Renaissance in the context of Heliocentric

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.

A city-state is an independent sovereign city which serves as the center of political, economic, and cultural life over its contiguous territory, as opposed to a regular state or country comprising a capital city and other cities and/or a countryside. City-states have existed in many parts of the world throughout history, including cities such as Rome, Carthage, Athens and Sparta and the Italian city-states during the Middle Ages and Renaissance, such as Florence, Venice, Genoa and Milan.

With the rise of nation states worldwide, there remains some disagreement on the number of modern city-states that still exist; Singapore, Monaco and Vatican City are the candidates most commonly discussed. Out of these, Singapore is the largest and most populous city-state in the world, with full sovereignty, international borders, its own currency, a robust military, and substantial international influence in its own right. The Economist refers to it as the "world's only fully functioning city-state".

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.

Early Islamic philosophy or classical Islamic philosophy is a period of intense philosophical development beginning in the 2nd century AH of the Islamic calendar (early 9th century CE) and lasting until the 6th century AH (late 12th century CE). The period is known as the Islamic Golden Age, and the achievements of this period had a crucial influence in the development of modern philosophy and science. For Renaissance Europe, "Muslim maritime, agricultural, and technological innovations, as well as much East Asian technology via the Muslim world, made their way to western Europe in one of the largest technology transfers in world history." This period starts with al-Kindi in the 9th century and ends with Averroes (Ibn Rushd) at the end of 12th century. The death of Averroes effectively marks the end of a particular discipline of Islamic philosophy usually called the Peripatetic Arabic School, and philosophical activity declined significantly in Western Islamic countries, namely in Islamic Spain and North Africa, though it persisted for much longer in the Eastern countries, in particular Persia and India where several schools of philosophy continued to flourish: Avicennism, Illuminationist philosophy, Mystical philosophy, and Transcendent theosophy.

Intellectual innovations, achievements, and advancements of this period included, within jurisprudence, the development of ijtihad, a method or methodological approach to legal reasoning, interpretation, and argument based on independent inquiry and analogical deduction; within science and the philosophy of science, the development of empirical research methods emphasizing controlled experimentation, observational evidence, and reproducibility, as well as early formulations of empiricist epistemologies; commentaries and developments in Aristotelian logic, as well as innovations in non-Aristotelian temporal modal logic and inductive logic; and developments in research practice and methodology, including, within medicine, the first documented peer review process and within jurisprudence and theology, a strict science of citation, the isnad or "backing".

In the history of Europe, the Middle Ages or medieval period lasted approximately from the 5th to the late 15th centuries, comparable with the post-classical period of global history. It began with the fall of the Western Roman Empire and transitioned into the Renaissance and the Age of Discovery. The Middle Ages is the middle period of the three traditional divisions of Western history: classical antiquity, the medieval period, and the modern period. The medieval period is itself subdivided into the Early, High, and Late Middle Ages.

Population decline, counterurbanisation, the collapse of centralised authority, invasions, and mass migrations of tribes, which had begun in Late antiquity (c. ~3rd–8th centuries) and into the Early Middle Ages (c. 5th–10th centuries). The large-scale movements of the Migration Period, including various Germanic peoples, formed new kingdoms in what remained of the Western Roman Empire. In the 7th century, North Africa and the Middle East—once part of the Byzantine Empire—came under the rule of the Umayyad Caliphate, an Islamic empire, after conquest by Muhammad's successors. Although there were substantial changes in society and political structures, the break with classical antiquity was incomplete. The still-sizeable Byzantine Empire, Rome's direct continuation, survived in the Eastern Mediterranean and remained a major power. The empire's law code, the Corpus Juris Civilis or "Code of Justinian", was rediscovered in Northern Italy in the 11th century. In the West, most kingdoms incorporated the few extant Roman institutions. Monasteries were founded as campaigns to Christianise the remaining pagans across Europe continued. The Franks, under the Carolingian dynasty, briefly established the Carolingian Empire during the later 8th and early 9th centuries. It covered much of Western Europe but later succumbed to the pressures of internal civil wars combined with external invasions: Vikings from the north, Magyars from the east, and Saracens from the south.

Italy, officially the Italian Republic, is a country in Southern and Western Europe. It consists of a peninsula that extends into the Mediterranean Sea, with the Alps on its northern land border, as well as nearly 800 islands, notably Sicily and Sardinia. Italy shares land borders with France to the west; Switzerland and Austria to the north; Slovenia to the east; and the two enclaves of Vatican City and San Marino. It is the tenth-largest country in Europe by area, covering 301,340 km (116,350 sq mi), and the third-most populous member state of the European Union, with nearly 59 million inhabitants. Italy's capital and largest city is Rome; other major cities include Milan, Naples, Turin, Palermo, Bologna, Florence, Genoa, and Venice.

