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130-523: The points of the compass are a set of horizontal, radially arrayed compass directions (or azimuths ) used in navigation and cartography . A compass rose is primarily composed of four cardinal directions — north , east , south , and west —each separated by 90 degrees , and secondarily divided by four ordinal (intercardinal) directions—northeast, southeast, southwest, and northwest—each located halfway between two cardinal directions. Some disciplines such as meteorology and navigation further divide

260-410: A Cartesian system ) is called the pole , and the ray from the pole in the fixed direction is the polar axis . The distance from the pole is called the radial coordinate or radius , and the angle is the angular coordinate , polar angle , or azimuth . In the cylindrical coordinate system, there is a chosen reference axis and a chosen reference plane perpendicular to that axis. The origin of

390-421: A few families and still others lived on isolated farms spread over the countryside. There were also areas where the pattern was a mix of two or more of those systems. Unlike in the late Roman period, there was no sharp break between the legal status of the free peasant and the aristocrat, and it was possible for a free peasant's family to rise into the aristocracy over several generations through military service to

520-503: A guide for helmsmen. Prior to the modern three-figure method of describing directions (using the 360° of a circle), the 32-point compass was used for directions on most ships, especially among European crews. The smallest unit of measure recognized was 'one point', 1/32 of a circle, or 11 + 1 ⁄ 4 °. In the mariner's exercise of "boxing the compass", all thirty-two points of the compass are named in clockwise order. This exercise became more significant as navigation improved and

650-601: A king to rule over them all. By the late sixth century, this arrangement had been replaced by a permanent monarchy, the Kingdom of the Lombards . The invasions brought new ethnic groups to Europe, although some regions received a larger influx of new peoples than others. In Gaul for instance, the invaders settled much more extensively in the north-east than in the south-west. Slavs settled in Central and Eastern Europe and

780-567: A powerful lord. Roman city life and culture changed greatly in the early Middle Ages. Although Italian cities remained inhabited, they contracted significantly in size. Rome, for instance, shrank from a population of hundreds of thousands to around 30,000 by the end of the 6th century. Roman temples were converted into Christian churches and city walls remained in use. In Northern Europe, cities also shrank, while civic monuments and other public buildings were raided for building materials. The establishment of new kingdoms often meant some growth for

910-466: A practical skill rather than a sign of elite status. In the 4th century, Jerome (d. 420) dreamed that God rebuked him for spending more time reading Cicero than the Bible . By the 6th century, Gregory of Tours (d. 594) had a similar dream, but instead of being chastised for reading Cicero, he was chastised for learning shorthand . By the late 6th century, the principal means of religious instruction in

1040-618: A reference plane that passes through the origin and is orthogonal to the zenith, and a fixed reference direction in that plane. Middle Ages In the history of Europe , the Middle Ages or medieval period lasted approximately from the 5th to the late 15th centuries, similarly to the Post-classical period of global history . It began with the fall of the Western Roman Empire and transitioned into

1170-474: A small foothold in southern Spain. Justinian's reconquests have been criticised by historians for overextending his realm and setting the stage for the early Muslim conquests , but many of the difficulties faced by Justinian's successors were due not just to over-taxation to pay for his wars but to the essentially civilian nature of the empire, which made raising troops difficult. In the Eastern Empire

1300-410: Is " Quarto di Tramontana verso Greco "; and northeast-by-north is " Quarto di Greco verso Tramontana ". The table below shows how the 32 compass points are named. Each point has an angular range of 11 + 1 ⁄ 4 degrees where the azimuth midpoint is the horizontal angular direction (clockwise from north) of the given compass bearing; minimum is the lower (counterclockwise) angular limit of

1430-411: Is "Greco-Levante"; SSE is "Ostro-Scirocco", etc. The quarter winds are expressed with an Italian phrase, " Quarto di X verso Y" ( pronounced [ˈkwarto di X ˈvɛrso Y ] one quarter from X towards Y), or "X al Y" (X to Y) or "X per Y" (X by Y). There are no irregularities to trip over; the closest principal wind always comes first, the more distant one second, for example: north-by-east

