Presentation on the topic: "Thales of Miletus. Facts from the biography, scientific achievements." Thales of Miletus and his theorem presentation for a lesson in geometry (grade 8) on the topic Thales in science - Geometry

Strukova Maria

Interesting facts from the biography of Thales of Miletus. Brief information about his achievements.

Download:

Preview:

To use the preview of presentations, create a Google account (account) and sign in: https://accounts.google.com

Slides captions:

The presentation was made by Maria Strukova, a student of class 9 "B" of the MBOU "Gatchinskaya secondary school No. 9", teacher Rovno A.N. Thales of Miletus Facts from the biography, scientific achievements

Facts from the biography Thales was a noble family and received a good education in his homeland. The actual Milesian origin of Thales is questioned; it is reported that his family had Phoenician roots, and that he was an alien in Miletus. Thales is reported to have been a merchant 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 the Greeks to it. Some sources claim that Thales lived alone and shunned the affairs of state; others - that he was married, had a son Kibist; the third - that while remaining a bachelor, he adopted his sister's son.

Facts from the biography In general, the life of Thales is reduced to the period from 640-624 to 548-545 BC. e., i.e. Thales could die at the age of 76 to 95 years. 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. e., 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 scarce and contradictory, often anecdotal. The aforementioned prediction of the solar eclipse of 585 B.C. e. - 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 Lydia Croesus, Thales, in order to facilitate the crossing of the troops, let the Halys River along a new channel. Not far from the city of Mitel, he designed a dam and a drainage canal and himself supervised their construction. This construction significantly lowered the water level in Galis and made it possible for the troops to cross. Thales proved his business qualities 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.

Achievements in geometry It is believed that Thales was the first to formulate and prove several geometric theorems, the formulations of which are: vertical angles are equal; there is an equality of triangles on one side and two angles adjacent to it; the angles at the base of an isosceles triangle are equal; the diameter bisects the circle; An inscribed angle based on a diameter is a right angle. Thales learned to determine the distance from the coast to the ship, for which he used the similarity of triangles. This method is based on a theorem later called the Thales theorem: if parallel lines intersecting the sides of an angle cut off equal segments on one side of it, then they cut off equal segments on its other side. The legend tells that Thales, while in Egypt, struck 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 becomes equal to its height, and then measured the length of the shadow of the pyramid.

Achievements in Astronomy It is believed that Thales "discovered" for the Greeks the constellation Ursa Minor as a guiding tool; earlier 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 made five circles in the celestial sphere: the Arctic circle, the summer tropic, the celestial equator, the winter tropic, the Antarctic circle. He learned to calculate the time of the solstices and equinoxes, established the unequal intervals between them. Thales was the first to point out that the Moon shines by reflected light; that eclipses of the Sun occur when it is covered by the Moon. Thales was the first to determine the angular size of the Moon and the Sun; he found that the size of the Sun is 1/720 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 motion of celestial bodies. Thales introduced the Egyptian calendar (in which the year consisted of 365 days, divided into 12 months of 30 days, and five days remained falling out).

Achievements in physics to Thales are attributed to the following provisions: 1) the Earth floats in water (like a piece of wood, a ship or some other [body], which by nature tends to float in water); earthquakes, whirlwinds, and the movements of the stars are due to the fact that everything sways on the waves due to the mobility of water; 2) The Earth floats in water, and the Sun and other celestial bodies feed on the vapors of this water; 3) 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]. 4) the Earth is in the center of the Universe; When the Earth is destroyed, the whole world will collapse. 5) Life presupposes nutrition and breathing, in which functions water and the “divine principle”, the soul, act. That is, Thales claims that the Earth, as a land, as a body itself, is physically supported by a certain “support”, which has the properties of water (non-abstract, that is, concrete fluidity, instability).

