Hellenistic period in the context of "Medieval science"

Greece, officially the Hellenic Republic, is a country in Southeast Europe. Located on the southern tip of the Balkan peninsula, it shares land borders with Albania to the northwest, North Macedonia and Bulgaria to the north, and Turkey to the east. The Aegean Sea lies to the east of the mainland, the Ionian Sea to the west, and the Sea of Crete and the Mediterranean Sea to the south. Greece has the longest coastline on the Mediterranean basin, spanning thousands of islands and nine traditional geographic regions. It has a population of over 10 million. Athens is the nation's capital and largest city, followed by Thessaloniki, Patras and Heraclion.

Greece is considered the cradle of Western civilisation and the birthplace of democracy, Western philosophy, Western literature, historiography, political science, major scientific and mathematical principles, theatre, and the Olympic Games. The Ancient Greeks were organised into independent city-states, or poleis (singular polis), that spanned the Mediterranean and Black seas. Philip II of Macedon united most of present-day Greece in the fourth century BC, with his son Alexander the Great conquering much of the known ancient world from the Near East to northwestern India. The subsequent Hellenistic period saw the height of Greek culture and influence in antiquity. Greece was annexed by Rome in the second century BC and became an integral part of the Roman Empire and its continuation, the Byzantine Empire, where Greek culture and language were dominant. The Greek Orthodox Church, which emerged in the first century AD, helped shape modern Greek identity and transmitted Greek traditions to the wider Orthodox world.

Ancient Greece (Ancient Greek: Ἑλλάς, romanized: Hellás) was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity (c. 600 AD), that comprised a loose collection of culturally and linguistically related city-states and communities. Prior to the Roman period, most of these regions were officially unified only once under the Kingdom of Macedon from 338 to 323 BC. In Western history, the era of classical antiquity was immediately followed by the Early Middle Ages and the Byzantine period.

Three centuries after the decline of Mycenaean Greece during the Bronze Age collapse, Greek urban poleis began to form in the 8th century BC, ushering in the Archaic period and the colonization of the Mediterranean Basin. This was followed by the age of Classical Greece, from the Greco-Persian Wars to the death of Alexander the Great in 323 BC, and which included the Golden Age of Athens and the Peloponnesian War between Athens and Sparta. The unification of Greece by Macedon under Philip II and subsequent conquest of the Achaemenid Empire by Alexander the Great spread Hellenistic civilization across the Middle East. The Hellenistic period is considered to have ended in 30 BC, when the last Hellenistic kingdom, Ptolemaic Egypt, was annexed by the Roman Republic.

Ancient Greek philosophy arose in the 6th century BC. Philosophy was used to make sense of the world using reason. It dealt with a wide variety of subjects, including astronomy, epistemology, mathematics, political philosophy, ethics, metaphysics, ontology, logic, biology, rhetoric and aesthetics. Greek philosophy continued throughout the Hellenistic period and later evolved into Roman philosophy.

Greek philosophy has influenced much of Western culture since its inception, and can be found in many aspects of public education. Alfred North Whitehead once claimed: "The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato". Clear, unbroken lines of influence lead from ancient Greek and Hellenistic philosophers to Roman philosophy, early Islamic philosophy, medieval scholasticism, the European Renaissance and the Age of Enlightenment.

Western culture, also known as Western civilization, European civilization, Occidental culture, Western society, or simply the West, is the internally diverse culture of the Western world. The term "Western" encompasses the social norms, ethical values, traditional customs, belief systems, political systems, artifacts and technologies primarily rooted in European and Mediterranean histories. A broad concept, "Western culture" does not relate to a region with fixed members or geographical confines. It generally refers to the classical era cultures of Ancient Greece, Ancient Rome, and their Christian successors that expanded across the Mediterranean basin and Europe, and later circulated around the world predominantly through colonization and globalization.