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1560-641: Is given by where θ is the angle ∠ P 1 P 2 P 3 . This formula uses the law of sines . If the three points are given by their coordinates ( x 1 , y 1 ) , ( x 2 , y 2 ) , and ( x 3 , y 3 ) , the radius can be expressed as The radius r of a regular polygon with n sides of length s is given by r = R n s , where R n = 1 / ( 2 sin ⁡ π n ) . {\displaystyle R_{n}=1\left/\left(2\sin {\frac {\pi }{n}}\right)\right..} Values of R n for small values of n are given in

1690-672: Is no universally agreed upon end date. Depending on the context, events such as the conquest of Constantinople by the Turks in 1453, Christopher Columbus 's first voyage to the Americas in 1492, or the Protestant Reformation in 1517 are sometimes used. English historians often use the Battle of Bosworth Field in 1485 to mark the end of the period. For Spain, dates commonly used are the death of King Ferdinand II in 1516,

1820-539: The fyrd , which were led by the local elites. In military technology, one of the main changes was the return of the crossbow , which had been known in Roman times and reappeared as a military weapon during the last part of the Early Middle Ages. Another change was the introduction of the stirrup, which increased the effectiveness of cavalry as shock troops. A technological advance that had implications beyond

1950-717: The Alans , Vandals , and Suevi crossed into Gaul ; over the next three years they spread across Gaul and in 409 crossed the Pyrenees Mountains into modern-day Spain. The Migration Period began, when various peoples, initially largely Germanic peoples , moved across Europe. The Franks , Alemanni , and the Burgundians all ended up in northern Gaul while the Angles , Saxons , and Jutes settled in Britain , and

2080-529: The Benedictine Rule for Western monasticism during the 6th century, detailing the administrative and spiritual responsibilities of a community of monks led by an abbot . Monks and monasteries had a deep effect on the religious and political life of the Early Middle Ages, in various cases acting as land trusts for powerful families, centres of propaganda and royal support in newly conquered regions, and bases for missions and proselytisation. They were

2210-697: 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. During the High Middle Ages, which began after 1000, the population of Europe increased greatly as technological and agricultural innovations allowed trade to flourish and

2340-531: The Desert Fathers of Egypt and Syria . Most European monasteries were of the type that focuses on community experience of the spiritual life, called cenobitism , which was pioneered by Pachomius (d. 348) in the 4th century. Monastic ideals spread from Egypt to Western Europe in the 5th and 6th centuries through hagiographical literature such as the Life of Anthony . Benedict of Nursia (d. 547) wrote

2470-584: The Gregorian chant in liturgical music for the churches. An important activity for scholars during this period was the copying, correcting, and dissemination of basic works on religious and secular topics, with the aim of encouraging learning. New works on religious topics and schoolbooks were also produced. Grammarians of the period modified the Latin language, changing it from the Classical Latin of

2600-714: The Macedonian dynasty . Commerce revived and the emperors oversaw the extension of a uniform administration to all the provinces. The military was reorganised, which allowed the emperors John I (r. 969–976) and Basil II (r. 976–1025) to expand the frontiers of the empire on all fronts. The imperial court was the centre of a revival of classical learning, a process known as the Macedonian Renaissance . Writers such as John Geometres ( fl. early 10th century) composed new hymns, poems, and other works. Missionary efforts by both Eastern and Western clergy resulted in

2730-486: The Medieval Warm Period climate change allowed crop yields to increase. Manorialism , the organisation of peasants into villages that owed rent and labour services to the nobles , and feudalism , the political structure whereby knights and lower-status nobles owed military service to their overlords in return for the right to rent from lands and manors , were two of the ways society was organized in

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2860-590: The Middle Ages (with no obvious connection to the twelve classical compass winds of the ancient Greeks and Romans). The traditional mariner's wind names were expressed in Italian , or more precisely, the Italianate Mediterranean lingua franca common among sailors in the 13th and 14th centuries, which was principally composed of Genoese ( Ligurian ), mixed with Venetian , Sicilian , Provençal , Catalan , Greek , and Arabic terms from around

2990-700: 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 centralized authority, invasions, and mass migrations of tribes , which had begun in Late Antiquity , continued into

