189-469: Archimedes of Syracuse ( / ˌ ɑːr k ɪ ˈ m iː d iː z / AR -kim- EE -deez ; c. 287 – c. 212 BC ) was an Ancient Greek mathematician , physicist , engineer , astronomer , and inventor from the ancient city of Syracuse in Sicily . Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity . Regarded as
378-546: A 'strongman' was often the best solution. Athens fell under a tyranny in the second half of the 6th century BC. When this tyranny was ended, the Athenians founded the world's first democracy as a radical solution to prevent the aristocracy regaining power. A citizens' assembly (the Ecclesia ), for the discussion of city policy, had existed since the reforms of Draco in 621 BC; all citizens were permitted to attend after
567-469: A Circle . The actual value is approximately 1.7320508, making this a very accurate estimate. He introduced this result without offering any explanation of how he had obtained it. This aspect of the work of Archimedes caused John Wallis to remark that he was: "as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results." It
756-439: A ball into a container after each mile traveled. As legend has it, Archimedes arranged mirrors as a parabolic reflector to burn ships attacking Syracuse using focused sunlight. While there is no extant contemporary evidence of this feat and modern scholars believe it did not happen, Archimedes may have written a work on mirrors entitled Catoptrica , and Lucian and Galen , writing in the second century AD, mentioned that during
945-417: A century into the past, discussing 6th century BC historical figures such as Darius I of Persia , Cambyses II and Psamtik III , and alluding to some 8th century BC persons such as Candaules . The accuracy of Herodotus' works is debated. Herodotus was succeeded by authors such as Thucydides , Xenophon , Demosthenes , Plato and Aristotle . Most were either Athenian or pro-Athenian, which
1134-496: A circle. After four such steps, when the polygons had 96 sides each, he was able to determine that the value of π lay between 3 1 / 7 (approx. 3.1429) and 3 10 / 71 (approx. 3.1408), consistent with its actual value of approximately 3.1416. He also proved that the area of a circle was equal to π multiplied by the square of the radius of the circle ( π r 2 {\displaystyle \pi r^{2}} ). In On
1323-500: A coalition of 31 Greek city states, including Athens and Sparta, determined to resist the Persian invaders. At the same time, Greek Sicily was invaded by a Carthaginian force. In 480 BC, the first major battle of the invasion was fought at Thermopylae , where a small rearguard of Greeks, led by three hundred Spartans, held a crucial pass guarding the heart of Greece for several days; at the same time Gelon , tyrant of Syracuse, defeated
1512-609: A council of elders (the Gerousia ) and magistrates specifically appointed to watch over the kings (the Ephors ). Only free, land-owning, native born men could be citizens entitled to the full protection of the law in a city-state. In most city-states, unlike the situation in Rome , social prominence did not allow special rights. Sometimes families controlled public religious functions, but this ordinarily did not give any extra power in
1701-514: A cultural sense and the Greek language did not become extinct on the island, facilitating its re-hellenisation much later under the Byzantines. The once prosperous and contented island went into sharp decline when Verres became governor of Sicily (73 to 71 BC). In 70 BC noted figure Cicero condemned the misgovernment of Verres in his oration In Verrem . Various groups used the island as
1890-528: A decisive victory, and in 447 lost Boeotia again. Athens and Sparta signed the Thirty Years' Peace in the winter of 446/5, ending the conflict. Despite the treaty, Athenian relations with Sparta declined again in the 430s, and in 431 BC the Peloponnesian War began. The first phase of the war saw a series of fruitless annual invasions of Attica by Sparta, while Athens successfully fought
2079-628: A geographical perspective, also forming a part of Sicily is the Maltese Archipelago, the islands home to the republic of Malta . The autonomous region also includes several neighbouring islands: the Aegadian Islands , the Aeolian Islands, Pantelleria and Lampedusa . The mountains of Sicily form a significant part of the island's diverse landscape, with Mount Etna , one of the world's most active volcanoes, being
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#17327661642282268-436: A group of city-states allied themselves to defend Greece, the vast majority of poleis remained neutral, and after the Persian defeat, the allies quickly returned to infighting. Thus, the major peculiarities of the ancient Greek political system were its fragmented nature (and that this does not particularly seem to have tribal origin), and the particular focus on urban centers within otherwise tiny states. The peculiarities of
2457-414: A job but to become an effective citizen. Girls also learned to read, write and do simple arithmetic so they could manage the household. They almost never received education after childhood. Sicily Sicily ( Italian : Sicilia , Italian: [siˈtʃiːlja] ; Sicilian : Sicilia , Sicilian: [sɪˈ(t)ʃiːlja] ; officially Regione Siciliana ) is an island in
2646-408: A line which rotates with constant angular velocity . Equivalently, in modern polar coordinates ( r , θ ), it can be described by the equation r = a + b θ {\displaystyle \,r=a+b\theta } with real numbers a and b . This is an early example of a mechanical curve (a curve traced by a moving point ) considered by a Greek mathematician. This
2835-655: A loose collection of culturally and linguistically related city-states and other territories. Prior to the Roman period , most of these regions were officially unified 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
3024-431: A mischaracterization. Archimedes was able to use indivisibles (a precursor to infinitesimals ) in a way that is similar to modern integral calculus . Through proof by contradiction ( reductio ad absurdum ), he could give answers to problems to an arbitrary degree of accuracy, while specifying the limits within which the answer lay. This technique is known as the method of exhaustion , and he employed it to approximate
3213-460: A number that was greater than the grains of sand needed to fill the universe. In doing so, he challenged the notion that the number of grains of sand was too large to be counted. He wrote: There are some, King Gelo , who think that the number of the sand is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or uninhabited. To solve
3402-739: A person, and focuses on the war machines that he is said to have built in order to defend the city from the Romans. Polybius remarks how, during the Second Punic War , Syracuse switched allegiances from Rome to Carthage , resulting in a military campaign under the command of Marcus Claudius Marcellus and Appius Claudius Pulcher , who besieged the city from 213 to 212 BC. He notes that the Romans underestimated Syracuse's defenses, and mentions several machines Archimedes designed, including improved catapults , crane-like machines that could be swung around in an arc, and other stone-throwers . Although
3591-614: A power base at different times: slave insurgents occupied it during the First (135−132 BC) and Second (104−100 BC) Servile Wars . Sextus Pompey had his headquarters there during the Sicilian revolt of 44 to 36 BC. Christianity first appeared in Sicily during the years following AD 200; between this time and AD 313, when Emperor Constantine the Great lifted the prohibition on Christianity,
3780-619: A reference to the mathematical drawing that he was supposedly studying when disturbed by the Roman soldier. There is no reliable evidence that Archimedes uttered these words and they do not appear in Plutarch's account. A similar quotation is found in the work of Valerius Maximus (fl. 30 AD), who wrote in Memorable Doings and Sayings , " ... sed protecto manibus puluere 'noli' inquit, 'obsecro, istum disturbare' " ("... but protecting
3969-760: A result of Epaminondas ' liberation of Messenia from Spartan rule, the helot system there came to an end and the helots won their freedom. However, it did continue to persist in Laconia until the 2nd century BC. For most of Greek history, education was private, except in Sparta. During the Hellenistic period, some city-states established public schools . Only wealthy families could afford a teacher. Boys learned how to read, write and quote literature. They also learned to sing and play one musical instrument and were trained as athletes for military service. They studied not for
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#17327661642284158-532: A rich and unique culture in arts , music , literature , cuisine , and architecture . Its most prominent landmark is Mount Etna , the tallest active volcano in Europe, and one of the most active in the world, currently 3,357 m (11,014 ft) high. The island has a typical Mediterranean climate . It is separated from Calabria by the Strait of Messina . It is one of the five Italian autonomous regions and
4347-833: A significant number of Sicilians had become martyrs , including Agatha , Christina , Lucy , and Euplius . Christianity grew rapidly in Sicily over the next two centuries. Sicily remained a Roman province for around 700 years. The Western Roman Empire began falling apart after the invasion of Vandals , Alans, and Sueves across the Rhine on the last day of 406. Eventually the Vandals, after roaming about western and southern Hispania (present-day Iberia ) for 20 years, moved to North Africa in 429 and occupied Carthage in 439. The Franks moved south from present-day Belgium. The Visigoths moved west and eventually settled in Aquitaine in 418;
4536-407: A solution that applied the hydrostatics principle known as Archimedes' principle , found in his treatise On Floating Bodies : a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces. Using this principle, it would have been possible to compare the density of the crown to that of pure gold by balancing it on a scale with a pure gold reference sample of