Cosmology and philosophy in the life of Thales The cosmology of Thales is very reminiscent of the Egyptian doctrine. The universe, according to Thales, is a liquid mass, in the middle of which there is an air body, which has the shape of a bowl, turned open side down. The concave surface of this bowl is the sky; on the lower surface, in its center, a disk floats, streamlined by water. Stars are gods floating in the sky. Thales believed: water is the essence of everything, everything came from water and everything returns to water again. In favor of this opinion, Thales cited three arguments: firstly, the seed of all living beings is something that has moisture; secondly, all plants feed on moisture and, thanks to it, bear fruit, while plants deprived of moisture dry up; thirdly, even the fire of the sun and the luminaries is fed by the vapors of water. Thales said that God is the mind of the world, that everything is animated and full of demons. Divine power penetrates through the primary moisture, setting it in motion. Thales looked at the soul as an eternally moving and self-moving beginning. Thales also attributed the soul to the magnet, since it attracts iron.

Demonstrative stories associated with the glory and name of Thales. One day, a mule loaded with salt, while fording a river, suddenly slipped. The contents of the bales dissolved, and the animal, having risen lightly, realized what was the matter, and since then, when crossing, the mule deliberately dipped the bags into the water, leaning in both directions. Having heard about this, Thales ordered to fill the bags instead of salt with wool and sponges. The mule loaded with them tried to do the old trick, but achieved the opposite result: the load became much heavier. It is said that henceforth he crossed the river so carefully that he never soaked the load even by accident. There was such a legend about Thales (Aristotle repeated it with great willingness). When Thales, because of his poverty, was reproached for the futility of philosophy, having made a conclusion from the observation of the stars about the coming harvest of olives, even in the winter he hired all the oil presses in Miletus and Chios. He hired them for nothing (because no one gave more), and when the time came and the demand for them suddenly increased, he began to rent them out at his own discretion. By raising a lot of money in this way, he showed that philosophers can easily get rich if they want to, but that is not something they care about. Aristotle emphasizes that Thales predicted the harvest "by observing the stars", that is, thanks to knowledge. In the sixth year of the war, a battle took place between the Lydians and the Medes, during which "the day suddenly became night." It was the same solar eclipse of 585 BC. e., "in advance" predicted by Thales and happened exactly at the predicted time. The Lydians and Medes were so amazed and frightened that they stopped the battle and hastened to make peace.

Thank you for your attention! I believe that Thales of Miletus is a great scientist and philosopher of antiquity. He took the first step towards the development of sciences such as geometry, physics, astronomy. I think you need to respect this man for his achievements. Conclusion

slide 1

Description of the slide:

slide 2

Description of the slide:

slide 3

Description of the slide:

slide 4

Description of the slide:

slide 5

Description of the slide:

slide 6

Description of the slide:

Slide 7

Description of the slide:

All this brought Thales the glory of the first sage of the famous "seven wise men" of antiquity. Thales of Miletus had the title of one of the seven sages of Greece, he was truly the first philosopher, the first mathematician, astronomer and, in general, the first in all sciences in Greece. He was to Greece what Lomonosov was to Russia. All this brought Thales the glory of the first sage of the famous "seven wise men" of antiquity. Thales of Miletus had the title of one of the seven sages of Greece, he was truly the first philosopher, the first mathematician, astronomer and, in general, the first in all sciences in Greece. He was to Greece what Lomonosov was to Russia.

Slide 8

Description of the slide:

Plutarch cites the following original statements of Thales: “What is most beautiful of all? - The world, for everything that is beautifully arranged is part of it. What is the wisest thing? - Time, it gave birth to one thing and will give rise to another. What is common to all? - Hope: it has and those who have nothing else. What is most useful? - Virtue, because, thanks to it, everything else can find application and become useful. What is the most harmful? - Vice, because in its presence almost everything deteriorates. What is strongest? - Necessity, for it is irresistible. What is the easiest? - That which corresponds to nature, for even pleasures often tire" Plutarch cites the following original statements of Thales: "What is most beautiful of all? - The world, for everything that is beautifully arranged is part of it. What is wisest of all - Time, it has given birth to one thing and will give rise to another. What is common to all? - Hope: those who have nothing else have it. What is most useful? - Virtue, because thanks to it everything else can find application and become useful. What the most harmful? - Vice, for in its presence almost everything deteriorates. What is the strongest? - Necessity, because it is irresistible. What is the easiest? - That which corresponds to nature, for even pleasures are often tiring.