3120-482: The clockwise direction and "CCW" counterclockwise . The final three columns show three common naming conventions: No "by" avoids the use of "by" with fractional points. Colour coding shows whether each of the three naming systems matches the "CW" or "CCW" column. The traditional compass rose of eight winds (and its 16-wind and 32-wind derivatives) was invented by seafarers in the Mediterranean Sea during

3250-403: The radial distance or radius , while the angular coordinate is sometimes referred to as the angular position or as the azimuth . The radius and the azimuth are together called the polar coordinates , as they correspond to a two-dimensional polar coordinate system in the plane through the point, parallel to the reference plane. The third coordinate may be called the height or altitude (if

3380-468: The radius of a graph is the minimum over all vertices u of the maximum distance from u to any other vertex of the graph. The radius of the circle with perimeter ( circumference ) C is For many geometric figures, the radius has a well-defined relationship with other measures of the figure. The radius of a circle with area A is The radius of the circle that passes through the three non- collinear points P 1 , P 2 , and P 3

3510-468: The 17th-century German historian Christoph Cellarius divided history into three periods: ancient, medieval, and modern. The most commonly given starting point for the Middle Ages is around 500, with the date of 476 first used by Bruni. Later starting dates are sometimes used in the outer parts of Europe. For Europe as a whole, 1500 is often considered to be the end of the Middle Ages, but there

3640-510: The 32-wind compass rose comes from the eight principal winds, eight half-winds, and sixteen quarter-winds combined, with each compass point at an 11 + 1 ⁄ 4 ° angle from the next. By the middle of the 18th century, the 32-point system had been further extended by using half- and quarter-points to give a total of 128 directions. These fractional points are named by appending, for example, ⁠ 1 / 4 ⁠ east, ⁠ 1 / 2 ⁠ east, or ⁠ 3 / 4 ⁠ east to

3770-478: The 5th and the 7th centuries, going first to England and Scotland and then on to the continent. Under such monks as Columba (d. 597) and Columbanus (d. 615), they founded monasteries, taught in Latin and Greek, and authored secular and religious works. The Early Middle Ages witnessed the rise of monasticism in the West. The shape of European monasticism was determined by traditions and ideas that originated with

3900-731: The 5th century. The Eastern Empire was marked by closer relations between the political state and Christian Church, with doctrinal matters assuming an importance in Eastern politics that they did not have in Western Europe. Legal developments included the codification of Roman law ; the first effort—the Codex Theodosianus —was completed in 438. Under Emperor Justinian (r. 527–565), another compilation took place—the Corpus Juris Civilis . Justinian also oversaw

4030-685: The 6th and 7th centuries, all of them ruled by the Merovingian dynasty, who were descended from Clovis. The 7th century was a tumultuous period of wars between Austrasia and Neustria. Such warfare was exploited by Pippin (d. 640), the Mayor of the Palace for Austrasia who became the power behind the Austrasian throne. Later members of his family inherited the office, acting as advisers and regents. One of his descendants, Charles Martel (d. 741), won

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4160-651: The Arabs. The migrations and invasions of the 4th and 5th centuries disrupted trade networks around the Mediterranean. African goods stopped being imported into Europe, first disappearing from the interior and by the 7th century found only in a few cities such as Rome or Naples . By the end of the 7th century, under the impact of the Muslim conquests , African products were no longer found in Western Europe. The replacement of goods from long-range trade with local products

4290-536: The Bald received the western Frankish lands, comprising most of modern-day France. Charlemagne's grandsons and great-grandsons divided their kingdoms between their descendants, eventually causing all internal cohesion to be lost. In 987 the Carolingian dynasty was replaced in the western lands, with the crowning of Hugh Capet (r. 987–996) as king. In the eastern lands the dynasty had died out earlier, in 911, with

4420-551: The Balkan Peninsula. The settlement of peoples was accompanied by changes in languages. Latin , the literary language of the Western Roman Empire, was gradually replaced by vernacular languages which evolved from Latin, but were distinct from it, collectively known as Romance languages . These changes from Latin to the new languages took many centuries. Greek remained the language of the Byzantine Empire, but