4725-523: A special type of slaves called helots . Helots were Messenians enslaved en masse during the Messenian Wars by the state and assigned to families where they were forced to stay. Helots raised food and did household chores so that women could concentrate on raising strong children while men could devote their time to training as hoplites . Their masters treated them harshly, and helots revolted against their masters several times. In 370/69 BC, as
4914-403: A temple dedicated to the goddess Aphrodite among its facilities. The account also mentions that, in order to remove any potential water leaking through the hull, a device with a revolving screw-shaped blade inside a cylinder was designed by Archimedes. Archimedes' screw was turned by hand, and could also be used to transfer water from a low-lying body of water into irrigation canals. The screw
5103-405: A volcanic complex. The three volcanoes of Vulcano , Stromboli and Lipari are also active, although the last is usually dormant. Off the southern coast of Sicily, the underwater volcano of Ferdinandea , which is part of the larger Empedocles volcano , last erupted in 1831. It is located between the coast of Agrigento and the island of Pantelleria (which itself is a dormant volcano). From
5292-669: A war with the Roman Republic in the late 3rd century. Although the First Macedonian War was inconclusive, the Romans, in typical fashion, continued to fight Macedon until it was completely absorbed into the Roman Republic (by 149 BC). In the east, the unwieldy Seleucid Empire gradually disintegrated, although a rump survived until 64 BC, whilst the Ptolemaic Kingdom continued in Egypt until 30 BC when it too
5481-632: A year, the Thirty had been overthrown. The first half of the fourth century saw the major Greek states attempt to dominate the mainland; none were successful, and their resulting weakness led to a power vacuum which would eventually be filled by Macedon under Philip II and then Alexander the Great. In the immediate aftermath of the Peloponnesian war, Sparta attempted to extend their own power, leading Argos, Athens, Corinth, and Thebes to join against them. Aiming to prevent any single Greek state gaining
5670-605: Is 25,711 km (9,927 sq mi), while the Autonomous Region of Sicily (which includes the smaller surrounding islands of Lipari , Egadi , Ustica , and Pantelleria ) has an area of 27,708 km (10,698 sq mi). The terrain of inland Sicily is mostly hilly and is intensively cultivated wherever possible. Along the northern coast, the mountain ranges of Madonie , 2,000 m (6,600 ft), Nebrodi , 1,800 m (5,900 ft), and Peloritani , 1,300 m (4,300 ft), are an extension of
5859-467: Is 4 π r for the sphere, and 6 π r for the cylinder (including its two bases), where r is the radius of the sphere and cylinder. This work of 28 propositions is also addressed to Dositheus. The treatise defines what is now called the Archimedean spiral . It is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along
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6048-525: Is a work in 32 propositions addressed to Dositheus. In this treatise Archimedes calculates the areas and volumes of sections of cones , spheres, and paraboloids. Ancient Greece 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
6237-510: Is clear that he maintained collegial relations with scholars based there, including his friend Conon of Samos and the head librarian Eratosthenes of Cyrene . The standard versions of Archimedes' life were written long after his death by Greek and Roman historians. The earliest reference to Archimedes occurs in The Histories by Polybius ( c. 200–118 BC), written about 70 years after his death. It sheds little light on Archimedes as
6426-619: Is due to Sicily being geographically on the northern edge of the African Plate . Mount Etna is the largest active volcano in Europe and casts black ash over the island with its recurrent eruptions. It stands 3,403 metres (11,165 ft) high as of September 2024. It is the highest mountain in Italy south of the Alps . Etna covers an area of 1,190 km (459 sq mi) with a basal circumference of 140 km (87 mi). This makes it
6615-611: Is generally considered part of Southern Italy . The earliest archaeological record of human activity on the island is from around 14,000 BC. By around 750 BC, Sicily had three Phoenician and a dozen Greek colonies along its coasts, becoming one of the centers of Magna Graecia . The Sicilian Wars of 580–265 BC were fought between the Carthaginians and Greeks, and the Punic Wars of 264–146 BC were fought between Rome and Carthage. The Roman province of Sicilia ended with
6804-558: Is generally considered the cradle of Western civilization , the seminal culture from which the modern West derives many of its founding archetypes and ideas in politics, philosophy, science, and art. Classical antiquity in the Mediterranean region is commonly considered to have begun in the 8th century BC (around the time of the earliest recorded poetry of Homer) and ended in the 6th century AD. Classical antiquity in Greece
6993-458: Is mountainous, and as a result, ancient Greece consisted of many smaller regions, each with its own dialect, cultural peculiarities, and identity. Regionalism and regional conflicts were prominent features of ancient Greece. Cities tended to be located in valleys between mountains, or on coastal plains, and dominated a certain area around them. In the south lay the Peloponnese , consisting of
7182-502: Is possible that he used an iterative procedure to calculate these values. In Quadrature of the Parabola , Archimedes proved that the area enclosed by a parabola and a straight line is 4 / 3 times the area of a corresponding inscribed triangle as shown in the figure at right. He expressed the solution to the problem as an infinite geometric series with the common ratio 1 / 4 : If
7371-530: Is still in use today for pumping liquids and granulated solids such as coal and grain. Described by Vitruvius , Archimedes' device may have been an improvement on a screw pump that was used to irrigate the Hanging Gardens of Babylon . The world's first seagoing steamship with a screw propeller was the SS Archimedes , which was launched in 1839 and named in honor of Archimedes and his work on
7560-816: Is the largest protected natural area of Sicily; it contains the largest forest in Sicily, the Caronia . The Hundred Horse Chestnut ( Castagno dei Cento Cavalli ), in Sant'Alfio , on the eastern slopes of Mount Etna, is the largest and oldest known chestnut tree in the world at 2,000–4,000 years old. Sicily has a wide variety of fauna. Species include the European wildcat , red fox , least weasel , pine marten , fallow deer , wild boar , crested porcupine , European hedgehog , common toad , Vipera aspis , golden eagle , peregrine falcon , Eurasian hoopoe and black-winged stilt . Roe deer were driven to extinction on
7749-479: Is unclear exactly how this change occurred. For instance, in Athens, the kingship had been reduced to a hereditary, lifelong chief magistracy ( archon ) by c. 1050 BC; by 753 BC this had become a decennial, elected archonship; and finally by 683 BC an annually elected archonship. Through each stage, more power would have been transferred to the aristocracy as a whole, and away from a single individual. Inevitably,
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7938-440: Is unique in world history as the first period attested directly in comprehensive, narrative historiography , while earlier ancient history or protohistory is known from much more fragmentary documents such as annals, king lists, and pragmatic epigraphy . Herodotus is widely known as the "father of history": his Histories are eponymous of the entire field . Written between the 450s and 420s BC, Herodotus' work reaches about
8127-671: Is usually counted from the Roman victory over the Corinthians at the Battle of Corinth in 146 BC to the establishment of Byzantium by Constantine as the capital of the Roman Empire in 330 AD. Finally, Late Antiquity refers to the period of Christianization during the later 4th to early 6th centuries AD, consummated by the closure of the Academy of Athens by Justinian I in 529. The historical period of ancient Greece
8316-419: Is why far more is known about the history and politics of Athens than of many other cities. Their scope is further limited by a focus on political, military and diplomatic history, ignoring economic and social history. The archaic period, lasting from approximately 800 to 500 BC, saw the culmination of political and social developments which had begun in the Greek dark age, with the polis (city-state) becoming
8505-655: 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 . Classical Greek culture , especially philosophy, had a powerful influence on ancient Rome , which carried a version of it throughout the Mediterranean and much of Europe. For this reason, Classical Greece
8694-665: The Alcantara flows through the province of Messina and enters the sea at Giardini Naxos , and the Simeto , which flows into the Ionian Sea south of Catania . Other important rivers on the island are the Belice and Platani in the southwest. Sicily has for the most part a typical Mediterranean climate ( Köppen climate classification : Csa ) with mild and wet winters and hot, dry summers with changeable intermediate seasons. On
8883-710: The Archaic period , the Greek population grew beyond the capacity of the limited arable land of Greece proper, resulting in the large-scale establishment of colonies elsewhere: according to one estimate, the population of the widening area of Greek settlement increased roughly tenfold from 800 BC to 400 BC, from 800,000 to as many as 7 + 1 ⁄ 2 -10 million. This was not simply for trade, but also to found settlements. These Greek colonies were not, as Roman colonies were, dependent on their mother-city, but were independent city-states in their own right. Greeks settled outside of Greece in two distinct ways. The first
9072-647: The Battle of Aegospotami , and began to blockade Athens' harbour; driven by hunger, Athens sued for peace, agreeing to surrender their fleet and join the Spartan-led Peloponnesian League. Following the Athenian surrender, Sparta installed an oligarchic regime, the Thirty Tyrants , in Athens, one of a number of Spartan-backed oligarchies which rose to power after the Peloponnesian war. Spartan predominance did not last: after only
