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72-436: His father, Arend Roggeveen, was a mathematician with much knowledge of astronomy , geography , rhetorics, philosophy, and the theory of navigation as well. He occupied himself with study of the mythical Terra Australis, and even got a patent for an exploratory excursion, but it was to be his son who, at the age of 62, eventually equipped three ships and made the expedition. He became notary of Middelburg (the capital of

144-551: A "fighting together", with the Lydians. This has sometimes been interpreted as an alliance. Croesus was defeated before the city of Sardis by Cyrus the Great , who subsequently spared Miletus because it had taken no action. Cyrus was so impressed by Croesus’ wisdom and his connection with the sages that he spared him and took his advice on various matters. The Ionian cities should be demoi, or "districts". He counselled them to establish

216-469: A Greek. Diogenes continues, by delivering more conflicting reports: one that Thales married and either fathered a son (Cybisthus or Cybisthon) or adopted his nephew of the same name; the second that he never married, telling his mother as a young man that it was too early to marry, and as an older man that it was too late. Plutarch had earlier told this version: Solon visited Thales and asked him why he remained single; Thales answered that he did not like

288-779: A controversy. On 1 August 1721 he headed an expedition sponsored by the Dutch West India Company , the rivals of the VOC , to seek Terra Australis and to open a western trade route to the "Spice islands" in the East Indies. His fleet consisted of three ships, the Arend , the Thienhoven , and Afrikaansche Galey and had 223 men on crew. Roggeveen first sailed down to the Falkland Islands (which he renamed "Belgia Australis"), passed through

360-471: A financial economist might study the structural reasons why a company may have a certain share price , a financial mathematician may take the share price as a given, and attempt to use stochastic calculus to obtain the corresponding value of derivatives of the stock ( see: Valuation of options ; Financial modeling ). According to the Dictionary of Occupational Titles occupations in mathematics include

432-400: A manner which will help ensure that the plans are maintained on a sound financial basis. As another example, mathematical finance will derive and extend the mathematical or numerical models without necessarily establishing a link to financial theory, taking observed market prices as input. Mathematical consistency is required, not compatibility with economic theory. Thus, for example, while

504-766: A political dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked and scraping off her skin with clamshells (some say roofing tiles). Science and mathematics in the Islamic world during the Middle Ages followed various models and modes of funding varied based primarily on scholars. It was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. Funding for translation of scientific texts in other languages

576-595: A single seat of government, and pointed out Teos as the fittest place for it; "for that," he said, "was the centre of Ionia . Their other cities might still continue to enjoy their own laws, just as if they were independent states." Miletus, however, received favorable terms from Cyrus. The others remained in an Ionian League of twelve cities (excluding Miletus), and were subjugated by the Persians. Early Greeks, and other civilizations before them, often invoked idiosyncratic explanations of natural phenomena with reference to

648-420: Is mathematics that studies entirely abstract concepts . From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics , and at variance with the trend towards meeting the needs of navigation , astronomy , physics , economics , engineering , and other applications. Another insightful view put forth is that pure mathematics

720-451: Is a mathematical science with specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on problems, often concrete but sometimes abstract. As professionals focused on problem solving, applied mathematicians look into the formulation, study, and use of mathematical models in science , engineering , business , and other areas of mathematical practice. Pure mathematics

792-489: Is about an angle intercepted by two parallel lines, forming a pair of similar triangles . Modern scholars are skeptical that anyone in Thales's time was producing mathematical proofs to the standard of later Greek mathematics, though not enough direct evidence remains to draw firm conclusions. While Thales may have discovered some basic geometric relations and provided some justification for them, attribution to him of formal proofs

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864-412: Is also possible that he was of mixed ancestry, given his father had a Carian name and his mother had a Greek name. Diogenes Laërtius seems to also reference an alternative account: "Most writers, however, represent him as a genuine Milesian and of a distinguished family". Encyclopedia Britannica (1952) concluded that Thales was most likely a native Milesian of noble birth and that he was certainly

936-583: Is believed the Babylonians knew the theorem for special cases. The theorem is mentioned and proved as part of the 31st proposition in the third book of Euclid 's Elements . Dante's Paradiso refers to Thales's theorem in the course of a speech. The story is told in Diogenes Laërtius , Pliny the Elder , and Plutarch , sourced from Hieronymus of Rhodes , that when Thales visited Egypt , he measured

