you believe the legends, he tried to get the truth in an area where there could be no talk of practical goals - in philosophy. If Thales was a scientist, he was a philosopher. And it is not surprising that the first science to come into being was philosophy: from the point of view of the generality of its subject, it had the least practical significance, but was the most accessible theoretically.

This transition from practical skills to theoretical science occurred in Greece between the 7th and 6th centuries. Did Thales do it? Every time the Greek philosophers, looking for their predecessors, came to Thales, not finding anyone earlier than him. So, in this case, it is quite plausible that his philosophical theory was the first scientific theory that appeared in Europe, and perhaps in the world.

2. Transition from mythology to science. Thales argued: everything is water, comes from water and turns into water. One could assume that this was not a new view, that something similar was said even before Thales. Aristotle noted that ancient people viewed nature in a similar way. In their opinion, Ocean and Thetis were the parents of everything that exists in the world. But here the difference is fundamental: Thales speaks of water, and his predecessors speak of water deities; he speaks of a real object, and they speak of fantastic creatures. When speaking about Oceanus and Thetis, the ancients did not mean science, but mythology. For the emergence of science, it was necessary for a revolution in the way of thinking to occur: it was necessary to break not only with the mythological, but also with the practical way of thinking. This turn was achieved by Ionian thinkers, the first of whom was Thales. The task he set for himself was to explain phenomena. From this position he was no different from the creators of mythology, but the fact is that his method of explanation was different.

Thales' task was to explain the origin of the world. He asked not who created the world, but what the world was like in the beginning. It was not about what happened before the world, but about what was, strictly speaking, its beginning. In this sense, the beginning of the world was the first philosophical problem. The fact that this was the first problem of philosophy was not surprising: to people at that level of development when they were not very interested in scientific criticism, it seemed that the way they see the world is the way it is. They expected something different from the sage, namely, to say what the world was like. At the same time, the thinking of that time was inclined to believe that the primary form of a thing is most important, and Thales admitted that, ultimately, after all kinds of changes, the world would return to the original state from which it began to develop. The original view of the world, in his understanding, was not only the first, but also essential.

It was still a rather archaic philosophy, different from mythology, but in its questions and answers standing on the border of myth. It still does not contain many of those features of Greek thinking that emerged in the course of further development. At the same time, the philosophy of the Greeks of this period did not differ from the speculations of other peoples who stood at the same level of civilization.

3. First philosophical problems. The subject of the aspirations of Thales and his immediate followers was nature. Aristotle called these most ancient philosophers physiologists, or theorists of nature. In the spirit of their time, they were interested primarily in its beginning. The initial question they asked themselves was: what was the beginning of nature? And this question for them meant the following: what was the original type of bodies from which nature develops? Later the question was formulated: what was the primary matter? The very concept of “matter” was not yet used by these first philosophers. Moreover, they did not use the concept of matter that the later Greeks used. They dealt with matter as a collection of concrete bodies; they did not know the abstract concept of matter, according to which it is one of the elements of the body, distinct from its other elements, such as shape or force. They did not think of matter as something not yet formed. The distinction between matter and form was an idea of ​​later generations of Greek philosophers.

Philosophers of that time understood matter not as a powerless mass that requires the influence of an external force in order to move. Distinguishing between matter and driving force was also the result of later reflections. The concepts that these ancient philosophers used to solve the problems of the beginning of the world were not yet clearly identified by them and were not abstract. It did not occur to them that force could be outside of matter. On the contrary, they believed that the ability to move is the fundamental essence of matter. They understood the ability to move animistically, as a manifestation of life and soul. Thales said that “everything is alive, as can be seen in amber and magnesia.” This inseparability of matter from force, life and soul was so characteristic of the first group of Greek philosophers that they were called "hylozoists", or those who considered life to be inseparable from matter. Some historians consider them materialists. Indeed, they did not know objects other than material ones, and these were materialists who had not yet comprehended the pure concept of matter and attributed spiritual traits to all material objects and, quite in accordance with the thought of that time, were inclined to see the activity of the soul in life.

