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Thales
Kelly Dwyer
Feb 5, 2014
Thales was born around 624 BC, and is believed to have died around 546 BC (Thales,
2014). Thales was born in Miletus, an ancient Greek Ionian city, to Examyes and Cleobuline,
who belonged to the royal Phoenicia family (Thales, 2014). Although Thales was supposedly an
engineer by trade, he was also considered a businessman, politician, philosopher, teacher, and
mathematician. In addition to these, Thales is regarded as the first Greek philosopher by
Aristotle, the father of science, and “the first true mathematician (Thales, 2014)”. With all of
these titles, it is no wonder that Thales was recognized as the first of the Seven Sages (Thales,
2014; Biography of Thales, 2009).
Thales lived a modest life, as it seems many philosophers did. This lifestyle was looked
down upon by others. Thales set out to prove that he could use his intelligence to make money if
he wanted to (Thales, 2014; O’Grady). One story of Thales’ business ventures involves the
purchase and sale of the olive presses in Miletus. Thales is said to have predicted a particularly
bountiful olive harvest one year. In anticipation of this event, Thales bid all of the olive presses
in Miletus, and was able to get them at a low price. When the time came, the olive harvest was in
fact plentiful. Thales was than able to rent out the presses for a considerable profit(Thales, 2014;
Biography of Thales, 2009; Khalaf, 2014; O’Grady). Miletus had an expansive maritime trade
system (O’Grady). Thales used the information he gathered in his studies of astrology to improve
the trade system. He recognized that the constellation Ursa Minor was more practical for
navigation than Ursa Major, which at the time was widely used (Khalaf, 2014; Biography of
Thales, 2009; O’Grady). This would have been very valuable for the Greeks of Miletus.
Thales also had a hand in politics. At the time, the Ionians were helping defend Anatolia
from the Persians. Thales is said to have consulted on the matter. He urged the Ionian cities to
form a union with a capital at Teos, a city in the center of Ionia (Thales, 2014; Khalaf, 2014).
There is also a story in which the army was said to have come to a river, Halys, which they were
not able to cross. Thales engineered a structure upstream that caused the water to change course,
making it possible for the army to cross (Thales, 2014; Lendering, 2005). However, McKirahan
(2011) states that these historical events would have occurred after Thales’ time.
In a way, Thales was involved in the peace agreement between the Medes and Lydians,
who had been at war for over five years. Thales predicted that a solar eclipse would occur in the
year 585 BC (Thales, 2014; Biography of Thales, 2009; Lendering, 2005; Khalaf, 2014;
O’Grady; McKirahan, 2011). In the fifth year of fighting, 585 BC, there was in fact a solar
eclipse. It was recounted that on observation of the event, the two armies ceased fighting and
came to a peace agreement (Khalaf, 2014; O’Grady). Predicting this event within the year was an
impressive feat for the Greeks, not even Babylonian astronomers were able to predict with
greater accuracy (Lendering, 2005) and each solar eclipse is visible only in a certain region
making the pattern more difficult to establish than that of lunar eclipses (Khalaf, 2014).
As a philosopher, Thales attempted to define the base of all life without the use of the
Greek Gods (Thales, 2014; Biography of Thales, 2009; Khalaf, 2014). This was a revolutionary
idea for his time; what’s more, Thales was the first philosopher to think this way (Lendering,
2005; Khalaf, 2014), making him “the founder of the school of natural philosophy” (O’Grady).
Thales believed that the first principle was water, meaning all things came from water (Thales,
2014). According to Aristotle, Thales may have concluded this by observing that most living
things have moisture (O’Grady). Thales believed that the Earth floated on water. He explained
earthquakes in a way that supported this notion, saying that because Earth floats on water, and
water moves, there are earthquakes (Khalaf, 2014). Although the theory that all things come
from water has been disproved, the idea of taking mythology out of philosophy revolutionized
Thales
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Feb 5, 2014
science (Thales, 2014).
As a highly esteemed individual and innovative philosopher, Thales was the considered
the founder of the Ionian school of philosophy in Miletus (Biography of Thales, 2009). Thales
taught Anaximander, the teacher of Pythagoras (Biography of Thales, 2009). As a teacher,
Thales advised Pythagoras to visit Egypt to further his studies. Thales’ students were encouraged
to pursue their own ideas, be critical of ideas, and open to discussion (O’Grady). This was is
likely due to Thales’ methods of questioning and explaining, which laid the foundation for the
scientific method (Biography of Thales, 2009; O’Grady).
In addition to being known as a philosopher, Thales was known as a mathematician. He
had a theoretical and practical understanding of geometry and is believed to have introduced the
notion of logical proofs of abstract concepts(Biography of Thales, 2009). Eves (1990) states that
“demonstrative geometry began with Thales” (p.72). That is, Thales was one of the first to ask
why things were true, rather than how, which had previously been sufficient. At this time,
deductive reasoning became and to this day remains a key component of mathematical thinking
(Eves, 1990).
In his studies, Thales traveled to Egypt, where he observed workers measuring property
boundaries after the flooding of the Nile (O’Grady; Biography of Thales, 2009). While in Egypt,
Thales is also said to have measured the height of a pyramid. To do this, Thales waited until the
length of his shadow measured the same as his height, recognizing that the same proportion
would hold true for the pyramid (Biography of Thales, 2009). He then introduced these ideas to
Greece upon his return (Biography of Thales, 2009; Khalaf, 2014; O’Grady), calling it geometry
meaning, “earth measure” (Biography of Thales, 2009). After returning to Greece, Thales
converted what he had seen the land surveyors doing using stakes and ropes to create a system of
points and lines (Biography of Thales, 2009). He continued to study geometry and is credited
several important findings.
First, Thales is credited with defining the diameter of a circle as its bisector. It is not
exactly known how Thales proved this theory. McKirahan (2011) suggests that it may have been
as simple as cutting out a circle and folding it over on itself. Thales also recognized that the base
angles of an isosceles triangle and pairs of vertical angles had equal measures (O’Grady;
Lendering, 2005; Biography of Thales, 2009). Again, it is not exactly certain how Thales’ proved
that the base angles of an isosceles triangle were congruent. It is likely that Thales proved that
vertical angles were congruent using a logical explanation involving
straight angles (Figure 1). It was known that all straight angles were
equal. Therefore, Thales knew that a c  c  b. Thus,
Figure 1
vertical angles a and b are equal (Eves, 1990).
Thales is also credited with the discovery of the angle-side-angle
and angle-angle-side triangle congruencies (O’Grady; Lendering, 2005;
Biography of Thales, 2009). It is 
believedthat Thales used
these concepts
to calculate the distance of ships from the shore (O’Grady). Knowing the
distance of ships at sea was important to the city of Miletus. The
tradesmen needed to know when shipments of goods were coming in to
the city. The government in Miletus also benefited by knowing if enemies
were approaching the shore (Biography of Thales, 2009). Figure 2
demonstrates a possible method for finding the distance. In this case,
Thales is standing at point A looking out at the boat. Thales first would Figure 2
have constructed a segment AG perpendicular to his line of sight from the shore to the boat and