4550-643: The Battle of Poitiers in 732, halting the advance of Muslim armies across the Pyrenees. Great Britain was divided into small states dominated by the kingdoms of Northumbria , Mercia , Wessex , and East Anglia which descended from the Anglo-Saxon invaders. Smaller kingdoms in present-day Wales and Scotland were still under the control of the native Britons and Picts . Ireland was divided into even smaller political units, usually known as tribal kingdoms, under

4680-577: The Byzantine Empire, as the assumption of the imperial title by the Carolingians asserted their equivalence to the Byzantine state. There were several differences between the newly established Carolingian Empire and both the older Western Roman Empire and the concurrent Byzantine Empire. The Frankish lands were rural in character, with only a few small cities. Most of the people were peasants settled on small farms. Little trade existed and much of that

4810-523: The Byzantine Empire, which he sealed with the marriage of his son Otto II (r. 967–983) to Theophanu (d. 991), daughter of an earlier Byzantine Emperor Romanos II (r. 959–963). By the late 10th century Italy had been drawn into the Ottonian sphere after a period of instability; Otto III (r. 996–1002) spent much of his later reign in the kingdom. The western Frankish kingdom was more fragmented, and although kings remained nominally in charge, much of

4940-648: The Christian period as nova (or "new"). Petrarch regarded the post-Roman centuries as " dark " compared to the "light" of classical antiquity . Leonardo Bruni was the first historian to use tripartite periodisation in his History of the Florentine People (1442), with a middle period "between the fall of the Roman Empire and the revival of city life sometime in late eleventh and twelfth centuries". Tripartite periodisation became standard after

5070-660: The Church had widened to the extent that the cultural and religious differences were greater than the similarities. The formal break, known as the East–West Schism , came in 1054, when the papacy and the patriarchy of Constantinople clashed over papal supremacy and excommunicated each other, which led to the division of Christianity into two Churches—the Western branch became the Roman Catholic Church and

5200-499: The Church had become music and art rather than the book. Most intellectual efforts went towards imitating classical scholarship, but some original works were created, along with now-lost oral compositions. The writings of Sidonius Apollinaris (d. 489), Cassiodorus (d. c.  585 ), and Boethius (d. c. 525) were typical of the age. Changes also took place among laymen, as aristocratic culture focused on great feasts held in halls rather than on literary pursuits. Clothing for

5330-704: The Dnieper River in modern Ukraine to the Adriatic Sea. By 1018, the last Bulgarian nobles had surrendered to the Byzantine Empire. Few large stone buildings were constructed between the Constantinian basilicas of the 4th century and the 8th century, although many smaller ones were built during the 6th and 7th centuries. By the beginning of the 8th century, the Carolingian Empire revived the basilica form of architecture. One feature of

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5460-585: The Early Middle Ages are mostly illuminated manuscripts and carved ivories , originally made for metalwork that has since been melted down. Objects in precious metals were the most prestigious form of art, but almost all are lost except for a few crosses such as the Cross of Lothair , several reliquaries , and finds such as the Anglo-Saxon burial at Sutton Hoo and the hoards of Gourdon from Merovingian France, Guarrazar from Visigothic Spain and Nagyszentmiklós near Byzantine territory. There are survivals from

5590-715: The Early Middle Ages. 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,

5720-530: The Eastern branch the Eastern Orthodox Church . The ecclesiastical structure of the Roman Empire survived the movements and invasions in the west mostly intact, but the papacy was little regarded, and few of the Western bishops looked to the bishop of Rome for religious or political leadership. Many of the popes prior to 750 were more concerned with Byzantine affairs and Eastern theological controversies. The register, or archived copies of

5850-538: The Eastern emperors to pay tribute. They remained a strong power until 796. An additional problem to face the empire came as a result of the involvement of Emperor Maurice (r. 582–602) in Persian politics when he intervened in a succession dispute . This led to a period of peace, but when Maurice was overthrown, the Persians invaded and during the reign of Emperor Heraclius (r. 610–641) controlled large chunks of