Slide 9

Description of the slide:

Slide 10

Description of the slide:

The Canon of the Seven Sages · "Measure is the most important thing," - Cleobulus used to say Linden; · In Sparta "Know thyself!" - Chilo preached; · Restrain anger exhorted Periander, a native of Corinth; · "Lishku in anything!" - the proverb was Pittaka's Mytilene; · "Watch the end of life!" - repeated by Solon of Athens; · "The worst everywhere are the majority!" - said Biant Priensky; "Don't vouch for anyone!" - Thales of Miletus word.

Thales of Miletus - a name known to everyone Thales of Miletus - an ancient Greek philosopher and
mathematician, a theorem is named after him, which
still studied in geometry classes. He
counts
ancestor
Greek
And
European philosophy and opens the list
world famous philosophers. Although his scientific
works
Not
preserved
By
words
Aristotle, it was Thales who laid the foundations
Greek statehood.

Biography facts

Thales was a noble Phoenician family and received good
education. The Milesian origin of Thales is questioned;
report that his family had Phoenician roots, and that in Miletus he was
alien (this is indicated, for example, by Herodotus, who is the most
an ancient source of information about the life and work of Thales).
Thales is reported to have been a merchant and traveled widely.
For some time he lived in Egypt, in Thebes and Memphis, where he studied with
priests, studied the causes of floods, demonstrated a way
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 disciples who formed the Milesian
school.
Some sources claim that Thales lived alone and
shunned public affairs; others - that he was married, had a son
Kibista; the third - that, remaining a bachelor, he adopted his sister's son.

Biography facts

Being a military engineer in the service of King Lydia Croesus, Thales, in order to
facilitate the crossing of the troops, let the river Galis along a new channel.
Not far from the city of Mitel, he designed a dam and a drainage channel and
he supervised their construction. This building significantly reduced
the water level in Galis and made it possible for the troops to cross.
Thales proved his business qualities by seizing a monopoly on trade
olive oil; however, in the biography of Thales, this fact has
episodic and, most likely, "didactic" character.
Thales was a supporter of some unification of the Ionian policies
(like a confederation, centered on the island of Chios), as counteractions
the threat from Lydia, and later the Achaemenid powers. And Thales
in assessing external dangers, apparently considered a threat from Persia
more evil than from Lydia; mentioned building episode
the dam took place during the war of Croesus (King of Lydia) with the Persians. At that
At the same time, Thales opposed the conclusion of an alliance between the Milesians and Croesus, than
saved the city after the victory of Cyrus (king of Persia).

Thales in science - Astronomy

It is believed that Thales "discovered" for the Greeks the constellation Ursa Minor as a guiding
tool; earlier 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 spent on the celestial
sphere five circles: arctic circle, summer tropic, celestial equator, winter tropic,
antarctic circle. He learned to calculate the times of the solstices and equinoxes, set
uneven spacing between them.
Thales was the first to point out that the Moon shines by reflected light; that solar eclipses 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 1/720 of its circular path, and the size of the Moon is
the same part from the lunar path. It can be argued that Thales created the "mathematical method"
in the study of the motion of celestial bodies.
Thales introduced the Egyptian calendar (in which the year consisted of 365 days, divided into
12 months of 30 days, and five days were left out).

Thales in Science - Geometry

The geometric theorem on proportional (equal) is named after Thales
segments and parallel lines.
It is believed that Thales was the first to formulate and prove several geometric
theorems, namely:
vertical angles are equal;
equality of triangles on one side and two adjacent to
her corners;
the angles at the base of an isosceles triangle are equal;
the diameter divides the circle into two equal parts;
An inscribed angle based on a diameter is a right angle.
Thales learned to determine the distance from the coast
used similar triangles. At the heart of this
later called the Thales theorem: if
intersecting the sides of the angle, cut off equal segments
they cut off equal segments on its other side as well.
to the ship, why
method lies the theorem,
parallel lines,
on one side, then
The legend tells that Thales, while in Egypt, struck
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 becomes equal to its height, and
then measured the length of the shadow of the pyramid.