The history of Italy goes back to numerous Italic peoples – notably including the ancient Romans, who conquered the Mediterranean world during the Roman Republic and ruled it for centuries during the Roman Empire. With the spread of Christianity, Rome became the seat of the Catholic Church and the Papacy. Barbarian invasions and other factors led to the decline and fall of the Western Roman Empire between late antiquity and the Early Middle Ages. By the 11th century, Italian city-states and maritime republics expanded, bringing renewed prosperity through commerce and laying the groundwork for modern capitalism. The Italian Renaissance flourished during the 15th and 16th centuries and spread to the rest of Europe. Italian explorers discovered new routes to the Far East and the New World, contributing significantly to the Age of Discovery.

Classical republicanism, also known as civic republicanism or civic humanism, is a form of republicanism developed in the Renaissance inspired by the governmental forms and writings of classical antiquity, especially such classical writers as Aristotle, Polybius, and Cicero. Classical republicanism is built around concepts such as liberty as non-domination, self-government, rule of law, property-based personality, anti-corruption, abolition of monarchy, civics, civil society, common good, civic virtue, civic participation, popular sovereignty, patriotism and mixed government.

Vitruvius (/vɪˈtruːviəs/ vi-TROO-vee-əs; Latin: [wɪˈtruːwi.ʊs]; c. 80–70 BC – after c. 15 BC) was a Roman architect and engineer during the 1st century BC, known for his multi-volume work titled De architectura. As the only treatise on architecture to survive from antiquity, it has been regarded since the Renaissance as the first book on architectural theory, as well as a major source on the canon of classical architecture. It is not clear to what extent his contemporaries regarded his book as original or important.

He states that all buildings should have three attributes: firmitas, utilitas, and venustas ("strength", "utility", and "beauty"), principles reflected in much Ancient Roman architecture. His discussion of perfect proportion in architecture and the human body led to the famous Renaissance drawing of the Vitruvian Man by Leonardo da Vinci.

Cultural heritage is the tangible and intangible legacy of a group or society that is inherited from past generations. Not all legacies of past generations are "heritage"; rather, heritage is a product of selection by society.

Cultural heritage includes tangible culture (such as buildings, monuments, landscapes, archive materials, books, works of art, and artifacts), intangible culture (such as folklore, traditions, language, and knowledge), and natural heritage (including culturally significant landscapes, and biodiversity). The term is often used in connection with issues relating to the protection of Indigenous intellectual property.

Medieval literature is a broad subject, encompassing essentially all written works available in Europe and beyond during the Middle Ages (that is, the one thousand years from the fall of the Western Roman Empire ca. AD 500 to the beginning of the Renaissance in the 14th, 15th or 16th century, depending on country). The literature of this time was composed of religious writings as well as secular works. Like modern literature, it is a broad field of study, from the utterly sacred to the exuberantly profane, touching all points in between. Works of literature are often grouped by place of origin, language, and genre.

Euclid (/ˈjuːklɪd/; Ancient Greek: Εὐκλείδης; fl. 300 BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics.

Very little is known of Euclid's life, and most information comes from the scholars Proclus and Pappus of Alexandria many centuries later. Medieval Islamic mathematicians invented a fanciful biography, and medieval Byzantine and early Renaissance scholars mistook him for the earlier philosopher Euclid of Megara. It is now generally accepted that he spent his career in Alexandria and lived around 300 BC, after Plato's students and before Archimedes. There is some speculation that Euclid studied at the Platonic Academy and later taught at the Musaeum; he is regarded as bridging the earlier Platonic tradition in Athens with the later tradition of Alexandria.

Apollonius of Perga (Ancient Greek: Ἀπολλώνιος ὁ Περγαῖος Apollṓnios ho Pergaîos; c. 240 BC – c. 190 BC) was an ancient Greek geometer and astronomer known for his work on conic sections. Beginning from the earlier contributions of Euclid and Archimedes on the topic, he brought them to the state prior to the invention of analytic geometry. His definitions of the terms ellipse, parabola, and hyperbola are the ones in use today. With his predecessors Euclid and Archimedes, Apollonius is generally considered among the greatest mathematicians of antiquity.

Aside from geometry, Apollonius worked on numerous other topics, including astronomy. Most of this work has not survived, where exceptions are typically fragments referenced by other authors like Pappus of Alexandria. His hypothesis of eccentric orbits to explain the apparently aberrant motion of the planets, commonly believed until the Middle Ages, was superseded during the Renaissance. The Apollonius crater on the Moon is named in his honor.