Why did Thales believe that only water, and not other types of matter, was the beginning of nature? Perhaps there was a mythological tradition and a connection with the Ocean and Thetis at work here; Meanwhile, Thales could give a different explanation for his position. It was based on observations of certain phenomena: what is alive is wet, lives with moisture, and what is dead dries up, any embryo is wet, and food is juicy. These observations made it possible to conclude that water gives life and has those features that are necessary and sufficient for all nature to develop from it. This first philosophical theory had the most imaginative justification.

The solution to philosophical problems proposed by Thales did not meet with much response, since other observations and facts suggested that other types of matter were the beginning of the world. These other principles have found enough supporters. One of Thales' followers argued that the primary type of matter was fire, another - that air. But they posed this question in the same way as Thales, and therefore became his followers. Thales's student was Anaximander, and Anaximander's students were Anaximenes and Heraclitus, as well as many generations of philosophers. The Greeks considered Thales the founder of their philosophy.

Thales's main merit was not in the answers, but in the questions he posed. The answers could not be very satisfactory because the questions were hopelessly difficult. How could Thales know what was the beginning of the world? It must be assumed that the first philosopher was an outstanding person. He learned a variety of skills in various areas of life in other countries; the transition from skills to philosophy may not have required much mental effort, but the act itself was quite courageous.

Read the biography of the philosopher: briefly about life, main ideas, teachings, philosophy
THALES OF MILETOS
(c. 625 or 640 - c. 547 or 545 BC)

Ancient Greek thinker, founder of ancient philosophy and science, founder of the Milesian school, one of the first recorded philosophical schools. He raised all the diversity of things to a single element - water.

Modern European philosophy, like all modern civilization, originates in Ancient Greece, where the word “philosophy” (“love of wisdom”) came to us. However, the first philosophical systems arose in the 6th-5th centuries BC. e. not in Greece itself, but on the western coast of Asia Minor, in the Ionian cities, which were founded by the Greeks and in which industry, trade and spiritual culture began to develop earlier than in Greece itself. The largest of all Greek cities in Asia Minor was Miletus.

Very little is known about the first ancient Greek philosophers. There is almost no exact information. All evidence is usually presented with reservations.

In those distant times, the Greeks did not write biographies of prominent people. Subsequently, when Hellenistic scientists began to compile biographies, trying to systematize the available information of a historical and chronological nature, it was extremely difficult to establish the reliability of certain information. Later ancient authors, for example, the Athenian grammarian Diogenes Laertius (3rd century BC), who drew his information from the “Chronicles” of Allolodorus, which have not reached us, could not provide accurate biographical data. The writings of the authors of late antiquity contain more legends, anecdotes and various kinds of fabrications that have developed over the centuries and associated with the names of Heraclitus and other thinkers of the distant past than reliable information. It is customary to begin a story about philosophy with a mention of the seven Greek sages and the first of them, Thales of Miletus.

Seven Greek wise men - who are they? Called different names. But the name of Thales is repeated, most often included in the list of the seven wise men. Apparently, he was the most popular, the wisest of them. There are many legends about this. Diogenes Laertius in his book “On the Life, Teachings and Sayings of Famous Philosophers” says the following: fishermen found a tripod in the sea; The Milesians decided to give the tripod to the wisest of the sages. They gave it to Thales, who gave it to another sage, and the other to a third. But in the end the tripod still returned to Thales. According to other testimonies, the cup of King Croesus was intended for the wisest of the wise Hellenes, and in a circle it returned to Thales, which is captured in ancient verses: “... and how wise among the seven wise men Thales is in observing the stars.” There are several versions regarding the life of Thales of Miletus. Diogenes Laertius: “Allolodorus in the “Chronology” writes that Thales was born in the 1st year of the 39th Olympiad, lived seventy-eight years (or, according to Sosicrates, ninety) and died in the 58th Olympiad. Thus, he lived under Croesus, for whom he diverted the current of the Halys in order to cross the river without bridges."