9261-745: The Boeotian League and finally to the League of Corinth led by Macedon . This period was shaped by the Greco-Persian Wars , the Peloponnesian War , and the Rise of Macedon . Following the Classical period was the Hellenistic period (323–146 BC), during which Greek culture and power expanded into the Near and Middle East from the death of Alexander until the Roman conquest. Roman Greece
9450-655: 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 . The unification of Greece by Macedon under Philip II and subsequent conquest of
9639-564: The Byzantine Greek architect Isidore of Miletus ( c. 530 AD ), while commentaries on the works of Archimedes written by Eutocius in the same century helped bring his work to a wider audience. Archimedes' work was translated into Arabic by Thābit ibn Qurra (836–901 AD), and into Latin via Arabic by Gerard of Cremona (c. 1114–1187). Direct Greek to Latin translations were later done by William of Moerbeke (c. 1215–1286) and Iacobus Cremonensis (c. 1400–1453). During
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#17327661642289828-576: The Delian League gradually transformed from a defensive alliance of Greek states into an Athenian empire, as Athens' growing naval power intimidated the other league states. Athens ended its campaigns against Persia in 450, after a disastrous defeat in Egypt in 454, and the death of Cimon in action against the Persians on Cyprus in 450. As the Athenian fight against the Persian empire waned, conflict grew between Athens and Sparta. Suspicious of
10017-682: The Elymians and the Sicels . The most prominent and by far the earliest of these were the Sicani , who ( Thucydides writes) arrived from the Iberian Peninsula (perhaps Catalonia ). Some modern scholars, however, suggest classifying the Sicani as possibly an Illyrian tribe. Important historical evidence has been discovered in the form of cave drawings by the Sicani, dated from the end of
10206-531: The Emirate of Sicily began to fragment as intra-dynastic quarreling fractured the Muslim government. In 1038, seventy years after losing their last cities in Sicily, the Byzantines under the Greek general George Maniakes invaded the island together with their Varangian and Norman mercenaries. Maniakes was killed in a Byzantine civil war in 1043 before completing a reconquest and the Byzantines withdrew. Later
10395-820: The First Punic War (264 to 241 BC) and won, making Sicily–with the exception of Syracuse–the first Roman province outside of the Italian Peninsula by 242 BC. In the Second Punic War (218 to 201 BC), the Carthaginians attempted to recapture Sicily. Some of the Greek cities on the island who were loyal to Rome switched sides to help the Carthaginians, prompting a Roman military response. Archimedes , who lived in Syracuse, helped defend his city from Roman invasion; Roman troops killed him after they captured Syracuse in 213 BC. The Carthaginian attempt failed, and Rome became more unrelenting in its annihilation of
10584-466: The Kingdom of England . The court of Roger II became the most luminous centre of culture in the Mediterranean, both from Europe and the Middle East, like the multi-ethnic Caliphate of Córdoba , then only just eclipsed. This attracted scholars, scientists, poets, artists, and artisans of all kinds. Laws were issued in the language of the community to whom they were addressed in Norman Sicily, at
10773-740: The Paeonians due north, the Thracians to the northeast, and the Illyrians , with whom the Macedonians were frequently in conflict, to the northwest. Chalcidice was settled early on by southern Greek colonists and was considered part of the Greek world, while from the late 2nd millennium BC substantial Greek settlement also occurred on the eastern shores of the Aegean , in Anatolia . During
10962-431: The Pleistocene epoch around 8000 BC. The Elymians , thought to have come from the area of the Aegean Sea , became the next tribe to join the Sicanians on Sicily. No evidence survives of warring between tribes, but the Sicanians moved eastwards when the Elymians settled in the northwest corner of the island. The Sicels are thought to have originated in Liguria ; they arrived from mainland Italy in 1200 BC and forced
11151-404: The Qanat to improve irrigation systems for agriculture. Around 1050, the western half of Sicily was ethnically and culturally distinct from central and eastern Sicily. During this time, there was also a small Jewish presence in Sicily, evidence seen in the catacombs discovered on the island. Palermo was initially ruled by the Aghlabids ; later it was the centre of the Emirate of Sicily, which
11340-561: The Renaissance and again in the 17th century , while the discovery in 1906 of previously lost works by Archimedes in the Archimedes Palimpsest has provided new insights into how he obtained mathematical results. Archimedes was born c. 287 BC in the seaport city of Syracuse , Sicily , at that time a self-governing colony in Magna Graecia . The date of birth is based on a statement by the Byzantine Greek scholar John Tzetzes that Archimedes lived for 75 years before his death in 212 BC. Plutarch wrote in his Parallel Lives that Archimedes
11529-429: The Renaissance , the Editio princeps (First Edition) was published in Basel in 1544 by Johann Herwagen with the works of Archimedes in Greek and Latin. The following are ordered chronologically based on new terminological and historical criteria set by Knorr (1978) and Sato (1986). This is a short work consisting of three propositions. It is written in the form of a correspondence with Dositheus of Pelusium, who
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#173276616422811718-406: The Strait of Messina , about 3 km (1.9 mi) wide in the north, and about 16 km (9.9 mi) wide in the southern part. The northern and southern coasts are each about 280 km (170 mi) long measured as a straight line, while the eastern coast measures around 180 km (110 mi); total coast length is estimated at 1,484 km (922 mi). The total area of the island
11907-426: The heliocentric theory of the solar system proposed by Aristarchus of Samos , as well as contemporary ideas about the size of the Earth and the distance between various celestial bodies . By using a system of numbers based on powers of the myriad , Archimedes concludes that the number of grains of sand required to fill the universe is 8 × 10 in modern notation. The introductory letter states that Archimedes' father
12096-452: The lever , he gave a mathematical proof of the principle involved in his work On the Equilibrium of Planes . Earlier descriptions of the principle of the lever are found in a work by Euclid and in the Mechanical Problems , belonging to the Peripatetic school of the followers of Aristotle , the authorship of which has been attributed by some to Archytas . There are several, often conflicting, reports regarding Archimedes' feats using
12285-449: The poleis grouped themselves into leagues, membership of which was in a constant state of flux. Later in the Classical period, the leagues would become fewer and larger, be dominated by one city (particularly Athens , Sparta and Thebes ); and often poleis would be compelled to join under threat of war (or as part of a peace treaty). Even after Philip II of Macedon conquered the heartlands of ancient Greece, he did not attempt to annex
12474-437: The siege of Syracuse Archimedes had burned enemy ships. Nearly four hundred years later, Anthemius , despite skepticism, tried to reconstruct Archimedes' hypothetical reflector geometry. The purported device, sometimes called " Archimedes' heat ray ", has been the subject of an ongoing debate about its credibility since the Renaissance . René Descartes rejected it as false, while modern researchers have attempted to recreate
12663-445: The siege of Syracuse , when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting Archimedes' tomb, which was surmounted by a sphere and a cylinder that Archimedes requested be placed there to represent his most valued mathematical discovery. Unlike his inventions, Archimedes' mathematical writings were little known in antiquity. Alexandrian mathematicians read and quoted him, but
12852-411: The 146 BC conquest of Greece after the Battle of Corinth. Macedonia became a Roman province while southern Greece came under the surveillance of Macedonia's prefect ; however, some Greek poleis managed to maintain a partial independence and avoid taxation. The Aegean Islands were added to this territory in 133 BC. Athens and other Greek cities revolted in 88 BC, and the peninsula was crushed by
13041-444: The 455 sack of Rome, at Agrigento, but were defeated decisively by Ricimir in a naval victory off Corsica in 456. The island remained under Roman rule until 469. The Vandals lost possession of the island 8 years later in 477 to the East Germanic tribe of the Ostrogoths , who then controlled Italy and Dalmatia. The island was returned to the Ostrogoths by payment of tribute to their king Odoacer . He ruled Italy from 476 to 488 in
13230-408: The Arabs failed to make permanent gains. They returned to Syria with their booty. Raids seeking loot continued until the mid-8th century. The Eastern Roman Emperor Constans II moved from Constantinople to Syracuse in 660. The following year he launched an assault from Sicily against the Lombard Duchy of Benevento , which occupied most of southern Italy. Rumors that the capital of the empire
13419-494: The Athenian army and their ships, selling most of the survivors into slavery . The Greek kingdom of Syracuse controlled most of eastern Sicily while Carthage controlled the western side. The two cultures began to clash, leading to the Greek-Punic wars (between 580 and 265 BC). The Greek states had begun to make peace with the Roman Republic in 262 BC, before the Romans sought to annex Sicily as their republic's first province . Rome attacked Carthage's holdings in Sicily in
13608-469: The Burgundians settled in present-day Savoy in 443. The Vandals found themselves in a position to threaten Sicily – only 100 miles away from their North African bases. After taking Carthage, the Vandals, personally led by King Gaiseric , laid siege to Palermo in 440 as the opening act in an attempt to wrest the island from Roman rule. The Vandals made another attempt to take the island one year after