1008-454: Is both "applied to those whose boasts exceed what they are" and "a warning to pay no attention to the opinion of the multitude." Diogenes Laërtius relates several stories of an expensive, gold tripod or bowl that is to go to the most wise . In one version (that Laërtius credits to Callimachus in his Iambics ) Bathycles of Arcadia states in his will that an expensive bowl " 'should be given to him who had done most good by his wisdom.' So it

1080-437: Is considered possible that Thales visited Egypt, since Miletus had a permanent colony there (namely Naucratis ). It is also said Thales had close contacts with the priests of Thebes who instructed him, or even that he instructed them in geometry. It is also possible Thales knew about Egypt from accounts of others, without actually visiting it. Aside from Egypt, the other mathematically advanced, ancient civilization before

1152-468: Is controversial." Others historians, such as D. R. Dicks, take issue with the idea of Babylonian influence on Greek mathematics. For until around the time of Hipparchus (c. 190–120 BC) their sexagesimal system was unknown. Herodotus wrote the Greeks learnt the gnomon from the Babylonians. Thales's follower Anaximander is credited with introducing the gnomon to the Greeks. Herodotus also wrote that

1224-400: Is his own thinking, his statement that Thales held it as water is generally accepted as genuinely originating with Thales. Writing centuries later, Diogenes Laërtius also states that Thales taught "Water constituted ( ὑπεστήσατο , 'stood under') the principle of all things." According to Aristotle: That from which is everything that exists and from which it first becomes and into which it

1296-400: Is not necessarily applied mathematics : it is possible to study abstract entities with respect to their intrinsic nature, and not be concerned with how they manifest in the real world. Even though the pure and applied viewpoints are distinct philosophical positions, in practice there is much overlap in the activity of pure and applied mathematicians. To develop accurate models for describing

1368-698: Is now thought to represent speculative rationalization and reconstruction by later authors, rather than concrete accomplishments of Thales himself or his contemporaries. According to one author, while visiting Egypt, Thales observed that when the Egyptians drew two intersecting lines, they would measure the vertical angles to make sure that they were equal. Thales concluded that one could prove that all vertical angles are equal if one accepted some general notions such as: all straight angles are equal, equals added to equals are equal, and equals subtracted from equals are equal. Pamphila says that, having learnt geometry from

1440-402: Is rendered at last, its substance remaining under it, but transforming in qualities, that they say is the element and principle of things that are. …For it is necessary that there be some nature ( φύσις ), either one or more than one, from which become the other things of the object being saved... [The first philosophers] do not all agree as to the number and the nature of these principles. Thales

1512-570: Is the unity of substance. Not merely the empirical claim that all is water, but the deeper philosophical claim that all is one. For example, Friedrich Nietzsche , in his Philosophy in the Tragic Age of the Greeks , wrote: Greek philosophy seems to begin with an absurd notion, with the proposition that water is the primal origin and the womb of all things. Is it really necessary for us to take serious notice of this proposition? It is, and for three reasons. First, because it tells us something about

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1584-634: The Pythagorean school , whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypatia of Alexandria ( c.  AD 350 – 415). She succeeded her father as librarian at the Great Library and wrote many works on applied mathematics. Because of

1656-656: The Schock Prize , and the Nevanlinna Prize . The American Mathematical Society , Association for Women in Mathematics , and other mathematical societies offer several prizes aimed at increasing the representation of women and minorities in the future of mathematics. Several well known mathematicians have written autobiographies in part to explain to a general audience what it is about mathematics that has made them want to devote their lives to its study. These provide some of

1728-590: The Strait of Le Maire , and continued south to beyond 60 degrees south to enter the Pacific Ocean . He made landfall near Valdivia, Chile . He visited the Juan Fernández Islands , where he spent 24 February to 17 March. The expedition later arrived at Easter Island (Rapa Nui) on Easter Sunday , 5 April 1722 (whereupon he reported seeing 2,000–3,000 inhabitants). Roggeveen charted the location of six islands in

1800-650: The Tuamotu Archipelago , two islands in the Society Islands , and four islands in Samoa , losing his flagship, Afrikaansche Galey at Takapoto atoll. At Makatea , he opened fire on a crowded beach in retaliation for a violent encounter with the inhabitants, and in return the Makateans ambushed a shore party, killing ten of his crewmen. The remaining two vessels sailed past New Guinea to reach Batavia in 1722, where he