It is believed that there is at least one exact date associated with his life - 585, when there was a solar eclipse in Miletus and when Thales is said to have predicted it. If Thales predicted a solar eclipse, then he was most likely already a man of mature age. Consequently, VII-VI centuries BC. e. and there is approximately the time of life of Thales and, perhaps, other ancient Greek sages.

Little is known about the origin of the thinker. Diogenes Laertius: “Thales (according to the agreement of Herodotus, Durid, and Democritus) was the son of Examius and Cleobulina from the family of the Felids, and this family was Phoenician, the most noble, neighbors of the descendants of Cadmus and Agenor. He was one of the seven sages, which is confirmed by Plato, and when, under the Athenian archon Damasius, these seven received the title of wise men, he was the first to receive such a name (as Demetrius of Phalerus says in the “List of Archons”). In Miletus, he was recorded as a citizen when he appeared there along with Neleus, expelled from Phenicia. However, the majority claims that he was a native of Miletus, and, moreover, from a noble family."

The narrative of Heraclides says that Thales lived in solitude as a simple citizen. According to some sources, he was married and had a son, Kibisf, while others say that he never married, but adopted his sister’s son. When asked why he doesn't have children, he replied: "Because I love them"; when his mother forced him to marry, Thales is said to have replied: “Too early!”, and when she asked the same question to him as an adult, he replied: “Too late.”

Philosophers often express directly opposite judgments about Thales. Some (say, Aristotle) ​​speak of Thales as a practical man who stood firmly on the ground and was very inventive in everyday affairs. Other authors (Plato), on the contrary, consider the Milesian a thinker immersed in abstract reasoning, who was no longer at all interested in practical matters. Thales loved to travel. He visited Egypt Central Asia, tried to collect the remnants of ancient knowledge in these countries.

“He had no teachers,” writes Diogenes Laertius, “except for the fact that he traveled to Egypt and lived there with the priests. Jerome says that he measured the height of the pyramids by their shadow, waiting for the hour when our shadow was the same length as us He also lived with Thrasybulus, the Milesian tyrant (as Minius reports).

It is quite possible that Thales, while traveling, ended up in Phenicia (there are even suggestions whether Thales was Phoenician by origin, although most researchers still agree that he was a Milesian). From Phoenician and Egyptian astronomy in those centuries it was already known how to navigate the sea using the stars.

Thales brought Eastern knowledge (and the first scientific instruments - for example, a protractor) to Greece. Having remarkably developed this knowledge, he began European science. He was the first who wanted to use knowledge to explain the structure of the world - something that had previously only been told; replace the will of the gods with the laws of nature - the East did not do this. And finally, Thales knew how to wonderfully explain what was invented.

In an effort to understand the world in which we live, Thales was primarily interested in what happens between heaven and earth, what the Greeks called meteors (aerial phenomena). The fact is that Thales lived in a city of Greek merchants. In his search, he was guided by considerations of utility: he wanted ships to be able to deliver their cargo to the port, and therefore sought to find out why it rains, what the wind is, what the stars are by which a ship can be steered. Science has no other origin than practice.

The later tradition attributed to Thales five theorems of geometry (including the equality of angles at the base of an isosceles triangle and the division of a circle by diameter in half). New knowledge, problems and topics have also accumulated in connection with astronomy. For example, the Phoenicians, Egyptians and Greeks replaced lunar calendar it's sunny. The Greeks had already switched to a similar modern division of the year into months, days, etc., that is, they switched to a solar calendar. And often the accumulation of this kind of knowledge is associated with the name of Thales. Here is the testimony of Apuleius: “Thales of Miletus, undoubtedly the most outstanding of those famous seven wise men (he was the first discoverer of geometry among the Greeks, and the most accurate tester of nature, and the most experienced observer of luminaries), discovered the greatest things in small lines: the cycles of the seasons, the blowing winds, stars, the movements of thunder, the wondrous rumblings, the winding paths of the planets, the annual turns of the Sun, and also [explained] the waxing of the emerging Moon, the waning of the aging Moon, and the eclipsing of obstacles. Moreover, already in his old age he came up with a divine calculation [proportion] relating to the Sun. , [calculating] how many times the sun measures the circle it runs with its size [diameter]. This evidence most likely attributes to the legendary Thales the body of knowledge accumulated in that distant era different people. Scientists judge the works of philosophers before Plato by “fragments” in the works of later authors. Usually these are short, inaccurate retellings of individual thoughts. It is not even known about the works of Thales whether he wrote them at all. It is most likely that he created “Marine Astronomy” (in verse, like all early thinkers); two more of his astronomical treatises were called (on the equinox, on the solstice), but the exact fragments have not reached us. Still, it can be said that Thales’ philosophy was based on astronomy, which no one had studied in Greece before him.

