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Thales
Thales of Miletus ( ; grc-gre, Θαλῆς; ) was a Greek mathematician, astronomer, statesman, and pre-Socratic philosopher from Miletus in Ionia, Asia Minor. He was one of the Seven Sages of Greece. Many, most notably Aristotle, regarded him as the first philosopher in the Greek tradition, and he is otherwise historically recognized as the first individual known to have entertained and engaged in scientific philosophy.Frank N. Magill''The Ancient World: Dictionary of World Biography'', Volume 1 Routledge, 2003 He is often referred to as the Father of Science. Thales is recognized for breaking from the use of mythology to explain the world and the universe, instead explaining natural objects and phenomena by offering naturalistic theories and hypotheses. Almost all the other pre-Socratic philosophers followed him in explaining nature as deriving from a unity of everything based on the existence of a single ultimate substance instead of using mythological explanations. A ...
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Θαλῆς
Thales of Miletus ( ; grc-gre, wikt:Θαλῆς, Θαλῆς; ) was a Greeks, Greek Greek Mathematics, mathematician, astronomer, statesman, and Pre-Socratic philosophy, pre-Socratic philosopher from Miletus in Ionia, Asia Minor. He was one of the Seven Sages of Greece. Many, most notably Aristotle, regarded him as the first philosopher in the Greek philosophy, Greek tradition, and he is otherwise historically recognized as the first individual known to have entertained and engaged in History of science#Pre-socratics, scientific philosophy.Frank N. Magill''The Ancient World: Dictionary of World Biography'', Volume 1 Routledge, 2003 He is often referred to as the Father of Science. Thales is recognized for breaking from the use of mythology to explain the world and the universe, instead explaining natural objects and phenomena by offering Naturalism (philosophy), naturalistic Theory, theories and hypothesis, hypotheses. Almost all the other Pre-Socratic philosophy, pre-Socrat ...
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Thales' Theorem
In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line is a diameter, the angle ABC is a right angle. Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid's '' Elements''. It is generally attributed to Thales of Miletus, but it is sometimes attributed to Pythagoras. History There is nothing extant of the writing of Thales. Work done in ancient Greece tended to be attributed to men of wisdom without respect to all the individuals involved in any particular intellectual constructions; this is true of Pythagoras especially. Attribution did tend to occur at a later time. Reference to Thales was made by Proclus, and by Diogenes Laërtius documenting Pamphila's statement that Thales "was the first to inscribe in a circle a right-angle triangle". Babylonian mathematicians knew this for special cases before Thales proved it. It is bel ...
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Pre-Socratic Philosophy
Pre-Socratic philosophy, also known as early Greek philosophy, is ancient Greek philosophy before Socrates. Pre-Socratic philosophers were mostly interested in cosmology, the beginning and the substance of the universe, but the inquiries of these early philosophers spanned the workings of the natural world as well as human society, ethics, and religion. They sought explanations based on natural law rather than the Divinity, actions of gods. Their work and writing has been almost entirely lost. Knowledge of their views comes from ''testimonia'', i.e. later authors' discussions of the work of pre-Socratics. Philosophy found fertile ground in the ancient Greek world because of the close ties with neighboring civilizations and the rise of autonomous civil entities, ''polis, poleis''. Pre-Socratic philosophy began in the 6th century BCE with the three Milesian school, Milesians: Thales, Anaximander, and Anaximenes of Miletus, Anaximenes. They all attributed the ''arche'' (a word that ...
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Intercept Theorem
The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem is an important theorem in elementary geometry about the ratios of various line segments that are created if two intersecting lines are intercepted by a pair of parallels. It is equivalent to the theorem about ratios in similar triangles. It is traditionally attributed to Greek mathematician Thales. It was known to the ancient Babylonians and Egyptians, although its first known proof appears in Euclid's '' Elements''. Formulation Suppose S is the intersection point of two lines and A, B are the intersections of the first line with the two parallels, such that B is further away from S than A, and similarly C, D are the intersections of the second line with the two parallels such that D is further away from S than C. # The ratio of any two segments on the first line equals the ratio of the according segments on the second line: , SA , : , AB , =, SC , : , CD , , ...
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Anaximander
Anaximander (; grc-gre, Ἀναξίμανδρος ''Anaximandros''; ) was a pre-Socratic Greek philosopher who lived in Miletus,"Anaximander" in ''Chambers's Encyclopædia''. London: George Newnes, 1961, Vol. 1, p. 403. a city of Ionia (in modern-day Turkey). He belonged to the Milesian school and learned the teachings of his master Thales. He succeeded Thales and became the second master of that school where he counted Anaximenes and, arguably, Pythagoras amongst his pupils. Little of his life and work is known today. According to available historical documents, he is the first philosopher known to have written down his studies, although only one fragment of his work remains. Fragmentary testimonies found in documents after his death provide a portrait of the man. Anaximander was an early proponent of science and tried to observe and explain different aspects of the universe, with a particular interest in its origins, claiming that nature is ruled by laws, just like human soc ...