1872-541: The archonship of Damasius at Athens about 582 BC and that Thales was the first sage. The sages were associated with the Delphic maxims , a quote or maxim attributed to each one inscribed on the Temple of Apollo at Delphi . Thales has arguably the most famous of all, gnothi seauton or know thyself . According to the 10th-century Byzantine encyclopedia the Suda , the proverb

1944-478: The graduate level . In some universities, a qualifying exam serves to test both the breadth and depth of a student's understanding of mathematics; the students who pass are permitted to work on a doctoral dissertation . Mathematicians involved with solving problems with applications in real life are called applied mathematicians . Applied mathematicians are mathematical scientists who, with their specialized knowledge and professional methodology, approach many of

2016-438: The seked from the height of the stick and its distance from the point of insertion to the line of sight. Thales was also a noted astronomer, acknowledged in antiquity for describing the position of Ursa Minor , and he thought the constellation might be useful as a guide for navigation at sea. He calculated the duration of the year and the timings of the equinoxes and solstices . He is additionally attributed with calculating

2088-474: The Egyptians, Thales was the first to inscribe in a circle a right-angled triangle, whereupon he sacrificed an ox . This is sometimes cited as history's first mathematical discovery. Due to the variations among testimonies, such as the story of the ox sacrifice being accredited to Pythagoras upon discovery of the Pythagorean theorem rather than Thales, some historians (such as D. R. Dicks) question whether such anecdotes have any historical worth whatsoever. It

2160-522: The Eminent Philosophers . While it is all we have, Diogenes wrote some eight centuries after Thales's death and his sources often contained "unreliable or even fabricated information". It is known Thales was from Miletus , a mercantile city settled at the mouth of the Maeander river . The dates of Thales's life are not exactly known, but are roughly established by a few datable events mentioned in

2232-416: The Greeks was Babylonia, another commonplace attribution of travel for a mathematically-minded philosopher. At least one ancient historian, Josephus , claims Thales visited Babylonia. Historians Roger L. Cooke and B.L. Van der Waerden come down on the side of Babylonian mathematics influencing the Greeks, citing the use of e. g. the sexagesimal system (or base 60). Cooke notes "This relation, however,

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2304-578: The Italian and German universities, but as they already enjoyed substantial freedoms and autonomy the changes there had begun with the Age of Enlightenment , the same influences that inspired Humboldt. The Universities of Oxford and Cambridge emphasized the importance of research , arguably more authentically implementing Humboldt's idea of a university than even German universities, which were subject to state authority. Overall, science (including mathematics) became

2376-409: The best glimpses into what it means to be a mathematician. The following list contains some works that are not autobiographies, but rather essays on mathematics and mathematicians with strong autobiographical elements. Thales of Miletus Thales of Miletus ( / ˈ θ eɪ l iː z / THAY -leez ; Ancient Greek : Θαλῆς ; c.  626/623   – c.  548/545 BC )

2448-405: The discovery that a circle is bisected by its diameter, that the base angles of an isosceles triangle are equal and that vertical angles are equal. Two fundamental theorems of elementary geometry are customarily called Thales's theorem : one of them has to do with a triangle inscribed in a circle and having the circle's diameter as one side; the other, also called the intercept theorem ,

2520-500: The earliest known mathematicians was Thales of Miletus ( c.  624  – c.  546 BC ); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry , by deriving four corollaries to Thales's theorem . The number of known mathematicians grew when Pythagoras of Samos ( c.  582  – c.  507 BC ) established

2592-454: The existence of a single ultimate substance . Thales theorized that this single substance was water . Thales thought the Earth floated on water. In mathematics, Thales is the namesake of Thales's theorem , and the intercept theorem can also be known as Thales's theorem. Thales was said to have calculated the heights of the pyramids and the distance of ships from the shore. In science, Thales

2664-447: The first among them. Also, while the other Seven Sages were strictly law-givers and statesmen and not speculative philosophers, Plutarch noted "it would seem that Thales was the only wise man of the time who carried his speculations beyond the realm of the practical." Thales's most famous idea was his philosophical and cosmological thesis that all is water, which comes down to us through a passage from Aristotle 's Metaphysics . In