According to Herodotus, during the war between the Lydians and the Medes, “during one battle, the day suddenly turned into night. This suppression of the day was predicted by Thales of Miletus to the Ionians and even precisely determined in advance the year in which it occurred. When the Lydians and Medes saw that the day had turned into night, they stopped the battle and hastened to make peace."

However, many doubt that Thales was really able to predict this. Some authors admit that Thales could have predicted an eclipse, but consider this prediction to be practical rather than scientific. After all, even before him, people predicted eclipses by observing a certain repeatability of phenomena and making astronomical calculations.

Perhaps Herodotus, like other ancient authors, reported that Thales linked the time cycle ( lunar months) with the fact of a solar eclipse. When news of the battle that occurred due to an eclipse came to Miletus, rumor simply could not help but compare this with the teaching of the famous Milesian that the Sun was eclipsed by the Moon. Thales actually predicted that a solar eclipse could only be expected on a new moon, and the prophecy was confirmed.

Thales and the first Ionian scientists sought to establish what matter the world was made of. He believed that everything that exists is generated by water, while understanding water as a wet primary substance. Water is the source from which everything constantly comes. Moreover, water and everything that came from it are not dead, they are animated. As an example to illustrate his thought, Thales cited substances such as magnet and amber: since a magnet and amber generate movement, it means they have a soul. Thales imagined the whole world as animated, permeated with life. According to Thales, nature, both living and inanimate, has a moving principle, which is called by such names as soul and God.

Thales considers water to be the original element from which earth arose, which is, as it were, a sediment of this original element, as well as air and fire, its constituent vapors, the evaporation of water. Everything arises from water and turns back into water.

If water is the fundamental principle, then the Earth should rest on water. According to Thales, the Earth floats in the freshwater Ocean like a ship. Then rivers turn out to be like flows in the bottom of a ship, and earthquakes are like the rocking of a ship: “The circle of the earth is supported by water and floats like a ship, and when they say that the Earth shakes, it actually rocks on the waves.” Contemporaries listened to his speeches with admiration. Thales tried to formulate the basic laws of the universe, but his contemporaries best remembered his moral teachings. Plutarch in his book “The Feast of the Seven Wise Men” cites the following original statements of Thales:

"What is most beautiful? The world, for everything that is beautifully constructed is part of it.

What is the wisest thing? Time, it gave birth to one thing and will give birth to another.

What does everyone have in common? Hope: even those who have nothing else have it.

What's the healthiest thing? Virtue, because through it everything else can find use and become useful.

What's the most harmful thing? Vice, because in its presence almost everything deteriorates.

What's the strongest? Necessity, because it is irresistible.

What's the easiest thing? That which is in accordance with nature, for even pleasures often tire us."

Thales said that you need to remember your friends in person and in absentia, that you need to be good-looking, not good-looking. “Don’t get rich by bad means,” he taught, “and don’t let any rumors turn you away from those who trusted you.” “If you supported your parents,” he said, “expect the same support from your children.” Of the short aphorisms that are attributed exclusively to him, the most characteristic of his genius are undoubtedly the following. “Ignorance is a heavy burden”, “When in power, rule yourself.” The following legend was told about Thales in ancient times (Aristotle repeated it with great pleasure). “They say that when Thales, due to his poverty, was reproached for the uselessness of philosophy, he, realizing from the observation of the stars about the future [rich] harvest of olives, back in the winter - fortunately he had little money - distributed them as a deposit for all the oil presses in Miletus and Chios. He hired them for next to nothing, since no one would give more, and when the time came and the demand for them suddenly increased, he began to rent them out at his own discretion and, having collected a lot of money, showed that philosophers could easily do it if they wanted. to get rich, but that’s not what they care about. This is how, they say, Thales showed his wisdom.” Aristotle emphasizes that Thales predicted the harvest “by observing the stars,” that is, thanks to knowledge.