Thales
Kelly Dwyer
Feb 5, 2014
a line perpendicular to AG at G. Next, he would have constructed the midpoint, H, of AG . From
the midpoint, he could construct the angle between HA and the boat. Next, he could construct
the vertical angle of H . By extending the rays of the angle and finding its intersection with the
perpendicular line at G, we can find point I. By Thales’ understood theorem of angle-side-angle,


he knew that ABH  GIH . Thus, AB  GI , giving Thales an easily measured distance on the

shore (Ross, 2010).

Lastly, Thales stated that any angle inscribed in a semicircle is a right angle. This final idea is known as Thales’ Theorem
(O’Grady; Lendering, 2005; Biography of Thales, 2009). Thales

used his knowledge of the fact that the sum of two right angles
made a triangle and his previous theorems. Because AD, AB, AC
are all radii of circle A, he know that they were congruent. This
also meant that ABD and ABC were isosceles, which to Thales
meant that their base angles were congruent. From here, it is not
exactly sure how Thales proceeded. A 
modern proof of this
theorem states that 2    180 , 2   180, and     180.
 we arrive at the conclusion that     90.
Usingsubstitution,
However, Thales would not have used this method because he had no notion of degrees in angle
measures.


As with many historical figuresof this time, it is difficult to know if the discoveries

attributed to Thales are actually his. It is important to be critical of his so-called
findings and
mathematical discoveries. Although some ancient historians mention their existence, there is no
physical evidence of Thales’ writings. The information gathered on Thales comes from the
accounts of Greek historians, which may have been embellished. Many modern historians are
doubtful of Thales’ involvement in many of the stories told. It may be that Thales’ did all of
these things or only a few of them. The ideas could have been original, he could have learned
about them from others and improved upon them, or he could have simply repeated what he
learned from others. In any case, Thales was a contributor most importantly to philosophy and
mathematics.
Thales’ was the first to look at the world from a more modern scientific way, rather than
a mythological way. Although his philosophy the base of all things is water was wrong, he relied
on explanations that did not involve mythology. Thales looked for logical explanations and
reasoning to his philosophical and mathematical theories. Scientists are still studying what the
base of all things is. The mathematics attributed to Thales is still used today and taught in
schools around the world. Thales would not accept things for what they appeared to be. He
wanted to know what they were true. By rejecting the norms of society of his time, Thales laid
the foundation for modern science and mathematics.
Thales
Kelly Dwyer
Feb 5, 2014
Works Cited
Biography of Thales. (2009). Retrieved 2014, 28-Jan from Math Open Reference:
http://www.mathopenref.com/thales.html
Eves, H. (1990). An Introduction to the History of Mathematics (Sixth Edition). Pacific Grove,
CA: Thomson Learning, Inc.
Khalaf, S. G. (2014). Thales of Miletus. Retrieved 2014, 28-Jan from
http://phoenicia.org/thales.html
Lendering, J. (2005). Thales of Miletus. Retrieved 2014, 28-Jan from Livius.org:
http://www.livius.org/th/thales/thales.html
McKirahan, R. D. (2011). Philosophy Before Socrates : An Introduction With Texts and
Commentary (2nd Edition). Indianapolis, IN: Hackett Publishing Co.
O’Grady, P. (n.d.). Thales of Miletus. Retrieved 2014 28-Jan from Internet Encyclopedia of
Philosophy: http://www.iep.utm.edu/thales/
Ross, W. T. (2010, Sept 4). Thales. Retrieved February 5, 2014, from Nature of Mathematics:
http://natureofmathematics.wordpress.com/lecture-notes/thales/
Thales. (2014). Retrieved 2014, 28-Jan from The Famous People:
http://www.thefamouspeople.com/profiles/thales-263.php