2736-593: The first person in the western world to apply deductive reasoning to geometry, making him the West's "first mathematician." He is also credited with the West's oldest definition of number : a "collection of units", "following the Egyptian view". The evidence for the primacy of Thales comes to us from a book by Proclus , who lived a thousand years afterward but is believed to have had a copy of Eudemus 's lost book History of Geometry (4th century BC). Proclus wrote that Thales

2808-494: The focus of universities in the 19th and 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge. The German university system fostered professional, bureaucratically regulated scientific research performed in well-equipped laboratories, instead of

2880-992: The following. There is no Nobel Prize in mathematics, though sometimes mathematicians have won the Nobel Prize in a different field, such as economics or physics. Prominent prizes in mathematics include the Abel Prize , the Chern Medal , the Fields Medal , the Gauss Prize , the Nemmers Prize , the Balzan Prize , the Crafoord Prize , the Shaw Prize , the Steele Prize , the Wolf Prize ,

2952-406: The founder of this type of philosophy says that it is water. Aristotle further adds: Presumably he derived this assumption from seeing that the nutriment of everything is moist, and that heat itself is generated from moisture and depends upon it for its existence (and that from which a thing is generated is always its first principle). He derived his assumption from this; and also from the fact that

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3024-402: The height of the pyramids by their shadows at the moment when his own shadow was equal to his height. According to Plutarch, it pleased the pharoah Amasis . More practically, Thales was said to have the ability to measure the distances of ships at sea. These stories indicate familiarity with the intercept theorem, and for this reason the 26th proposition in the first book of Euclid's Elements

3096-512: The idea of having to worry about children. Nevertheless, several years later, anxious for family, he adopted his nephew Cybisthus. The culture of Archaic Greece was heavily influenced by those of the Levant and Mesopotamia . It is said Thales was engaged in trade and visited either Egypt or Babylonia . However, there is no strong evidence that Thales ever visited countries in the Near East , and

3168-629: The imposing problems presented in related scientific fields. With professional focus on a wide variety of problems, theoretical systems, and localized constructs, applied mathematicians work regularly in the study and formulation of mathematical models . Mathematicians and applied mathematicians are considered to be two of the STEM (science, technology, engineering, and mathematics) careers. The discipline of applied mathematics concerns itself with mathematical methods that are typically used in science, engineering, business, and industry; thus, "applied mathematics"

3240-402: The issue is disputed among scholars. Visits to such places were a commonplace attribution to various philosophers by later writers, especially when these writers tried to explain the origin of their mathematical knowledge, such as with Thales or Pythagoras or Eudoxus . Several ancient authors assume that Thales, at one point in his life, visited Egypt , where he learned about geometry. It

3312-569: The kind of research done by private and individual scholars in Great Britain and France. In fact, Rüegg asserts that the German system is responsible for the development of the modern research university because it focused on the idea of "freedom of scientific research, teaching and study." Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education , and then proceed to specialize in topics of their own choice at

3384-470: The king of Prussia , Fredrick William III , to build a university in Berlin based on Friedrich Schleiermacher 's liberal ideas; the goal was to demonstrate the process of the discovery of knowledge and to teach students to "take account of fundamental laws of science in all their thinking." Thus, seminars and laboratories started to evolve. British universities of this period adopted some approaches familiar to

3456-474: The liberal preacher Pontiaan van Hattem by publishing his leaflet De val van 's werelds afgod (The fall of the world's idol). The first part appeared in 1718 in Middelburg, and was subsequently confiscated by the city council and burned. Roggeveen fled from Middelburg to nearby Flushing . Thereafter he established himself in the small town of Arnemuiden , and published parts 2 and 3 of the series, again raising

3528-652: The position of the Pleiades . Plutarch indicates that in his day (c. AD 100) there was an extant work, the Astronomy , composed in verse and attributed to Thales. While some say he left no writings, others say that he wrote On the Solstice and On the Equinox . The Nautical Star-guide has also been attributed to him, but this was disputed even in ancient times. No writing attributed to him has survived. Lobon of Argus asserted that

3600-398: The practice of dividing the day into 12 parts, and the polos , came to the Greeks from the Babylonians. Yet this too is disputed, for example by historian L. Zhmud, who points out the gnomon was known to both Egyptians and Babylonians, the division of the day into twelve parts (and by analogy the year) was known to the Egyptians already in the 2nd millennium BC , and the idea of the polos