Thales in science - The device of the cosmos

Thales believed that everything is born from water; everything comes from
water and turns into it. The beginning of the elements, the things that exist -
water; the beginning and end of the universe is water. Everything is made from water
by its hardening / freezing, as well as evaporation; at
when condensed, water becomes earth; when evaporated, it becomes
air.
Cause
education/movement
-
spirit,
"nesting" in the water.
According to the remark of Heraclitus the Allegorist: “Wet substance, with
easily transforming (own. "Clinging") into
all kinds of [bodies], takes on a variegated variety
forms. The evaporating part of it turns into air, and
the thinnest air ignites in the form of ether. Falling out in
sediment and turning into silt, water turns into earth.
Therefore, from the quaternary of elements, Thales declared water
the most causal element."
According to Plutarch: “The Egyptians say that the Sun and
The moon circles the sky not in chariots, but in ships,
alluding to their birth from moisture and nourishment from moisture. They think
that Homer considers water to be the beginning and "parent" of all
things, like Thales having learned from the Egyptians.
Thales believed that the Cosmos is one. Water and everything from it
happened, are not dead, but animated; Space
animated and full of divine powers. Soul as an active force
and the bearer of rationality, is involved in the divine [system
of things]. Nature, both living and non-living, has
driving start.
Thales represents the soul in the form of a subtle ethereal substance. By
Plutarch’s remark: “After him, Anacharsis remarked:
“Thales perfectly believes that in all the most important and
the greatest parts of the cosmos have a soul, and therefore not
it is worth wondering that by the providence of God
the finest deeds."

Thales in science - Physics

Thales is credited with the following provisions:
1. The earth floats in water (like a piece of wood, a ship or
some other [body], which by nature
tend to stay afloat in the water) [; earthquakes,
whirlwinds and movements of stars occur because everything
sways on the waves due to the mobility of the water.
2. The Earth floats in water, while the Sun and other celestial bodies
they feed on the vapors of this water.
3. The stars are made of earth, but they are red-hot;
The sun is of earthy composition [consists of earth]; Moon -
earthy composition [consists of earth].
4. The earth is at the center of the universe; upon destruction
Earth will collapse the whole world.
5. Life involves nutrition and breathing, in which
functions are water and the "divine principle", the soul.
That is, Thales claims that the Earth is like dry land, like
the body itself, physically rests on a certain “support”,
which has the properties of water (non-abstract, i.e.
specifically fluidity, instability, etc.).

Philosophy of Thales of Miletus

The earliest information about the philosophy of Thales of Miletus came to us from Aristotle. In the Aristotelian
"Metaphysics" says: "Of those who first took up philosophy, the majority considered the beginning of all things alone
only beginnings in the form of matter: that of which all things are composed, from which they first arise, and into which ultimately
they leave, and the main remains, but changes according to its properties, and they consider this an element and the beginning of things.
And so they believe that nothing comes into existence and nothing perishes, since such a basic nature is always
is preserved ... Not everyone indicates the quantity and form for such a beginning in the same way, but Thales is the ancestor of such
kind of philosophy - considers it water.
The water of Thales is a philosophical rethinking of the Homeric Ocean, the Sumerian-Akkadian Abzu (Alsu). Is it true,
the title of his work "On the Beginnings" admits that Thales rose to the concept of the beginning, otherwise he would not have become
philosopher. Thales, understanding water as the beginning, naively makes the earth float on it - in this form he and
represents the substantiality of water, it literally resides under everything, everything floats on it.
On the other hand, it is not just water, but "reasonable", divine water. The world is full of gods (polytheism). However, these
the gods act in the world of force, they are also souls as sources of self-movement of bodies. So, for example, a magnet, according to
philosophy of Thales, has a soul, because it attracts iron. The sun and other celestial bodies feed
evaporation of water. What has been said can be summarized by the words of Diogenes Laertes about Thales: “He believed that the beginning of everything
water, and considered the world animated and full of deities.