13797-583: The Carthaginian invasion at the Battle of Himera . The Persians were decisively defeated at sea by a primarily Athenian naval force at the Battle of Salamis , and on land in 479 BC at the Battle of Plataea . The alliance against Persia continued, initially led by the Spartan Pausanias but from 477 by Athens, and by 460 Persia had been driven out of the Aegean. During this long campaign,
13986-525: The Corinthian empire in northwest Greece and defended its own empire, despite a plague which killed the leading Athenian statesman Pericles . The war turned after Athenian victories led by Cleon at Pylos and Sphakteria , and Sparta sued for peace, but the Athenians rejected the proposal. The Athenian failure to regain control of Boeotia at Delium and Brasidas ' successes in northern Greece in 424 improved Sparta's position after Sphakteria. After
14175-528: The Earth" ( Greek : δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω ). Olympiodorus later attributed the same boast to Archimedes' invention of the baroulkos , a kind of windlass , rather than the lever. A large part of Archimedes' work in engineering probably arose from fulfilling the needs of his home city of Syracuse . Athenaeus of Naucratis quotes a certain Moschion in a description on how King Hiero II commissioned
14364-517: The Earth, Sun, and Moon, as well as Aristarchus ' heliocentric model of the universe, in the Sand-Reckoner . Without the use of either trigonometry or a table of chords, Archimedes determines the Sun's apparent diameter by first describing the procedure and instrument used to make observations (a straight rod with pegs or grooves), applying correction factors to these measurements, and finally giving
14553-578: The Expedition of the Thousand, an invasion led by Giuseppe Garibaldi , and a plebiscite. Sicily was given special status as an autonomous administrative division on 15 May 1946, 18 days before the 1946 Italian institutional referendum . Sicily has a roughly triangular shape, earning it the name Trinacria . To the north-east, it is separated from Calabria and the rest of the Italian mainland by
14742-668: The Greek city-states. It greatly widened the horizons of the Greeks and led to a steady emigration of the young and ambitious to the new Greek empires in the east. Many Greeks migrated to Alexandria, Antioch and the many other new Hellenistic cities founded in Alexander's wake, as far away as present-day Afghanistan and Pakistan , where the Greco-Bactrian Kingdom and the Indo-Greek Kingdom survived until
14931-460: The Greek colonies Syracusae ( Συράκουσαι ), Neapolis ( Νεάπολις ), Massalia ( Μασσαλία ) and Byzantion ( Βυζάντιον ). These colonies played an important role in the spread of Greek influence throughout Europe and also aided in the establishment of long-distance trading networks between the Greek city-states, boosting the economy of ancient Greece . Ancient Greece consisted of several hundred relatively independent city-states ( poleis ). This
15120-578: The Greek colony Sybaris in southern Italy, its allies, and the Serdaioi. In 499 BC, the Ionian city states under Persian rule rebelled against their Persian-supported tyrant rulers. Supported by troops sent from Athens and Eretria , they advanced as far as Sardis and burnt the city before being driven back by a Persian counterattack. The revolt continued until 494, when the rebelling Ionians were defeated. Darius did not forget that Athens had assisted
15309-420: The Greek system are further evidenced by the colonies that they set up throughout the Mediterranean , which, though they might count a certain Greek polis as their 'mother' (and remain sympathetic to her), were completely independent of the founding city. Inevitably smaller poleis might be dominated by larger neighbors, but conquest or direct rule by another city-state appears to have been quite rare. Instead
15498-815: The Greeks began 250 years of expansion, settling colonies in all directions. To the east, the Aegean coast of Asia Minor was colonized first, followed by Cyprus and the coasts of Thrace , the Sea of Marmara and south coast of the Black Sea . Eventually, Greek colonization reached as far northeast as present-day Ukraine and Russia ( Taganrog ). To the west the coasts of Illyria , Southern Italy (called " Magna Graecia ") were settled, followed by Southern France , Corsica , and even eastern Spain . Greek colonies were also founded in Egypt and Libya . Modern Syracuse , Naples , Marseille and Istanbul had their beginnings as
15687-423: The Greeks were very aware of their tribal origins; Herodotus was able to extensively categorise the city-states by tribe. Yet, although these higher-level relationships existed, they seem to have rarely had a major role in Greek politics. The independence of the poleis was fiercely defended; unification was something rarely contemplated by the ancient Greeks. Even when, during the second Persian invasion of Greece,
15876-535: The Ionian revolt, and in 490 he assembled an armada to retaliate. Though heavily outnumbered, the Athenians—supported by their Plataean allies—defeated the Persian hordes at the Battle of Marathon , and the Persian fleet turned tail. Ten years later, a second invasion was launched by Darius' son Xerxes . The city-states of northern and central Greece submitted to the Persian forces without resistance, but
16065-483: The League of Corinth following the death of Philip, Alexander began his campaign against Persia in 334 BC. He conquered Persia, defeating Darius III at the Battle of Issus in 333 BC, and after the Battle of Gaugamela in 331 BC proclaimed himself king of Asia. From 329 BC he led expeditions to Bactria and then India; further plans to invade Arabia and North Africa were halted by his death in 323 BC. The period from
16254-465: The Normans invaded in 1061 and after taking Apulia and Calabria , Roger I occupied Messina with an army of 700 knights. In 1068, Roger I was victorious at Misilmeri . Most crucial was the siege of Palermo, whose fall in 1071 eventually resulted in all Sicily coming under Norman control. The conquest was completed in 1091 when they captured Noto the last Arab stronghold. Palermo continued to be
16443-634: The Roman general Sulla . The Roman civil wars devastated the land even further, until Augustus organized the peninsula as the province of Achaea in 27 BC. Greece was a key eastern province of the Roman Empire, as the Roman culture had long been in fact Greco-Roman . The Greek language served as a lingua franca in the East and in Italy , and many Greek intellectuals such as Galen would perform most of their work in Rome . The territory of Greece
16632-468: The Romans ultimately captured the city, they suffered considerable losses due to Archimedes' inventiveness. Cicero (106–43 BC) mentions Archimedes in some of his works. While serving as a quaestor in Sicily, Cicero found what was presumed to be Archimedes' tomb near the Agrigentine gate in Syracuse, in a neglected condition and overgrown with bushes. Cicero had the tomb cleaned up and was able to see
16821-663: The Sicanians to move back across Sicily and to settle in the middle of the island. Other minor Italic groups who settled in Sicily included the Ausones ( Aeolian Islands , Milazzo ) and the Morgetes of Morgantina . The Phoenician settlements in the western part of the island predate the arrival of Greek colonists. From about 750 BC, the Greeks began to live in Sicily ( Ancient Greek : Σικελία – Sikelia ), establishing many significant settlements. The most important colony
17010-527: The Sphere and Cylinder , Archimedes postulates that any magnitude when added to itself enough times will exceed any given magnitude. Today this is known as the Archimedean property of real numbers. Archimedes gives the value of the square root of 3 as lying between 265 / 153 (approximately 1.7320261) and 1351 / 780 (approximately 1.7320512) in Measurement of
17199-616: The age of seven or eight until 17 or 18 Theodoric had become a Byzantine hostage; he resided in the great palace of Constantinople, was favored by Emperor Leo I ( r. 457–474 ) and learned to read, write and do arithmetic. After taking areas occupied by the Vandals in North Africa, Justinian I retook Italy as an ambitious attempt to recover the lost provinces in the West. The re-conquests marked an end to over 150 years of accommodating policies with tribal invaders. His first target
17388-579: The ancient Greeks did not think in terms of race . Most families owned slaves as household servants and laborers, and even poor families might have owned a few slaves. Owners were not allowed to beat or kill their slaves. Owners often promised to free slaves in the future to encourage slaves to work hard. Unlike in Rome, freedmen did not become citizens. Instead, they were mixed into the population of metics , which included people from foreign countries or other city-states who were officially allowed to live in
17577-404: The area under a parabola , the volume of a segment of a paraboloid of revolution , the volume of a segment of a hyperboloid of revolution , and the area of a spiral . Archimedes' other mathematical achievements include deriving an approximation of pi ( π ) , defining and investigating the Archimedean spiral , and devising a system using exponentiation for expressing very large numbers . He
17766-412: The areas of figures and the value of π . In Measurement of a Circle , he did this by drawing a larger regular hexagon outside a circle then a smaller regular hexagon inside the circle, and progressively doubling the number of sides of each regular polygon , calculating the length of a side of each polygon at each step. As the number of sides increases, it becomes a more accurate approximation of
17955-515: The best examples of unspoiled coastal wilderness in Sicily. Marine Life of the Straits of Messina includes varieties of birds and marine life, including larger species such as greater flamingo and fin whale . The name Sicilia was given to the Roman province in 241 BC. It is named after the Sicels , who inhabited the eastern part of the island during the Iron Age . The ancient name of