The Republic of Florence (Latin: Res publica Florentina; Old Italian: Republica di Fiorenza), known officially as the Florentine Republic, was a medieval and early modern state that was centered on the Italian city of Florence in Tuscany, Italy. The republic originated in 1115, when the Florentine people rebelled against the Margraviate of Tuscany upon the death of Matilda of Tuscany, who controlled vast territories that included Florence. The Florentines formed a commune in Rabodo's (Matilda’s successor) successors' place. The republic was ruled by a council known as the Signoria of Florence. The signoria was chosen by the gonfaloniere (titular ruler of the city), who was elected every two months by Florentine guild members.

During the Republic's history, Florence was an important cultural, economic, political and artistic force in Europe. Its coin, the florin, was the dominant trade coin of Western Europe for large scale transactions and became widely imitated throughout the continent. During the Republican period, Florence was also the birthplace of the Renaissance, which is considered a fervent period of European cultural, artistic, political and economic "rebirth".

The Duchy of Milan (Italian: Ducato di Milano; Lombard: Ducaa de Milan) was a state in Northern Italy, created in 1395 by Gian Galeazzo Visconti, then the lord of Milan, and a member of the important Visconti family, which had been ruling the city since 1277. At that time, it included twenty-six towns and the wide rural area of the middle Padan Plain east of the hills of Montferrat. During much of its existence, it was wedged between Savoy to the west, Republic of Venice to the east, the Swiss Confederacy to the north, and separated from the Mediterranean by the Republic of Genoa to the south. The duchy was at its largest at the beginning of the 15th century, at which time it included almost all of what is now Lombardy and parts of what are now Piedmont, Veneto, Tuscany, and Emilia-Romagna.

Under the House of Sforza, Milan experienced a period of great prosperity with the introduction of the silk industry, becoming one of the wealthiest states during the Renaissance. From the late 15th century, the Duchy of Milan was contested between the forces of the Habsburg Monarchy and the Kingdom of France. It was ruled by Habsburg Spain from 1556 and it passed to Habsburg Austria in 1707 during the War of the Spanish Succession. The duchy remained an Austrian possession until 1796 when a French army under Napoleon Bonaparte conquered it, and it ceased to exist a year later as a result of the Treaty of Campo Formio, when Austria ceded it to the new Cisalpine Republic.

A world map is a map of most or all of the surface of Earth. World maps, because of their scale, must deal with the problem of projection. Maps rendered in two dimensions by necessity distort the display of the three-dimensional surface of the Earth. While this is true of any map, these distortions reach extremes in a world map. Many techniques have been developed to present world maps that address diverse technical and aesthetic goals.

Charting a world map requires global knowledge of the Earth, its oceans, and its continents. From prehistory through the Middle Ages, creating an accurate world map would have been impossible because less than half of Earth's coastlines and only a small fraction of its continental interiors were known to any culture. With exploration that began during the European Renaissance, knowledge of the Earth's surface accumulated rapidly, such that most of the world's coastlines had been mapped, at least roughly, by the mid-1700s and the continental interiors by the twentieth century.

Milan (/mɪˈlæn/ mil-AN, US also /mɪˈlɑːn/ mil-AHN, Milanese: [miˈlãː] ; Italian: Milano [miˈlaːno] ) is the regional capital of Lombardy, in northern Italy, and the second-most populous city in Italy, with a population of 1.36 million in 2025. The Metropolitan City of Milan is the largest city in Italy by urban area. Its wider metropolitan area is the largest in Italy, and the fourth-largest in the European Union, with an estimated population of 6.1 million.

Founded around 590 BC by a Celtic tribe, Milan was conquered by the Romans in 222 BC, who Latinized the name of the city into Mediolanum and made it the capital of the Western Roman Empire. In the Late Medieval period, the wealthy Duchy of Milan was one of the greatest forces behind the Renaissance. As a major center of the Italian Enlightenment during the Early modern period, Milan's cultural and political struggle against Austrian domination was crucial in the reunification of the Kingdom of Italy. From the 19th century onwards, Milan led the industrial and financial development of Italy.

Humanities are important academic disciplines that study aspects of human society and culture, including certain fundamental questions asked by humans. During the Renaissance, the term "humanities" referred to the study of classical literature and language, as opposed to the study of religion, or "divinity". The study of the humanities was a key part of the secular curriculum in universities at the time. Today, the humanities are more frequently defined as any fields of study outside of natural sciences, social sciences, formal sciences (like mathematics), and applied sciences (or professional training). They use methods that are primarily critical, speculative, or interpretative and have a significant historical element—as distinguished from the mainly empirical approaches of science.

The humanities include the academic study of philosophy, religion, history (sometimes considered part of the social sciences instead), language arts (literature, writing, oratory, rhetoric, poetry, etc.), the performing arts (theater, music, dance, etc.), and the visual arts (painting, sculpture, photography, filmmaking, etc.).