3672-480: The primal origin of all things; second, because it does so in language devoid of image or fable, and finally, because contained in it, if only embryonically, is the thought, "all things are one." Megiston topos: apanta gar chorei ( Μέγιστον τόπος· ἄπαντα γὰρ χωρεῖ. ) The greatest is space, for it holds all things. —attributed to Thales Thales was known for introducing the theoretical and practical use of geometry to Greece, and has been described as

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3744-531: The probability and likely cost of the occurrence of an event such as death, sickness, injury, disability, or loss of property. Actuaries also address financial questions, including those involving the level of pension contributions required to produce a certain retirement income and the way in which a company should invest resources to maximize its return on investments in light of potential risk. Using their broad knowledge, actuaries help design and price insurance policies, pension plans, and other financial strategies in

3816-735: The province of Zeeland , where he was born). On 12 August 1690, he graduated as a doctor of the law at the University of Harderwijk . About this time he married Marija Margaerita Vincentius. She died around 3 to 4 years later in October 1694. In 1706, he joined the Dutch East Indies Company (VOC), and between 1707 and 1714 worked as a Raadsheer van Justitie ("Council Lord of Justice") at Batavia, Dutch East Indies (now Jakarta ). He married Anna Adriana Clement there, but she died soon afterward. In 1714, he returned to Middelburg by himself. He became involved in religious controversies, supporting

3888-484: The real world, many applied mathematicians draw on tools and techniques that are often considered to be "pure" mathematics. On the other hand, many pure mathematicians draw on natural and social phenomena as inspiration for their abstract research. Many professional mathematicians also engage in the teaching of mathematics. Duties may include: Many careers in mathematics outside of universities involve consulting. For instance, actuaries assemble and analyze data to estimate

3960-439: The seeds of everything have a moist nature, whereas water is the first principle of the nature of moist things." The 1870 book Dictionary of Greek and Roman Biography and Mythology noted: In his dogma that water is the origin of things, that is, that it is that out of which every thing arises, and into which every thing resolves itself, Thales may have followed Orphic cosmogonies, while, unlike them, he sought to establish

4032-403: The seventeenth century at Oxford with the scientists Robert Hooke and Robert Boyle , and at Cambridge where Isaac Newton was Lucasian Professor of Mathematics & Physics . Moving into the 19th century, the objective of universities all across Europe evolved from teaching the "regurgitation of knowledge" to "encourag[ing] productive thinking." In 1810, Alexander von Humboldt convinced

4104-564: The sources. According to the historian Herodotus , writing in the 5th century BC, Thales predicted a solar eclipse in 585 BC. Assuming one's acme (or floruit ) occurred at the age of 40, the chronicle of Apollodorus of Athens , written during the 2nd century BC, therefore placed Thales's birth about the year 625 BC. While the probability is that Thales was as Greek as most Milesians, Herodotus described Thales as "a Phoenician by remote descent". Diogenes Laërtius references Herodotus, Duris , and Democritus , who all agree "that Thales

4176-507: The stars were balls of dirt on fire. He seemed to correctly gather that the moon reflects the Sun's light. A crater on the Moon is named in his honor. Rather than assuming that earthquakes were the result of supernatural whims, Thales explained them by theorizing that the Earth floats on water and that earthquakes occur when the Earth is rocked by waves. He is attributed with the first observation of

4248-514: The truth of the assertion. Hence, Aristotle, immediately after he has called him the originator of philosophy brings forward the reasons which Thales was believed to have adduced in confirmation of that assertion; for that no written development of it, or indeed any book by Thales, was extant, is proved by the expressions which Aristotle uses when he brings forward the doctrines and proofs of the Milesian. (p. 1016) Most agree that Thales's stamp on thought

4320-492: The will of anthropomorphic gods and heroes . Instead, Thales aimed to explain natural phenomena via rational hypotheses that referenced natural processes themselves— Logos rather than mythos . Many, most notably Aristotle, regard him as the first philosopher in the Greek tradition . Rather than theologoi or mythologoi , Aristotle referred to the first philosophers as physiologoi , or natural philosophers, and Thales as

4392-433: The work, Aristotle reported Thales's theory that the arche or originating principle of nature was a single material substance : water. Aristotle then proceeded to proffer a number of conjectures based on his own observations to lend some credence to why Thales may have advanced this idea (though Aristotle did not hold it himself). While Aristotle's conjecture on why Thales held water as the originating principle of matter