18144-541: The capital under the Normans . The Normans formed a small but violent ruling class. They destroyed many of the Arab towns in Sicily, and very few physical remains survive from the Arab era. The Norman Hauteville family appreciated and admired the rich and layered culture in which they now found themselves. They also introduced into Sicily their own culture, customs, and politics from Normandy . Many Normans in Sicily adopted
18333-414: The capture of Syracuse and Archimedes' role in it. Plutarch (45–119 AD) provides at least two accounts on how Archimedes died after Syracuse was taken. According to the most popular account, Archimedes was contemplating a mathematical diagram when the city was captured. A Roman soldier commanded him to come and meet Marcellus, but he declined, saying that he had to finish working on the problem. This enraged
18522-419: The capture of Syracuse in the Second Punic War , Marcellus is said to have taken back to Rome two mechanisms which were constructed by Archimedes and which showed the motion of the Sun, Moon and five planets. Cicero also mentions similar mechanisms designed by Thales of Miletus and Eudoxus of Cnidus . The dialogue says that Marcellus kept one of the devices as his only personal loot from Syracuse, and donated
18711-428: The carving and read some of the verses that had been added as an inscription. The tomb carried a sculpture illustrating Archimedes' favorite mathematical proof , that the volume and surface area of the sphere are two-thirds that of an enclosing cylinder including its bases. He also mentions that Marcellus brought to Rome two planetariums Archimedes built. The Roman historian Livy (59 BC–17 AD) retells Polybius's story of
18900-666: The center, while in the east lay Boeotia , Attica , and Megaris . Northeast lay Thessaly , while Epirus lay to the northwest. Epirus stretched from the Ambracian Gulf in the south to the Ceraunian Mountains and the Aoos river in the north, and consisted of Chaonia (north), Molossia (center), and Thesprotia (south). In the northeast corner was Macedonia , originally consisting Lower Macedonia and its regions, such as Elimeia , Pieria , and Orestis . Around
19089-466: The central Mediterranean Sea , south of the Italian Peninsula in continental Europe and is one of the 20 regions of Italy . With 4.8 million inhabitants, including 1.3 million in and around the capital city of Palermo , it is the most populous island in the Mediterranean Sea . It is named after the Sicels , who inhabited the eastern part of the island during the Iron Age . Sicily has
19278-543: The church of Rome to that of Constantinople, placing the island within the eastern branch of the Church. In 826 Euphemius , the Byzantine commander in Sicily, having apparently killed his wife, forced a nun to marry him. Emperor Michael II caught wind of the matter and ordered general Constantine to end the marriage and cut off Euphemius' head. Euphemius rose up, killed Constantine, and then occupied Syracuse; he, in turn,
19467-461: The coasts, especially in the southwest, the climate is affected by the African currents and summers can be hot. Snow falls above 900 metres, but it can fall in the hills. The interior mountains, especially Nebrodi , Madonie , and Etna , enjoy a mountain climate, with heavy snowfalls during winter. The summit of Mount Etna is usually snow-capped from October to May. In the summer, the sirocco –
19656-499: The construction of these mechanisms entitled On Sphere-Making . Modern research in this area has been focused on the Antikythera mechanism , another device built c. 100 BC probably designed with a similar purpose. Constructing mechanisms of this kind would have required a sophisticated knowledge of differential gearing . This was once thought to have been beyond the range of the technology available in ancient times, but
19845-455: The course of the archaic period. Already in the seventh century, the right of all citizen men to attend the assembly appears to have been established. After a failed coup led by Cylon of Athens around 636 BC, Draco was appointed to establish a code of laws in 621. This failed to reduce the political tension between the poor and the elites, and in 594 Solon was given the authority to enact another set of reforms, which attempted to balance
20034-473: The course of the eighth and seventh century. According to Spartan tradition, this constitution was established by the legendary lawgiver Lycurgus . Over the course of the first and second Messenian wars , Sparta subjugated the neighbouring region of Messenia , enserfing the population. In the sixth century, Greek city-states began to develop formal relationships with one another, where previously individual rulers had relied on personal relationships with
20223-461: The death of Alexander the Great in 323 BC until the death of Cleopatra , the last Macedonian ruler of Egypt, is known as the Hellenistic period. In the early part of this period, a new form of kingship developed based on Macedonian and Near Eastern traditions. The first Hellenistic kings were previously Alexander's generals, and took power in the period following his death, though they were not part of existing royal lineages and lacked historic claims to
20412-552: The death of Alexander the Great in 323 BC. The Classical Period is characterized by a "classical" style, i.e. one which was considered exemplary by later observers, most famously in the Parthenon of Athens. Politically, the Classical Period was dominated by Athens and the Delian League during the 5th century, but displaced by Spartan hegemony during the early 4th century BC, before power shifted to Thebes and
20601-423: The deaths of Cleon and Brasidas, the strongest proponents of war on each side, a peace treaty was negoitiated in 421 by the Athenian general Nicias . The peace did not last, however. In 418 BC allied forces of Athens and Argos were defeated by Sparta at Mantinea . In 415 Athens launched an ambitious naval expedition to dominate Sicily; the expedition ended in disaster at the harbor of Syracuse , with almost
20790-467: The density would be lower than that of gold. Archimedes found that this is what had happened, proving that silver had been mixed in. The story of the golden crown does not appear anywhere in Archimedes' known works. The practicality of the method described has been called into question due to the extreme accuracy that would be required to measure water displacement . Archimedes may have instead sought
20979-454: The design of a huge ship, the Syracusia , which could be used for luxury travel, carrying supplies, and as a display of naval power . The Syracusia is said to have been the largest ship built in classical antiquity and, according to Moschion's account, it was launched by Archimedes. The ship presumably was capable of carrying 600 people and included garden decorations, a gymnasium , and
21168-613: The dialect of ancient Syracuse. Many written works by Archimedes have not survived or are only extant in heavily edited fragments; at least seven of his treatises are known to have existed due to references made by other authors. Pappus of Alexandria mentions On Sphere-Making and another work on polyhedra , while Theon of Alexandria quotes a remark about refraction from the now-lost Catoptrica . Archimedes made his work known through correspondence with mathematicians in Alexandria . The writings of Archimedes were first collected by
21357-521: The discovery of the Antikythera mechanism in 1902 has confirmed that devices of this kind were known to the ancient Greeks. While he is often regarded as a designer of mechanical devices, Archimedes also made contributions to the field of mathematics . Plutarch wrote that Archimedes "placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life", though some scholars believe this may be
21546-674: The dominance that would allow it to challenge Persia, the Persian king initially joined the alliance against Sparta, before imposing the Peace of Antalcidas ("King's Peace") which restored Persia's control over the Anatolian Greeks. By 371 BC, Thebes was in the ascendancy, defeating Sparta at the Battle of Leuctra , killing the Spartan king Cleombrotus I , and invading Laconia. Further Theban successes against Sparta in 369 led to Messenia gaining independence; Sparta never recovered from
21735-409: The domination of politics and concomitant aggregation of wealth by small groups of families was apt to cause social unrest in many poleis . In many cities a tyrant (not in the modern sense of repressive autocracies), would at some point seize control and govern according to their own will; often a populist agenda would help sustain them in power. In a system wracked with class conflict , government by
21924-424: The dust with his hands, said 'I beg of you, do not disturb this ' "). The most widely known anecdote about Archimedes tells of how he invented a method for determining the volume of an object with an irregular shape. According to Vitruvius , a crown for a temple had been made for King Hiero II of Syracuse , who supplied the pure gold to be used. The crown was likely made in the shape of a votive wreath . Archimedes
22113-726: The east to the Indian king Chandragupta Maurya in exchange for war elephants, and later lost large parts of Persia to the Parthian Empire . By the mid-third century, the kingdoms of Alexander's successors was mostly stable, though there continued to be disputes over border areas. The great capitals of Hellenistic culture were Alexandria in the Ptolemaic Kingdom and Antioch in the Seleucid Empire . The conquests of Alexander had numerous consequences for
22302-605: The effect using only the means that would have been available to Archimedes, mostly with negative results. It has been suggested that a large array of highly polished bronze or copper shields acting as mirrors could have been employed to focus sunlight onto a ship, but the overall effect would have been blinding, dazzling , or distracting the crew of the ship rather than fire. Using modern materials and larger scale, sunlight-concentrating solar furnaces can reach very high temperatures, and are sometimes used for generating electricity . Archimedes discusses astronomical measurements of