Ironically, it was the genius Thales who was made the target of ridicule by passers-by and maidservants by folk legend. This caustic story is conveyed by Aesop, and Plato also conveys it.

“They say that, while watching the stars and looking up, Thales fell into a well, and some Thracian woman - a pretty and witty servant - made him laugh; he supposedly wants to know what is in the sky, and what is in front of him and underfoot, he doesn’t notice.”

The end of Thales' life came during the reign of the legendary rich Croesus, king of Lydia, who subjugated, in particular, Ionia. The date of death of the first philosopher is unknown. Diogenes Laertius writes: “Thales died while watching gymnastic competitions, from heat, thirst and senile weakness. On his tomb it is written: This tomb is small, but the glory above it is immense. In it, the multi-intelligent Thales is hidden before you.
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I am grateful to fate for three things:

firstly, because I was born a man and not a beast;

secondly - that a man, not a woman;

thirdly, that he is a Hellenic and not a barbarian.

Thales of Miletus

Thales of Miletus (about 625 - 547 BC) - ancient Greek philosopher and mathematician from Miletus (Asia Minor), the founder of European science and philosophy. Representative and founder of the Milesian (Ionian) school, with which the history of European science begins. Traditionally considered the founder of Greek philosophy and science - he invariably opened the list of "seven wise men" who laid the foundations Greek culture and statehood, whose sayings and wisdom have survived to this day. The following are attributed to Thales:

• Older than all things is God, for he is unborn.
• The most beautiful thing is space, for it is the creation of God.
• Most of all is space, because it accommodates everyone.
• Time is the wisest thing, for it reveals everything.
• The fastest thing is thought, because it runs without stopping.
• The strongest thing is necessity, for it overcomes everyone.

The name of Thales already in the 5th century BC. became a household name for the sage. Thales was already called the “Father of Philosophy” in ancient times.

Thales was of noble family and received a good education in his homeland. The actual Milesian origin of Thales is questioned; they report that his family had Phoenician roots, and that he was an alien in Miletus (this is indicated, for example, by Herodotus, who is the most ancient source of information about the life and activities of Thales).

It is reported that Thales was a trader and traveled widely. For some time he lived in Egypt, in Thebes and Memphis, where he studied with the priests, studied the causes of floods, and demonstrated a method for measuring the height of the pyramids. It is believed that it was he who “brought” geometry from Egypt and introduced it to the Greeks. His activities attracted followers and students who formed the Milesian (Ionian) school, and of which Anaximander and Anaximenes are the best known today.

Tradition portrays Thales not only as a philosopher and scientist, but also as a “subtle diplomat and wise politician.” Thales tried to rally the cities of Ionia into a defensive alliance against Persia. It is reported that Thales was a close friend of the Milesian tyrant Thrasybulus; was associated with the temple of Apollo Didyma, the patron saint of maritime colonization.

Some sources claim that Thales lived alone and avoided state affairs; others - that he was married and had a son, Kibist; still others - that while remaining a bachelor, he adopted his sister’s son.

There are several versions regarding the life of Thales. The most consistent tradition states that he was born between the 35th and 39th Olympiads, and died in the 58th at the age of 78 or 76 years, that is, from approximately 625 to 547 BC.

It is reported that Thales died while watching gymnastic competitions, from the heat and, most likely, crush. It is believed that there is one exact date associated with his life - 585 BC, when there was a solar eclipse in Miletus, which he predicted (according to modern calculations, the eclipse occurred on May 28, 585 BC, during the war between Lydia and Media).

Information about the life of Thales is scanty and contradictory, often anecdotal.