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Ionian School (philosophy)
The Ionian school of Pre-Socratic philosophy was centred in Miletus, Ionia in the 6th century BC. Miletus and its environment was a thriving mercantile melting pot of current ideas of the time. The Ionian School included such thinkers as Thales, Anaximander, Anaximenes, Heraclitus, Anaxagoras, and Archelaus. The collective affinity of this group was first acknowledged by Aristotle who called them ''physiologoi'' (φυσιολόγοι), meaning 'those who discoursed on nature'. The classification can be traced to the second-century historian of philosophy Sotion. They are sometimes referred to as cosmologists, since they were largely physicalists who tried to explain the nature of matter. Most cosmologists thought that, although matter could change from one form to another, all matter had something in common which did not change. They did not agree on what all things had in common, and did not experiment to find out, but used abstract reasoning rather than religion or mythology ...
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Milesian School
The Ionian school of Pre-Socratic philosophy was centred in Miletus, Ionia in the 6th century BC. Miletus and its environment was a thriving mercantile melting pot of current ideas of the time. The Ionian School included such thinkers as Thales, Anaximander, Anaximenes, Heraclitus, Anaxagoras, and Archelaus. The collective affinity of this group was first acknowledged by Aristotle who called them ''physiologoi'' (φυσιολόγοι), meaning 'those who discoursed on nature'. The classification can be traced to the second-century historian of philosophy Sotion. They are sometimes referred to as cosmologists, since they were largely physicalists who tried to explain the nature of matter. Most cosmologists thought that, although matter could change from one form to another, all matter had something in common which did not change. They did not agree on what all things had in common, and did not experiment to find out, but used abstract reasoning rather than religion or mythol ...
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Pythagoras
Pythagoras of Samos ( grc, Πυθαγόρας ὁ Σάμιος, Pythagóras ho Sámios, Pythagoras the Samos, Samian, or simply ; in Ionian Greek; ) was an ancient Ionians, Ionian Ancient Greek philosophy, Greek philosopher and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, the Western philosophy, West in general. Knowledge of his life is clouded by legend, but he appears to have been the son of Mnesarchus, a gem-engraver on the island of Samos. Modern scholars disagree regarding Pythagoras's education and influences, but they do agree that, around 530 BC, he travelled to Crotone, Croton in southern Italy, where he founded a school in which initiates were sworn to secrecy and lived a communal, asceticism, ascetic lifestyle. This lifestyle entailed a number of dietary prohibitions, traditionally said to have included vegetarianism, although m ...
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Miletus
Miletus (; gr, Μῑ́λητος, Mī́lētos; Hittite transcription ''Millawanda'' or ''Milawata'' (exonyms); la, Mīlētus; tr, Milet) was an ancient Greek city on the western coast of Anatolia, near the mouth of the Maeander River in ancient Ionia. Its ruins are located near the modern village of Balat in Aydın Province, Turkey. Before the Persian rule that started in the 6th century BC, Miletus was considered among the greatest and wealthiest of Greek cities. Evidence of first settlement at the site has been made inaccessible by the rise of sea level and deposition of sediments from the Maeander. The first available evidence is of the Neolithic. In the early and middle Bronze Age the settlement came under Minoan influence. Legend has it that an influx of Cretans occurred displacing the indigenous Leleges, and the site was renamed Miletus after a place in Crete. Recorded history at Miletus begins with the records of the Hittite Empire, and the Mycenaean records of ...
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Greek Mathematics
Greek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly extant from the 7th century BC to the 4th century AD, around the shores of the Eastern Mediterranean. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean from Italy to North Africa but were united by Greek culture and the Greek language. The word "mathematics" itself derives from the grc, , máthēma , meaning "subject of instruction". The study of mathematics for its own sake and the use of generalized mathematical theories and proofs is an important difference between Greek mathematics and those of preceding civilizations. Origins of Greek mathematics The origin of Greek mathematics is not well documented. The earliest advanced civilizations in Greece and in Europe were the Minoan and later Mycenaean civilizations, both of which flourished during the 2nd millennium BCE. While these civilizations possessed writing and ...
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Anaximenes Of Miletus
Anaximenes of Miletus (; grc-gre, Ἀναξιμένης ὁ Μιλήσιος, translit=Anaximenēs ho Milēsios; ) was an Ancient Greek, Ionian Pre-Socratic philosopher from Miletus in Asia Minor (modern-day Turkey), active in the latter half of the 6th century BC. The details of his life are obscure because none of his work has been preserved. Anaximenes' ideas are only known today because of comments about him made by later writers, such as Aristotle. As the last of the three philosophers of the Milesian School, considered the first philosophers of the Western world, Anaximenes is best known and identified as a younger friend or student of Anaximander, who was himself taught by the first philosopher Thales. Each developed a distinct cosmology without completely rejecting their predecessors views. Each were material monists who sought to discover the ''arche;'' the one, underlying physical yet divine basis of everything. Thales proposed all was made of water; Anaximander propos ...
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Xenophanes
Xenophanes of Colophon (; grc, Ξενοφάνης ὁ Κολοφώνιος ; c. 570 – c. 478 BC) was a Greek philosopher A philosopher is a person who practices or investigates philosophy. The term ''philosopher'' comes from the grc, φιλόσοφος, , translit=philosophos, meaning 'lover of wisdom'. The coining of the term has been attributed to the Greek th ..., theologian, poet, and critic of Homer from Ionia who travelled throughout the Greek-speaking world in early Classical Antiquity. As a poet, Xenophanes was known for his critical style, writing poems that are considered among the first satires. He also composed elegiac couplets that criticised his society's traditional values of wealth, excesses, and athletic victories. He also criticised Homer and the other poets in his works for representing the gods as foolish or morally weak. His poems have not survived intact; only fragments of some of his work survives in quotations by later philosophers and literary c ...
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