22491-552: The elites of other cities. Towards the end of the archaic period, Sparta began to build a series of alliances, the Peloponnesian League , with cities including Corinth , Elis , and Megara , isolating Messenia and reinforcing Sparta's position against Argos , the other major power in the Peloponnese. Other alliances in the sixth century included those between Elis and Heraea in the Peloponnese; and between
22680-619: The end of the first century BC. The city-states within Greece formed themselves into two leagues; the Achaean League (including Corinth and Argos) and the Aetolian League (including Sparta and Athens). For much of the period until the Roman conquest, these leagues were at war, often participating in the conflicts between the Diadochi (the successor states to Alexander's empire). The Antigonid Kingdom became involved in
22869-553: The entire army killed, and the ships destroyed. Soon after the Athenian defeat in Syracuse, Athens' Ionian allies began to rebel against the Delian league, while Persia began to once again involve itself in Greek affairs on the Spartan side. Initially the Athenian position continued relatively strong, with important victories at Cyzicus in 410 and Arginusae in 406. However, in 405 the Spartan Lysander defeated Athens in
23058-540: The exact borders of the Hellenistic kingdoms were not settled. Antigonus attempted to expand his territory by attacking the other successor kingdoms until they joined against him, and he was killed at the Battle of Ipsus in 301 BC. His son Demetrius spent many years in Seleucid captivity, and his son, Antigonus II , only reclaimed the Macedonian throne around 276. Meanwhile, the Seleucid kingdom gave up territory in
23247-644: The fall of the Roman Empire in the 5th century AD. Sicily was ruled during the Early Middle Ages by the Vandals , the Ostrogoths , the Byzantine Empire , and the Emirate of Sicily . The Norman conquest of southern Italy led to the creation of the County of Sicily in 1071, that was succeeded by Kingdom of Sicily , a state that existed from 1130 until 1816 under various dynasties, and in 1816 it
23436-476: The feasibility of the claw, and in 2005 a television documentary entitled Superweapons of the Ancient World built a version of the claw and concluded that it was a workable device. Archimedes has also been credited with improving the power and accuracy of the catapult , and with inventing the odometer during the First Punic War . The odometer was described as a cart with a gear mechanism that dropped
23625-551: The first comprehensive compilation was not made until c. 530 AD by Isidore of Miletus in Byzantine Constantinople , while Eutocius ' commentaries on Archimedes' works in the same century opened them to wider readership for the first time. The relatively few copies of Archimedes' written work that survived through the Middle Ages were an influential source of ideas for scientists during
23814-519: The first term in this series is the area of the triangle, then the second is the sum of the areas of two triangles whose bases are the two smaller secant lines , and whose third vertex is where the line that is parallel to the parabola's axis and that passes through the midpoint of the base intersects the parabola, and so on. This proof uses a variation of the series 1/4 + 1/16 + 1/64 + 1/256 + · · · which sums to 1 / 3 . In The Sand Reckoner , Archimedes set out to calculate
24003-469: The founding of Greek colonies around the Mediterranean, with Euboean settlements at Al-Mina in the east as early as 800 BC, and Ischia in the west by 775. Increasing contact with non-Greek peoples in this period, especially in the Near East, inspired developments in art and architecture, the adoption of coinage, and the development of the Greek alphabet. Athens developed its democratic system over
24192-477: The globe, it happened that the Moon followed the Sun by as many turns on that bronze contrivance as in the sky itself, from which also in the sky the Sun's globe became to have that same eclipse, and the Moon came then to that position which was its shadow on the Earth when the Sun was in line. This is a description of a small planetarium . Pappus of Alexandria reports on a now lost treatise by Archimedes dealing with
24381-576: The government. In Athens, the population was divided into four social classes based on wealth. People could change classes if they made more money. In Sparta, all male citizens were called homoioi , meaning "peers". However, Spartan kings, who served as the city-state's dual military and religious leaders, came from two families. Women in Ancient Greece appear to have primarily performed domestic tasks, managed households, and borne and reared children. Slaves had no power or status. Slaves had
24570-401: The greatest mathematician of ancient history , and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying the concept of the infinitely small and the method of exhaustion to derive and rigorously prove a range of geometrical theorems . These include the area of a circle , the surface area and volume of a sphere , the area of an ellipse ,
24759-472: The growth of smallholdings , undermining the dominance of the latifundia . The Arabs further improved irrigation systems. The language spoken in Sicily under Arab rule was Siculo-Arabic and Arabic influence is present in some Sicilian words today. Although long extinct in Sicily, the language has developed into what is now the Maltese language on the islands of Malta today. A description of Palermo
24948-406: The habits and comportment of Muslim rulers and their Byzantine subjects in dress, language, literature, even to the extent of having palace eunuchs and, according to some accounts, a harem. While Roger I died in 1101, his wife Adelaide ruled until 1112 when their son Roger II of Sicily came of age. Having succeeded his brother Simon as Count of Sicily, Roger II was ultimately able to raise
25137-453: The highest and most notable peak. Other important mountain ranges include the Nebrodi , Madonie and Peloritani mountains ranges. Several rivers drain the island, most of which flow through the central area and enter the sea at the south of the island. The Salso flows through parts of Enna and Caltanissetta before entering the Mediterranean Sea at the port of Licata . To the east,
25326-547: The increasing Athenian power funded by the Delian League, Sparta offered aid to reluctant members of the League to rebel against Athenian domination. These tensions were exacerbated in 462 BC when Athens sent a force to aid Sparta in overcoming a helot revolt, but this aid was rejected by the Spartans. In the 450s, Athens took control of Boeotia, and won victories over Aegina and Corinth. However, Athens failed to win
25515-536: The invaders; Roman consul M. Valerian told the Roman Senate in 210 BC that "no Carthaginian remains in Sicily". As the Roman Republic's granary , Sicily ranked as an important province, divided into two quaestorships : Syracuse to the east and Lilybaeum to the west. Roman rule introduced the Latin language to the island, which underwent a slow process of latinisation but Sicily remained largely Greek in
25704-524: The island (dating to the second half of the third millennium BC) seem to offer new insights into the culture of primitive Sicily. The impact of at least two influences is clear: the European one coming from the Northwest, and the Mediterranean influence of an eastern heritage. The original classical-era inhabitants of Sicily comprised three defined groups of the ancient peoples of Italy : the Sicani ,
25893-561: The island is Trinacria (Greek Τρινακρία "having three headlands") for its triangular shape, likely a re-interpretation of earlier ( Homeric ) Thrinacia . The Greek name was rendered as Trīnācrĭa in classical Latin ( Virgil , Ovid ). Humans first colonized Sicily towards the end of the Late Pleistocene , around 16,000 years ago, by people associated with the Epigravettian culture. Discoveries of dolmens on
26082-609: The island was turned into an agricultural region. This gradually dried the climate, leading to a decline in rainfall and the drying of rivers. The central and southwest provinces are practically devoid of forest. In Northern Sicily, there are three important forests; near Mount Etna, in the Nebrodi Mountains and in the Bosco della Ficuzza Natural Reserve near Palermo . The Nebrodi Mountains Regional Park, established on 4 August 1993 and covering 86,000 hectares (210,000 acres),
26271-403: The island. The Sicilian wolf ( Canis lupus cristaldii ) was an endemic wolf subspecies that was driven to extinction in the 20th century. During the Late Pleistocene , a species of dwarf elephant , Palaeoloxodon mnaidriensis inhabited the island, with its latest records on Sicily dating to around 20,000 years ago. The Riserva naturale dello Zingaro (Zingaro Natural Reserve) is one of
26460-624: The island. Linguistically, the island shifted from being one-third Greek- and two-thirds Arabic-speaking at the time of the Norman conquest to becoming fully Latinised . In terms of religion the island became completely Roman Catholic (bearing in mind that until 1054 the Churches owing allegiance to the Pope and the Patriarch of Constantinople belonged to one Church); Sicily before the Norman conquest
26649-524: The largest city, Syracuse, held out until 878 and the Greek city of Taormina fell in 962. It was not until 965 that all of Sicily was conquered by the Arabs . In the 11th-century Byzantine armies carried out a partial reconquest of the island under George Maniakes , but it was their Norman mercenaries who would eventually complete the island's reconquest at the end of the century. The Arabs initiated land reforms , which increased productivity and encouraged
26838-473: The largest of the three active volcanoes in Italy , being about two and a half times the height of the next largest, Mount Vesuvius . In Greek mythology , the deadly monster Typhon was trapped under the mountain by Zeus , the god of the sky. Mount Etna is widely regarded as a cultural symbol and icon of Sicily. The Aeolian Islands in the Tyrrhenian Sea , to the northeast of mainland Sicily form
27027-415: The lever to lift very heavy objects. Plutarch describes how Archimedes designed block-and-tackle pulley systems, allowing sailors to use the principle of leverage to lift objects that would otherwise have been too heavy to move. According to Pappus of Alexandria , Archimedes' work on levers and his understanding of mechanical advantage caused him to remark: "Give me a place to stand on, and I will move