The above mentioned prediction of the solar eclipse of 585 BC. - apparently, the only indisputable fact from the scientific activity of Thales of Miletus; in any case, it is reported that it was after this event that Thales became famous and famous.

Being a military engineer in the service of King Croesus of Lydia, Thales, in order to facilitate the crossing of the army, diverted the Halys River along a new channel. He designed the dam and drainage canal and supervised their construction himself. This construction significantly lowered the water level in Halys and made the crossing of troops possible.

Thales proved his business skills by seizing a monopoly on the olive oil trade; however, in the biography of Thales, this fact has an episodic and, most likely, “didactic” character.

Thales was a supporter of some kind of unification of the Ionian city states (like a confederation, with a center on the island of Chios), as a counteraction to the threat from Lydia, and later Persia. Moreover, Thales, in assessing external dangers, apparently considered the threat from Persia a greater evil than from Lydia; the mentioned episode with the construction of the dam took place during the war of Croesus, king of Lydia, with the Persians. At the same time, Thales opposed the conclusion of an alliance between the Milesians and Croesus, which saved the city after the victory of Cyrus, king of Persia.

The works of Thales have not survived. Tradition attributes two works to Thales: “On Solstice” and “On Equinoxes”; their contents are known only in the transmission of later authors. It is reported that his entire legacy amounted to only 200 poems written in hexameter. However, it is possible that Thales did not write anything at all, and everything known about his teaching comes from secondary sources.

It is believed that Thales "discovered" the constellation Ursa Minor for the Greeks as a guiding tool; Previously, this constellation was used by the Phoenicians.

It is believed that Thales was the first to discover the inclination of the ecliptic to the equator and carried out celestial sphere five circles: Arctic circle, summer tropic, celestial equator, winter tropic, Antarctic circle. He learned to calculate the time of the solstices and equinoxes, and established the inequality of the intervals between them.

Thales was the first to point out that the Moon shines by reflected light; that eclipses of the Sun occur when the Moon covers it. Thales was the first to determine the angular size of the Moon and the Sun; he found that the size of the Sun is 1/720th of its circular path, and the size of the Moon is the same part of the lunar path. It can be argued that Thales created a “mathematical method” in the study of the movement of celestial bodies.

Thales introduced a calendar based on the Egyptian model, in which the year consisted of 365 days, divided into 12 months of 30 days, and five days were left out.

A geometric theorem is named after Thales:

If parallel lines intersecting the sides of an angle cut off equal segments on one side, then they cut off equal segments on the other side,

as well as its more general version:

Parallel lines intersecting two given lines cut off proportional segments on these lines.

It is believed that Thales was the first to formulate and prove several geometric theorems, namely:

• about the equality of vertical angles;
• about the equality of triangles along one side and two adjacent angles;
• on the equality of angles at the base of an isosceles triangle;
• about dividing the diameter of a circle in half;
• about the equality of an inscribed angle based on a diameter to a right angle.

Outside the Russian-language literature, Thales's theorem is sometimes called another theorem of planimetry, namely, the statement that the inscribed angle based on the diameter of a circle is right. The discovery of this theorem is indeed attributed to Thales, as evidenced by Proclus.

Thales learned to determine the distance from the shore to the ship. Some historians claim that for this he used the similarity feature of right triangles.

The legend says that Thales, while in Egypt, amazed Pharaoh Amasis by being able to accurately determine the height of the pyramid, waiting for the moment when the length of the shadow of the stick became equal to its height, and then he measured the length of the shadow of the pyramid.

According to Hieronymus of Rhodes, Thales, to solve this problem, measured the length of the shadow of the pyramid at the moment when the length of the shadow of the observer himself became equal to his height.

Plutarch of Chaeronea presents the matter in a different light. According to his story, Thales determined the height of the pyramid by placing a vertical pole at the end point of the shadow cast by it and showing, with the help of the two triangles thus formed, that the shadow of the pyramid relates to the shadow of the pole, as the pyramid itself relates to the pole. The solution to the problem thus turns out to be based on the doctrine of the similarity of triangles.