Philosophy of Thales of Miletus

The spontaneous materialism of Thales contained
the possibility of a later split. Deity of the cosmos
intelligence.
Before
us
Here
Not
only
anti-mythology of Thales, who put in place
Zeus mind, logos, son of Zeus, who denied
his father, but also embedded in the proto-philosophical
teaching the possibility of idealism.
The ontological monism of the philosophy of Thales is associated with its
epistemological monism: all knowledge must be reduced
to one single basis. Thales said: "Verbosity
is not at all an indicator of a reasonable opinion.
Here Thales spoke out against the mythological and
epic verbosity. "Look for something
wise, choose something good, so you
you will stop the idle talk of talkative people. That's the motto
the first ancient Western philosopher, his philosophical
will.

Philosopher or scientist?

So, Thales of Miletus managed to become
significant figure of his time and,
enjoying the respect of contemporaries of government officials and ordinary
citizens - did a lot for development
philosophy, astronomy and geometry.
His contribution to science has not been lost
relevance,
discoveries
Thales
humanity is still using it.
He perfectly combined the qualities of a scientist and
philosopher.

List of references and authors

Asmus V. F. Antique Philosophy. - M.: Higher school, 1998;
Panchenko D.V. Thales: the birth of philosophy and science // Some problems of history
ancient science: Collection of scientific papers / Ed. ed. A. I. Zaitsev, B. I. Kozlov: Home
Astronomical observatory;
Tchaikovsky Yu. V. Falesova science in a historical context
Tchaikovsky Yu. V. Two Thales - poet and mathematician.
Radlov E. L., Bobynin V. V. Fales Miletsky

To use the preview of presentations, create a Google account (account) and sign in: https://accounts.google.com

Slides captions:

Thales of Miletus and his theorem

Thales of Miletus, undoubtedly the most outstanding of the 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 shone "It is difficult to know oneself, it is easy to advise others"

Most likely, Thales was born in the period from 640 to 624 BC, and died in the period from 548 to 545 BC. e. Thus, Thales could die at the age of 76 to 95 years. Biography of Thales of Miletus

Thales is reported to have been a merchant 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. It is only known for certain that Thales was of a noble family, and received a good education in his homeland. The actual Milesian origin of Thales is questioned; it is reported that his family had Phoenician roots, and that he was an alien in Miletus. Some sources claim that Thales lived alone and shunned the affairs of state; others - that he was married, had a son Kibist; the third - that while remaining a bachelor, he adopted his sister's son.

Imagine such a picture. 600 BC Egypt. Before you is a huge Egyptian pyramid. To surprise the pharaoh and remain among his favorites, you need to measure the height of this pyramid. How will you do it? Yes, it turns out that everything is quite simple. This is what Thales of Miletus came up with. He waited until the length of his shadow and his height coincided, and then, using the triangle similarity theorem, he found the length of the shadow of the pyramid, which, accordingly, was equal to the shadow cast by the pyramid.

The merits of Thales in geometry It is believed that Thales was the first to prove several geometric theorems, namely: vertical angles are equal; triangles with equal one side and equal angles adjacent to it are equal; the angles at the base of an isosceles triangle are equal; the diameter bisects the circle; Thales was the first to inscribe a right-angled triangle in a circle and, in gratitude to the gods, sacrificed a bull

The merits of Thales It is believed that Thales was the first (of the ancient scientists known today) to study the movement of the Sun in the celestial sphere. He learned to calculate the time of solstices and equinoxes, established the unequal intervals between them. He was the first to claim that the Moon shines by reflected light; that eclipses of the Sun occur when the Moon passes between it and the Earth; and lunar eclipses occur when the moon is in the shadow of the earth.