5980-492: The European population remained rural peasants. Many were no longer settled in isolated farms but had gathered into small communities, usually known as manors or villages. These peasants were often subject to noble overlords and owed them rents and other services, in a system known as manorialism . There remained a few free peasants throughout this period and beyond, with more of them in the regions of Southern Europe than in

6110-733: The Frankish King Charles the Simple (r. 898–922) to settle in what became Normandy . The eastern parts of the Frankish kingdoms, especially Germany and Italy, were under continual Magyar assault until the invader's defeat at the Battle of Lechfeld in 955. The breakup of the Abbasid dynasty meant that the Islamic world fragmented into smaller political states, some of which began expanding into Italy and Sicily, as well as over

6240-578: The Franks and Celtic Britons set up small polities. Francia was centred in northern Gaul, and the first king of whom much is known is Childeric I (d. 481). His grave was discovered in 1653 and is remarkable for its grave goods , which included weapons and a large quantity of gold. Under Childeric's son Clovis I (r. 509–511), the founder of the Merovingian dynasty , the Frankish kingdom expanded and converted to Christianity. The Britons, related to

6370-685: The German tried to annex all of East Francia. Louis the Pious died in 840, with the empire still in chaos. A three-year civil war followed his death. By the Treaty of Verdun (843), a kingdom between the Rhine and Rhone rivers was created for Lothair to go with his lands in Italy, and his imperial title was recognised. Louis the German was in control of Bavaria and the eastern lands in modern-day Germany. Charles

6500-700: The Great (d. 526) and set up a kingdom marked by its co-operation between the Italians and the Ostrogoths, at least until the last years of Theodoric's reign. The Burgundians settled in Gaul, and after an earlier realm was destroyed by the Huns in 436, formed a new kingdom in the 440s. Between today's Geneva and Lyon , it grew to become the realm of Burgundy in the late 5th and early 6th centuries. Elsewhere in Gaul,

6630-560: The High Middle Ages. This period also saw the collapse of the unified Christian church, with the East-West Schism of 1054 . The Crusades , first preached in 1095, were military attempts by Western European Christians to regain control of the Holy Land from Muslims . Kings became the heads of centralised nation-states , reducing crime and violence but making the ideal of a unified Christendom more distant. Intellectual life

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6760-403: The Italian peninsula was conquered by the Ostrogoths . The Eastern Roman Empire, often referred to as the Byzantine Empire after the fall of its western counterpart, had little ability to assert control over the lost western territories. The Byzantine emperors maintained a claim over the territory, but while none of the new kings in the west dared to elevate himself to the position of emperor of

6890-619: The Late Middle Ages and beginning the early modern period . The Middle Ages is one of the three major periods in the most enduring scheme for analysing European history : classical civilisation or Antiquity , the Middle Ages and the Modern Period . The "Middle Ages" first appears in Latin in 1469 as media tempestas or "middle season". In early usage, there were many variants, including medium aevum , or "middle age", first recorded in 1604, and media saecula , or "middle centuries", first recorded in 1625. The adjective "medieval" (or sometimes "mediaeval" or "mediæval"), meaning pertaining to

7020-439: The Lombards, which freed the papacy from the fear of Lombard conquest and marked the beginnings of the Papal States . The coronation of Charlemagne as emperor on Christmas Day 800 is regarded as a turning point in medieval history, marking a return of the Western Roman Empire, since the new emperor ruled over much of the area previously controlled by the Western emperors. It also marks a change in Charlemagne's relationship with

7150-488: The Mediterranean basin. This Italianate patois was used to designate the names of the principal winds on the compass rose found in mariners' compasses and portolan charts of the 14th and 15th centuries. The traditional names of the eight principal winds are: Local spelling variations are far more numerous than listed, e.g. Tramutana, Gregale, Grecho, Sirocco, Xaloc, Lebeg, Libezo, Leveche, Mezzodi, Migjorn, Magistro, Mestre, etc. Traditional compass roses will typically have

7280-405: The Mediterranean, pottery remained prevalent and appears to have been traded over medium-range networks, not just produced locally. The various Germanic states in the west all had coinages that imitated existing Roman and Byzantine forms. Gold continued to be minted until the end of the 7th century in 693-94 when it was replaced by silver in the Merovingian kingdom. The basic Frankish silver coin