27216-514: The loss of Messenia's fertile land and the helot workforce it provided. The rising power of Thebes led Sparta and Athens to join forces; in 362 they were defeated by Thebes at the Battle of Mantinea . In the aftermath of Mantinea, none of the major Greek states were able to dominate. Though Thebes had won the battle, their general Epaminondas was killed, and they spent the following decades embroiled in wars with their neighbours; Athens, meanwhile, saw its second naval alliance, formed in 377, collapse in
27405-462: The mainland Apennines . The cone of Mount Etna dominates the eastern coast. In the southeast lie the lower Hyblaean Mountains , 1,000 m (3,300 ft). The mines of the Enna and Caltanissetta districts were part of a leading sulphur -producing area throughout the 19th century, but have declined since the 1950s. Sicily and its surrounding small islands have some highly active volcanoes. This
27594-495: The mid-350s. The power vacuum in Greece after the Battle of Mantinea was filled by Macedon, under Philip II . In 338 BC, he defeated a Greek alliance at the Battle of Chaeronea , and subsequently formed the League of Corinth . Philip planned to lead the League to invade Persia, but was murdered in 336 BC. His son Alexander the Great was left to fulfil his father's ambitions. After campaigns against Macedon's western and northern enemies, and those Greek states that had broken from
27783-443: The most important unit of political organisation in Greece. The absence of powerful states in Greece after the collapse of Mycenaean power, and the geography of Greece, where many settlements were separated from their neighbours by mountainous terrain, encouraged the development of small independent city-states. Several Greek states saw tyrants rise to power in this period, most famously at Corinth from 657 BC. The period also saw
27972-525: The name of the Byzantine (Eastern Roman) Emperor. The Vandals kept a toehold in Lilybaeum , a port on the west coast. They lost this in 491 after making one last attempt to conquer the island from this port. The Ostrogothic conquest of Sicily (and of Italy as a whole) under Theodoric the Great began in 488. The Byzantine Emperor Zeno had appointed Theodoric as a military commander in Italy. The Goths were Germanic, but Theodoric fostered Roman culture and government and allowed freedom of religion. In 461 from
28161-410: The new Ostrogoth king Totila counterattacked, moving down the Italian peninsula, plundering and conquering Sicily in 550. Totila was defeated and killed in the Battle of Taginae by Byzantine general Narses in 552 but Italy was in ruins. At the time of the reconquest Greek was still the predominant language spoken on the island. Sicily was invaded by the Arab forces of Caliph Uthman in 652, but
28350-479: The other to the Temple of Virtue in Rome. Marcellus's mechanism was demonstrated, according to Cicero, by Gaius Sulpicius Gallus to Lucius Furius Philus , who described it thus: Hanc sphaeram Gallus cum moveret, fiebat ut soli luna totidem conversionibus in aere illo quot diebus in ipso caelo succederet, ex quo et in caelo sphaera solis fieret eadem illa defectio, et incideret luna tum in eam metam quae esset umbra terrae, cum sol e regione. When Gallus moved
28539-410: The power of the rich and the poor. In the middle of the sixth century, Pisistratus established himself as a tyrant, and after his death in 527 his son Hippias inherited his position; by the end of the sixth century he had been overthrown and Cleisthenes carried out further democratising reforms. In Sparta, a political system with two kings, a council of elders , and five ephors developed over
28728-419: The principles derived to calculate the areas and centers of gravity of various geometric figures including triangles , parallelograms and parabolas . In this work of 24 propositions addressed to Dositheus, Archimedes proves by two methods that the area enclosed by a parabola and a straight line is 4/3 the area of a triangle with equal base and height. He achieves this in one of his proofs by calculating
28917-435: The problem, Archimedes devised a system of counting based on the myriad . The word itself derives from the Greek μυριάς , murias , for the number 10,000. He proposed a number system using powers of a myriad of myriads (100 million, i.e., 10,000 x 10,000) and concluded that the number of grains of sand required to fill the universe would be 8 vigintillion , or 8 × 10. The works of Archimedes were written in Doric Greek ,
29106-564: The reforms of Solon (early 6th century), but the poorest citizens could not address the assembly or run for office. With the establishment of the democracy, the assembly became the de jure mechanism of government; all citizens had equal privileges in the assembly. However, non-citizens, such as metics (foreigners living in Athens) or slaves , had no political rights at all. After the rise of democracy in Athens, other city-states founded democracies. However, many retained more traditional forms of government. As so often in other matters, Sparta
29295-420: The regions of Laconia (southeast), Messenia (southwest), Elis (west), Achaia (north), Korinthia (northeast), Argolis (east), and Arcadia (center). These names survive to the present day as regional units of modern Greece , though with somewhat different boundaries. Mainland Greece to the north, nowadays known as Central Greece , consisted of Aetolia and Acarnania in the west, Locris , Doris , and Phocis in
29484-400: The result in the form of upper and lower bounds to account for observational error. Ptolemy , quoting Hipparchus, also references Archimedes' solstice observations in the Almagest . This would make Archimedes the first known Greek to have recorded multiple solstice dates and times in successive years. Cicero's De re publica portrays a fictional conversation taking place in 129 BC. After
29673-518: The right to have a family and own property, subject to their master's goodwill and permission, but they had no political rights. By 600 BC, chattel slavery had spread in Greece. By the 5th century BC, slaves made up one-third of the total population in some city-states. Between 40–80% of the population of Classical Athens were slaves. Slaves outside of Sparta almost never revolted because they were made up of too many nationalities and were too scattered to organize. However, unlike later Western culture ,
29862-450: The same weight, then immersing the apparatus in water. The difference in density between the two samples would cause the scale to tip accordingly. Galileo Galilei , who invented a hydrostatic balance in 1586 inspired by Archimedes' work, considered it "probable that this method is the same that Archimedes followed, since, besides being very accurate, it is based on demonstrations found by Archimedes himself." While Archimedes did not invent
30051-414: The screw. Archimedes is said to have designed a claw as a weapon to defend the city of Syracuse. Also known as " the ship shaker ", the claw consisted of a crane-like arm from which a large metal grappling hook was suspended. When the claw was dropped onto an attacking ship the arm would swing upwards, lifting the ship out of the water and possibly sinking it. There have been modern experiments to test
30240-438: The settlers built many temples throughout Sicily, including several in the Valley of the Temples at Agrigento . Politics on the island became intertwined with those of Greece; Syracuse became desired by the Athenians who set out on the Sicilian Expedition (415–413 BC) during the Peloponnesian War . Syracuse gained Sparta and Corinth as allies and, as a result, defeated the Athenian expedition. The victors destroyed
30429-557: The soldier, who killed Archimedes with his sword. Another story has Archimedes carrying mathematical instruments before being killed because a soldier thought they were valuable items. Marcellus was reportedly angered by Archimedes' death, as he considered him a valuable scientific asset (he called Archimedes "a geometrical Briareus ") and had ordered that he should not be harmed. The last words attributed to Archimedes are " Do not disturb my circles " ( Latin , " Noli turbare circulos meos "; Katharevousa Greek , "μὴ μου τοὺς κύκλους τάραττε"),
30618-448: The state. City-states legally owned slaves. These public slaves had a larger measure of independence than slaves owned by families, living on their own and performing specialized tasks. In Athens, public slaves were trained to look out for counterfeit coinage , while temple slaves acted as servants of the temple's deity and Scythian slaves were employed in Athens as a police force corralling citizens to political functions. Sparta had
30807-448: The status of the island to a kingdom in 1130, along with his other holdings, which included the Maltese Islands and the Duchies of Apulia and Calabria . Roger II appointed the powerful Greek George of Antioch to be his "emir of emirs" and continued the syncretism of his father. During this period, the Kingdom of Sicily was prosperous and politically powerful, becoming one of the wealthiest states in all of Europe—even wealthier than
30996-412: The territories they controlled. The most important of these rulers in the decades after Alexander's death were Antigonus I and his son Demetrius in Macedonia and the rest of Greece, Ptolemy in Egypt, and Seleucus I in Syria and the former Persian empire; smaller Hellenistic kingdoms included the Attalids in Anatolia and the Greco-Bactrian kingdom . In the early part of the Hellenistic period,
31185-460: The territory or unify it into a new province, but compelled most of the poleis to join his own Corinthian League . Initially many Greek city-states seem to have been petty kingdoms; there was often a city official carrying some residual, ceremonial functions of the king ( basileus ), e.g., the archon basileus in Athens. However, by the Archaic period and the first historical consciousness, most had already become aristocratic oligarchies . It
31374-411: The time of Alexander I of Macedon , the Argead kings of Macedon started to expand into Upper Macedonia , lands inhabited by independent Macedonian tribes like the Lyncestae , Orestae and the Elimiotae and to the west, beyond the Axius river , into Eordaia , Bottiaea , Mygdonia , and Almopia , regions settled by Thracian tribes. To the north of Macedonia lay various non-Greek peoples such as