Thales introduced a calendar, following the Egyptian model (in which the year consisted of 365 days, divided into 12 months of 30 days, and five days remained falling out). It is believed that Thales was the first to divide the celestial sphere into five zones: the arctic always visible belt, the summer tropic, the celestial equator, the winter tropic, and the Antarctic invisible belt. It is believed that Thales "invented the globe." It can be argued that Thales (starting with the geometric study of angles) created a "mathematical method" in the study of the motion of celestial bodies.

Thales' theorem

If successively equal segments are laid out on one of the two straight lines and parallel lines are drawn through their ends, intersecting the second straight line, then they will cut off segments equal to each other on the second straight line. I case A 1 A 2 A 3 A 4 B 1 B 2 B 3 B 4 Given: lines A 1 A 4 and B 1 B 4 are parallel. A 1 A 2 \u003d A 2 A 3 \u003d A 3 A 4, straight lines A 1 B 1, A 2 B 2, A 3 B 3 and A 4 B 4 are parallel. Prove: B 1 B 2 \u003d B 2 B 3 \u003d B 3 B 4 Proof: Quadrangles A 2 A 1 B 1 B 2 and A 3 A 2 B 2 B 3 are parallelograms by definition. Hence, A 1 A 2 \u003d B 1 B 2 and A 2 A 3 \u003d B 2 B 3, as opposite sides of the parallelogram. But A 1 A 2 \u003d A 2 A 3, therefore B 1 B 2 \u003d B 2 B 3. Similarly, it is proved that B 2 B 3 \u003d B 3 B 4. Therefore B 1 B 2 \u003d B 2 B 3 \u003d B 3 B 4

If successively equal segments are laid out on one of the two straight lines and parallel lines are drawn through their ends, intersecting the second straight line, then they will cut off segments equal to each other on the second straight line. Case II A 1 A 2 A 3 A 4 B 1 B 2 B 3 B 4 Given: the lines A 1 A 4 and B 1 B 4 are not parallel. A 1 A 2 \u003d A 2 A 3 \u003d A 3 A 4, straight lines A 1 B 1, A 2 B 2, A 3 B 3 and A 4 B 4 are parallel. Prove: В 1 В 2 \u003d В 2 В 3 \u003d В 3 В 4 Proof: С D 1 3 2 4 Draw a line CD through point В 2 parallel to line А 1 А 4 . CB 2 \u003d B 2 D (I case) (cross-lying with parallel lines A 1 B 1 and A 3 B 3 and a secant CD). (vertical). So, on the second sign. Therefore, B 1 B 2 \u003d B 2 B 3. Similarly, it is proved that B 2 B 3 \u003d B 3 B 4. Therefore B 1 B 2 \u003d B 2 B 3 \u003d B 3 B 4.

slide 1

Description of the slide:

slide 2

Description of the slide:

slide 3

Description of the slide:

slide 4

Description of the slide:

slide 5

Description of the slide:

slide 6

Description of the slide:

Slide 7

Description of the slide:

Sayings of Thales: "What is most beautiful of all? - The world, for everything that is beautifully arranged is part of it. What is the wisest of all? - Time, it gave birth to one thing and will give rise to another. What is common to everyone? - Hope: those who have it also have there is nothing else. What is most useful? - Virtue, because through it everything else can find application and become useful. What is the most harmful? - Vice, because in its presence almost everything deteriorates. What is stronger than all? - Necessity, because it is irresistible. What the easiest? - That which corresponds to nature, for even pleasures are often tiring.

Slide 8

Description of the slide:

Slide 9

Description of the slide:

Slide 10

Description of the slide:

slide 11

Description of the slide:

Thales was also the first to calculate the height of one of the Egyptian pyramids from its shadow. Discovered the length of the year and divided it into 365 days. His saying: "Do not vouch for anyone," which Chilo echoes: "Bail and misfortune are always together." The most famous saying of Thales: "Respect the measure." Thales was also the first to calculate the height of one of the Egyptian pyramids from its shadow. Discovered the length of the year and divided it into 365 days. His saying: "Do not vouch for anyone," which Chilo echoes: "Bail and misfortune are always together." The most famous saying of Thales: "Respect the measure."

slide 12