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4464-524: The writings of Thales amounted to two hundred lines. Thales thought the Earth must be a flat disk or mound of land and dirt which is floating in an expanse of water. Heraclitus Homericus states that Thales drew his conclusion from seeing moist substance turn into air, slime and earth. It seems likely that Thales viewed the land as coming from the water on which it floated and the oceans that surround it, perhaps inspired by observing silt deposits. He thought

4536-938: Was Al-Khawarizmi . A notable feature of many scholars working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics , maths and astronomy of Ibn al-Haytham . The Renaissance brought an increased emphasis on mathematics and science to Europe. During this period of transition from a mainly feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: Luca Pacioli (founder of accounting ); Niccolò Fontana Tartaglia (notable engineer and bookkeeper); Gerolamo Cardano (earliest founder of probability and binomial expansion); Robert Recorde (physician) and François Viète (lawyer). As time passed, many mathematicians gravitated towards universities. An emphasis on free thinking and experimentation had begun in Britain's oldest universities beginning in

4608-639: Was an Ancient Greek pre-Socratic philosopher from Miletus in Ionia , Asia Minor . Thales was one of the Seven Sages , founding figures of Ancient Greece . Many regard him as the first philosopher in the Greek tradition , breaking from the prior use of mythology to explain the world and instead using natural philosophy . He is thus otherwise referred to as the first to have engaged in mathematics , science , and deductive reasoning . The first philosophers followed him in explaining all of nature as based on

4680-522: Was an astronomer who reportedly predicted the weather and a solar eclipse . The discovery of the position of the constellation Ursa Major is also attributed to Thales, as well as the timings of the solstices and equinoxes . He was also an engineer , known for having diverted the Halys River . The main source concerning the details of Thales's life and career is the doxographer Diogenes Laërtius , in his third-century-AD work Lives and Opinions of

4752-683: Was arrested for violating the monopoly of the VOC and had his ships confiscated. After a lengthy lawsuit in the Netherlands, the VOC was later forced to compensate him for his losses and to pay his crew. After his return, Roggeveen published part 4 of his work, De val van 's werelds afgod . Mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems . Mathematicians are concerned with numbers , data , quantity , structure , space , models , and change . One of

4824-419: Was attributed to Thales. They also indicate that he was familiar with the Egyptian seked , or seqed , the ratio of the run to the rise of a slope ( cotangent ). According to Kirk & Raven, all you need for this feat is three straight sticks pinned at one end and knowledge of your altitude. One stick goes vertically into the ground. A second is made level. With the third you sight the ship and calculate

4896-456: Was given to Thales, went the round of all the sages, and came back to Thales again. And he sent it to Apollo at Didyma , with this dedication...'Thales the Milesian, son of Examyas [dedicates this] to Delphinian Apollo after twice winning the prize from all the Greeks. ' " According to Diogenes Laërtius, Thales gained fame as a counselor when he advised the Milesians not to engage in a symmachia,

4968-454: Was not used outside of Greece at this time. Thales is recognized as one of the Seven Sages of Greece, semi-legendary wise statesmen and founding figures of Ancient Greece. While which seven one chooses may change, the seven has a canonical four which includes Thales, Solon of Athens, Pittacus of Mytilene , and Bias of Priene . Diogenes Laërtius tells us that the Seven Sages were created in

5040-431: Was ongoing throughout the reign of certain caliphs, and it turned out that certain scholars became experts in the works they translated, and in turn received further support for continuing to develop certain sciences. As these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences. An example of a translator and mathematician who benefited from this type of support

5112-430: Was the first to visit Egypt and bring the Egyptian study of mathematics to Greece, and that Thales "himself discovered many propositions and disclosed the underlying principles of many others to his successors, in some case his method being more general, in others more empirical." In addition to Proclus, Hieronymus of Rhodes (3rd century BC) also cites Thales as the first Greek mathematician. Proclus attributes to Thales

5184-513: Was the son of Examyas and Cleobulina, and belonged to the Thelidae who are Phoenicians and amongst the noblest descendants of Cadmus and Agenor " who had been banished from Phoenicia and that Thales was enrolled as a citizen in Miletus along with Neleus . However, Friedrich Nietzsche and others interpret this quote as meaning only that his ancestors were seafaring Cadmeians from Boeotia . It

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