On the other hand, the evidence of Greek writers has undoubtedly established that the doctrine of proportions was not known in Greece until Pythagoras, who was the first to bring it out of Babylon. Thus, only the version of Jerome of Rhodes can be considered consistent with the truth in view of the simplicity and elementaryness of the method of solving the problem indicated in it.

At present, in the history of mathematics, there is no doubt that the geometric discoveries that were attributed to Thales by his compatriots were in fact simply borrowed from Egyptian science. For Thales’ immediate students, who were not only unfamiliar with Egyptian science, but generally possessed extremely meager information, every message from their teacher seemed like complete news, previously unknown to anyone and therefore completely belonging to him.

The descendants of Thales owe him the fact that he was, perhaps, the first to introduce proof into science, and in particular into mathematics.

It is now known that many mathematical rules were discovered much earlier than in Greece. But everything is done empirically. Rigorous proof of the correctness of any proposals based on general provisions, accepted as reliable truths, was invented by the Greeks. A characteristic and completely new feature of Greek mathematics is the gradual transition by means of proof from one assumption to another. It was precisely this character that Thales devoted to mathematics. And even today, 25 centuries later, when you begin to prove, for example, the theorem on the properties of a rhombus, you, in essence, are reasoning almost as the students of Thales did.

It is difficult now to say what in the scientific list really belongs to Thales and what is attributed to him by his descendants, admired by his genius. Undoubtedly, in the person of Thales, Greece for the first time found simultaneously a philosopher, mathematician and natural scientist. It is no coincidence that the ancients ranked him among the “magnificent seven” sages of antiquity.

The following statements are attributed to Thales:

• The earth floats in water (like a piece of wood, a ship, or some other body that by nature tends to float in water); earthquakes, whirlwinds and movements of stars occur because everything sways on the waves due to the mobility of water;
• The earth floats in water, and the sun and others celestial bodies feed on the evaporation of this water;
• the stars are made of earth, but at the same time they are red-hot; The sun is of earthy composition (consists of earth); The Moon is of earthy composition (consists of earth);
• The Earth is at the center of the Universe; if the Earth is destroyed, the whole world will collapse;
• life presupposes nutrition and breathing, in which functions are water and the “divine principle,” the soul.

That is, Thales argues that the Earth, as dry land, as a body itself, is physically supported by some kind of “support”, which has the properties of water (non-abstract, that is, specifically fluidity, instability, etc.).

Statement 3) is an almost literal indication of physical nature stars, the Sun and the Moon - they consist of (the same) matter (as the Earth), and the temperature is very high.

Proposition 4) Thales claims that the Earth is the center around which the circulation of celestial phenomena occurs and thus Thales is the founder of the geocentric system of the world.

Although Thales’s idea of ​​primordial essence seems naive to us now, from a historical point of view it is extremely important: in the situation “everything is made of water”, resignation was given pagan gods, ultimately, to mythological thinking, and the path to a natural explanation of nature continues.

Thales first came up with the idea of ​​the unity of the universe. This idea, once born, never died: it was communicated to his students and the students of his students.

Thales also carried out the first experiments with amber, the first physical experiments in the field of electrical phenomena.

The knowledge and views of Thales go back to mythology and tradition, even to such ancient times, which cannot be recorded. As you know, having traveled around half of the world available at the time, Thales had the opportunity to get acquainted with various interpretations of this possible ancient knowledge.

But Thales translated this knowledge into the “plane of scientific interest,” that is, from a set of properties widespread in myths and similar sources, he derived a group of images that were scientific for his time. We can say that the merit of Thales (and the first natural philosophical school he created) is that he “published” a result suitable for scientific use. He identified a certain rational complex of concepts required for logical propositions. This is proven by the development of all subsequent ancient philosophy.

Illustrative stories related to the glory and name of Thales.