31563-420: The time when the culture was still heavily Arab and Greek. Governance was by rule of law which promoted justice. Muslims, Jews, Byzantine Greeks , Lombards, and Normans worked together fairly amicably. During this time many extraordinary buildings were constructed. However this situation changed as the Normans imported immigrants from Normandy , England , Lombardy, Piedmont, Provence and Campania to secure
31752-416: The value of a geometric series that sums to infinity with the ratio 1/4. In this two-volume treatise addressed to Dositheus, Archimedes obtains the result of which he was most proud, namely the relationship between a sphere and a circumscribed cylinder of the same height and diameter . The volume is 4 / 3 π r for the sphere, and 2 π r for the cylinder. The surface area
31941-413: The west; Val Demone in the northeast; and Val di Noto in the southeast. As dhimmis , that is as members of a protected class of approved monotheists, the Eastern Orthodox Christians were allowed freedom of religion , but had to pay a tax, the jizya (in lieu of the obligatory alms tax, the zakat , paid by Muslims), and were restricted from active participation in public affairs. By the 11th century,
32130-413: The wind from the Sahara – can be felt. Rainfall is scarce, and in some provinces a water crisis can occur. According to the Regional Agency for Waste and Water, on 10 August 1999, the weather station of Catenanuova (EN) recorded an unofficial maximum temperature of 48.5 °C (119 °F). On 11 August 2021, a new highest temperature record for Europe with a reading of 48.8 °C (119.8 °F)
32319-404: Was Sicily, leading to the Gothic War (535–554) between the Ostrogoths and the Eastern Roman Empire, also known as the Byzantine Empire . Justinian's general Belisarius was assigned to the military task. Sicily was used as a base for the Byzantines to conquer the rest of Italy, including Naples , Rome, and Milan . It took five years before the Ostrogoth capital Ravenna fell in 540. However,
32508-426: Was a notable exception to the rest of Greece, ruled through the whole period by not one, but two hereditary monarchs. This was a form of diarchy . The Kings of Sparta belonged to the Agiads and the Eurypontids, descendants respectively of Eurysthenes and Procles . Both dynasties' founders were believed to be twin sons of Aristodemus , a Heraclid ruler. However, the powers of these kings were held in check by both
32697-460: Was a situation unlike that in most other contemporary societies, which were either tribal or kingdoms ruling over relatively large territories. Undoubtedly, the geography of Greece —divided and sub-divided by hills, mountains, and rivers—contributed to the fragmentary nature of ancient Greece. On the one hand, the ancient Greeks had no doubt that they were "one people"; they had the same religion , same basic culture, and same language. Furthermore,
32886-411: Was a student of Conon of Samos . In Proposition II, Archimedes gives an approximation of the value of pi ( π ), showing that it is greater than 223 / 71 (3.1408...) and less than 22 / 7 (3.1428...). In this treatise, also known as Psammites , Archimedes finds a number that is greater than the grains of sand needed to fill the universe. This book mentions
33075-536: Was also one of the first to apply mathematics to physical phenomena , working on statics and hydrostatics . Archimedes' achievements in this area include a proof of the law of the lever , the widespread use of the concept of center of gravity , and the enunciation of the law of buoyancy known as Archimedes' principle . He is also credited with designing innovative machines , such as his screw pump , compound pulleys , and defensive war machines to protect his native Syracuse from invasion. Archimedes died during
33264-493: Was an astronomer named Phidias. The Sand Reckoner is the only surviving work in which Archimedes discusses his views on astronomy. There are two books to On the Equilibrium of Planes : the first contains seven postulates and fifteen propositions , while the second book contains ten propositions. In the first book, Archimedes proves the law of the lever , which states that: Magnitudes are in equilibrium at distances reciprocally proportional to their weights. Archimedes uses
33453-416: Was asked to determine whether some silver had been substituted by the goldsmith without damaging the crown, so he could not melt it down into a regularly shaped body in order to calculate its density . In this account, Archimedes noticed while taking a bath that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the golden crown's volume . Archimedes
33642-468: Was conquered by the Romans. The Aetolian league grew wary of Roman involvement in Greece, and sided with the Seleucids in the Roman–Seleucid War ; when the Romans were victorious, the league was effectively absorbed into the Republic. Although the Achaean league outlasted both the Aetolian league and Macedon, it was also soon defeated and absorbed by the Romans in 146 BC, bringing Greek independence to an end. The Greek peninsula came under Roman rule during
33831-444: Was defeated and driven out to North Africa. He offered the rule of Sicily to Ziyadat Allah , the Aghlabid Emir of Tunisia , in return for a position as a general and a place of safety. A Muslim army was then sent to the island consisting of Arabs , Berbers , Cretans , and Persians . The Muslim conquest of Sicily was a see-saw affair and met with fierce resistance. It took over a century for Byzantine Sicily to be conquered;
34020-560: Was given by Ibn Hawqal , an Arab merchant who visited Sicily in 950. A walled suburb, called the Al-Kasr (the palace), is the centre of Palermo to this day, with the great Friday mosque on the site of the later Roman cathedral. The suburb of al-Khalisa (modern Kalsa ) contained the Sultan 's palace, baths, a mosque, government offices, and a private prison. Ibn Hawqal estimated there were 7,000 butchers trading in 150 shops. The Muslim rule introduced lemons, oranges and sugar cane, as well as cotton and mulberries for sericulture, and introduced
34209-524: Was in Syracuse ; others grew up at Akragas , Selinunte , Gela , Himera and Zancle . The native Sicani and Sicel peoples became absorbed into the Hellenic culture with relative ease, and the area became part of Magna Graecia along with the coasts of the south of the Italian peninsula , which the Greeks had also colonised. Sicily had fertile soils, and the successful introduction of olives and grape vines fostered profitable trading. Greek culture significantly centered around Greek religion , and
34398-417: Was in permanent settlements founded by Greeks, which formed as independent poleis. The second form was in what historians refer to as emporia ; trading posts which were occupied by both Greeks and non-Greeks and which were primarily concerned with the manufacture and sale of goods. Examples of this latter type of settlement are found at Al Mina in the east and Pithekoussai in the west. From about 750 BC
34587-424: Was preceded by the Greek Dark Ages ( c. 1200 – c. 800 BC ), archaeologically characterised by the protogeometric and geometric styles of designs on pottery. Following the Dark Ages was the Archaic Period , beginning around the 8th century BC, which saw early developments in Greek culture and society leading to the Classical Period from the Persian invasion of Greece in 480 BC until
34776-530: Was related to King Hiero II , the ruler of Syracuse, although Cicero suggests he was of humble origin. In the Sand-Reckoner , Archimedes gives his father's name as Phidias, an astronomer about whom nothing else is known. A biography of Archimedes was written by his friend Heracleides, but this work has been lost, leaving the details of his life obscure. It is unknown, for instance, whether he ever married or had children, or if he ever visited Alexandria , Egypt, during his youth. From his surviving written works, it
34965-417: Was set near the city of Syracuse . Total precipitation is highly variable, generally increasing with elevation. In general, the southern and southeast coast receives the least rainfall (less than 50 cm (20 in)), and the northern and northeastern highlands the most (over 100 cm (39 in)). Sicily is an often-quoted example of man-made deforestation , which has occurred since Roman times when
35154-470: Was so excited by this discovery that he took to the streets naked, having forgotten to dress, crying " Eureka !" ( Greek : "εὕρηκα , heúrēka !, lit. ' I have found [it]! ' ). For practical purposes water is incompressible, so the submerged crown would displace an amount of water equal to its own volume. By dividing the mass of the crown by the volume of water displaced, its density could be obtained; if cheaper and less dense metals had been added,
35343-403: Was to be moved to Syracuse probably cost Constans his life, as he was assassinated in 668. His son Constantine IV succeeded him. A brief usurpation in Sicily by Mezezius was quickly suppressed by this emperor. Contemporary accounts report that the Greek language was widely spoken on the island during this period. In 740 Emperor Leo III the Isaurian transferred Sicily from the jurisdiction of
35532-445: Was under the nominal suzerainty of the Fatimid Caliphate . During the reign of this dynasty revolts by Byzantine Sicilians continuously occurred especially in the east where Greek-speaking Christians predominated. Parts of the island were re-occupied before revolts were quashed. Under the Arab rule the island was divided in three administrative regions , or "vals", roughly corresponding to the three "points" of Sicily: Val di Mazara in
35721-427: Was unified with the Kingdom of Naples into the Kingdom of the Two Sicilies . From the 1282 Sicilian Vespers until the 1860 Expedition of the Thousand , Sicily was ruled by Aragon and then Spain , either in personal union with the crown or by a cadet branch , with the exception of a period of Savoy and then Habsburg rule in 1713–1735. The island became part of the newly unified Italy in 1860 following
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