Historically, scholars have closely associated the idea of Western culture with the classical era of Greco-Roman antiquity. However, scholars also acknowledge that other cultures, like Ancient Egypt, the Phoenician city-states, and several Near-Eastern cultures stimulated and influenced it. The Hellenistic period also promoted syncretism, blending Greek, Roman, and Jewish cultures. Major advances in literature, engineering, and science shaped the Hellenistic Jewish culture from which the earliest Christians and the Greek New Testament emerged. The eventual Christianization of Europe in late-antiquity would ensure that Christianity, particularly the Catholic Church, remained a dominant force in Western culture for many centuries to follow.

Ancient Greek mathematics refers to the history of mathematical ideas and texts in Ancient Greece during classical and late antiquity, mostly from the 5th century BC to the 6th century AD. Greek mathematicians lived in cities spread around the shores of the ancient Mediterranean, from Anatolia to Italy and North Africa, but were united by Greek culture and the Greek language. The development of mathematics as a theoretical discipline and the use of deductive reasoning in proofs is an important difference between Greek mathematics and those of preceding civilizations.

The early history of Greek mathematics is obscure, and traditional narratives of mathematical theorems found before the fifth century BC are regarded as later inventions. It is now generally accepted that treatises of deductive mathematics written in Greek began circulating around the mid-fifth century BC, but the earliest complete work on the subject is Euclid's Elements, written during the Hellenistic period. The works of renown mathematicians Archimedes and Apollonius, as well as of the astronomer Hipparchus, also belong to this period. In the Imperial Roman era, Ptolemy used trigonometry to determine the positions of stars in the sky, while Nicomachus and other ancient philosophers revived ancient number theory and harmonics. During late antiquity, Pappus of Alexandria wrote his Collection, summarizing the work of his predecessors, while Diophantus' Arithmetica dealt with the solution of arithmetic problems by way of pre-modern algebra. Later authors such as Theon of Alexandria, his daughter Hypatia, and Eutocius of Ascalon wrote commentaries on the authors making up the ancient Greek mathematical corpus.

The League of Corinth, also referred to as the Hellenic League (Greek: κοινὸν τῶν Ἑλλήνων, koinòn tõn Hellḗnōn; or simply οἱ Ἕλληνες, the Héllēnes), was a federation of Greek states created by Philip II in 338–337 BC. The League was created in order to unify Greek military forces under Macedonian leadership (hegemony) in their combined conquest of the Persian Achaemenid Empire.

King Philip was initially urged by Isocrates in 346 BC to unify Greece against the Persians. After the Battle of Chaeronea, the League of Corinth was formed and controlled by Philip. Alexander utilized his father's league when planning his pan-Hellenic invasion of Asia to expand Macedon and take revenge on the Persian Empire. During the Hellenistic period, some Antigonid rulers of Macedon shortly revived the league, also known as the 'Hellenic Alliance'.

The earliest known world maps date to classical antiquity, the oldest examples of the 6th to 5th centuries BCE still based on the flat Earth paradigm. World maps assuming a spherical Earth first appear in the Hellenistic period. The developments of Greek geography during this time, notably by Eratosthenes and Posidonius culminated in the Roman era, with Ptolemy's world map (2nd century CE), which would remain authoritative throughout the Middle Ages. Since Ptolemy, knowledge of the approximate size of the Earth allowed cartographers to estimate the extent of their geographical knowledge, and to indicate parts of the planet known to exist but not yet explored as terra incognita.

With the Age of Discovery, during the 15th to 18th centuries, world maps became increasingly accurate; exploration of Antarctica, Australia, and the interior of Africa by western mapmakers was left to the 19th and early 20th century.

Ancient Greek (Ἑλληνική, Hellēnikḗ [hellɛːnikɛ́ː]) includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (c. 1400–1200 BC), Dark Ages (c. 1200–800 BC), the Archaic or Homeric period (c. 800–500 BC), and the Classical period (c. 500–300 BC).

Ancient Greek was the language of Homer and of fifth-century Athenian historians, playwrights, and philosophers. It has contributed many words to English vocabulary and has been a standard subject of study in educational institutions of the Western world since the Renaissance. This article primarily contains information about the Epic and Classical periods of the language, which are the best-attested periods and considered most typical of Ancient Greek.