• One day, a mule loaded with salt, while wading a river, suddenly slipped. The contents of the bales dissolved, and the animal, rising lightly, realized what was happening, and from then on, when crossing, the mule deliberately dipped the sacks into the water, leaning in both directions. Having heard about this, Thales ordered the bags to be filled with wool and sponges instead of salt. The mule loaded with them tried to do the old trick, but achieved the opposite result: the luggage became much heavier. They say that from now on he crossed the river so carefully that he never got his load wet, even by accident.
• The following legend was also passed down about Thales. When Thales, due to his poverty, was reproached for the uselessness of philosophy, he, having made a conclusion from the observation of the stars about the coming harvest of olives, hired all the oil presses in Miletus and Chios in the winter. He hired them for next to nothing (because no one would give more), and when the time came, and the demand for them suddenly increased, he began to rent them out at his own discretion. Having thus collected a lot of money, he showed that philosophers can easily get rich if they want, but this is not what they care about. Aristotle emphasizes: Thales predicted the harvest “by observing the stars,” that is, thanks to knowledge.

The following mathematical objects are named after Thales:

• Thales' theorem
• generalized Thales' theorem.

Based on Wikipedia and websites: fales-iz-mileta.narod.ru and school.xvatit.com.

Thales is an ancient Greek philosopher who discovered the list of the seven wise men. He is considered the father of ancient philosophy; the Milesian (Ionian) school he created became the starting point for the history of European science. Back in the 5th century BC. e. the name Thales was identical to the word “sage”, and his wisdom was interpreted both as abstract contemplation and as practical insight. It was with Thales, as Aristotle believed, that the history of metaphysics began, and Eudemus discovered the history of geometry and astronomy with his achievements.

There is no biography of Thales as such - there is isolated information, often contradictory friends friend and having the nature of legends. Historians can name only one exact date, relevant to his life: in 585 BC. e. The solar eclipse predicted by the philosopher occurred. As for the time of his life, the point of view according to which he was born in 640-624 is taken as a basis. BC e., and the period in which he could have died is 548-545. BC e.

It is known that Thales was the successor of a noble family, the owner good education, received in his homeland. However, the origin of the philosopher from Miletus is rather doubtful. There is evidence that he did not live there as a native inhabitant, but had Phoenician roots. Legend has it that the sage, being a merchant, undertook during his life large number travel. Living in Thebes in Egypt, Memphis, he communicated closely with the priests, learning their wisdom. It is generally accepted that in Egypt he acquired geometric knowledge, which he then introduced to his compatriots.

Upon returning to his homeland, he had his own students, and for them he created a famous school called Miletus. The most famous students are Anaximenes and Anaximander. Legends describe Thales as a versatile personality. So, he was not only a philosopher, but also served as a military engineer for Croesus, the king of Lydia. He created a drainage canal and a dam, thanks to which the Gales River flowed in a different direction. There is information that Thales had a monopoly on the sale of olive oil. He also proved himself as a diplomat, advocating the unity of the Ionian cities in the face of danger from first Lydia, then Persia. On the other hand, he was against the inhabitants of Miletus becoming allies of Croesus, and this saved the city.

Information has been preserved that Thales was friends with Thrasybulus, the Milesian tyrant, and had something to do with the temple of Apollo of Didyma. However, there are sources that say that Thales, who loved solitude, did not seek to participate in state affairs. Information about his personal life is also contradictory: along with statements that the sage was married and had a son, there is information that he never started a family, but adopted a nephew.

None of the works have reached our time. It is believed that there were two of them - “On the equinoxes” and “On the solstices”, the content of which we know only through the retelling of authors who lived later. There is information that 200 poems remained after him. It is possible that in in writing The works of Thales do not exist at all, and only from other sources can an idea of ​​his teaching be formed.

Be that as it may, it is Thales who is credited with formulating the two main problems of natural philosophy - the beginning and the universal. The philosopher believed that all things and phenomena existing in the world have a single basis - water, without dividing into living and nonliving, physical and mental, etc. As a man of science, Thales established the length of the year, determined the time of the equinoxes and solstices, and explained that the Sun moves in relation to the stars. According to Proclus, it is Thales who is credited with being the pioneer in proving geometric theorems.

The father of ancient philosophy died while a spectator at a gymnast competition: the heat and, most likely, the resulting crush took its toll.