7410-411: The Middle Ages, derives from medium aevum . Medieval writers divided history into periods such as the " Six Ages " or the " Four Empires ", and considered their time to be the last before the end of the world. When referring to their own times, they spoke of them as being "modern". In the 1330s, the Italian humanist and poet Petrarch referred to pre-Christian times as antiqua (or "ancient") and to

7540-496: The Middle East than Europe, losing control of sections of the Muslim lands. Umayyad descendants took over the Iberian Peninsula, the Aghlabids controlled North Africa, and the Tulunids became rulers of Egypt. By the middle of the 8th century, new trading patterns were emerging in the Mediterranean; trade between the Franks and the Arabs replaced the old Roman economy . Franks traded timber, furs, swords and slaves in return for silks and other fabrics, spices, and precious metals from

7670-501: The Pyrenees into the southern parts of the Frankish kingdoms. Efforts by local kings to fight the invaders led to the formation of new political entities. In Anglo-Saxon England , King Alfred the Great (r. 871–899) came to an agreement with the Viking invaders in the late 9th century, resulting in Danish settlements in Northumbria, Mercia, and parts of East Anglia. By the middle of the 10th century, Alfred's successors had conquered Northumbria, and restored English control over most of

7800-415: The Rhine and eastwards, leaving Charles West Francia with the empire to the west of the Rhineland and the Alps. Louis the German (d. 876), the middle child, who had been rebellious to the last, was allowed to keep Bavaria under the suzerainty of his elder brother. The division was disputed. Pepin II of Aquitaine (d. after 864), the emperor's grandson, rebelled in a contest for Aquitaine , while Louis

7930-515: The Roman Empire into a more flexible form to fit the needs of the Church and government. By the reign of Charlemagne, the language had so diverged from the classical Latin that it was later called Medieval Latin . Charlemagne planned to continue the Frankish tradition of dividing his kingdom between all his heirs, but was unable to do so as only one son, Louis the Pious (r. 814–840), was still alive by 813. Just before Charlemagne died in 814, he crowned Louis as his successor. Louis's reign of 26 years

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8060-443: The Romans and the invaders are often similar, and tribal items were often modelled on Roman objects. Much of the scholarly and written culture of the new kingdoms was also based on Roman intellectual traditions. An important difference was the gradual loss of tax revenue by the new polities. Many of the new political entities no longer supported their armies through taxes, instead relying on granting them land or rents. This meant there

8190-428: The United States Navy to box from north and south toward east and west, with the exception that divisions adjacent to a cardinal or inter-cardinal point are always referred to that point." The Royal Navy used the additional "rule that quarter points were never read from a point beginning and ending with the same letter." Compass roses very rarely named the fractional points and only showed small, unlabelled markers as

8320-423: The Vandals went on to cross the strait of Gibraltar after which they conquered the province of Africa . In the 430s the Huns began invading the empire; their king Attila (r. 434–453) led invasions into the Balkans in 442 and 447, Gaul in 451, and Italy in 452. The Hunnic threat remained until Attila's death in 453, when the Hunnic confederation he led fell apart. These invasions by the tribes completely changed

8450-455: The West were not uniform; some areas had greatly fragmented landholding patterns, but in other areas large contiguous blocks of land were the norm. These differences allowed for a wide variety of peasant societies, some dominated by aristocratic landholders and others having a great deal of autonomy. Land settlement also varied greatly. Some peasants lived in large settlements that numbered as many as 700 inhabitants. Others lived in small groups of

8580-453: The acceptance of figurative monumental sculpture in Christian art , and by the end of the period near life-sized figures such as the Gero Cross were common in important churches. During the later Roman Empire, the principal military developments were attempts to create an effective cavalry force as well as the continued development of highly specialised types of troops. The creation of heavily armoured cataphract -type soldiers as cavalry

8710-417: The basilica is the use of a transept , or the "arms" of a cross-shaped building that are perpendicular to the long nave . Other new features of religious architecture include the crossing tower and a monumental entrance to the church , usually at the west end of the building. Carolingian art was produced for a small group of figures around the court, and the monasteries and churches they supported. It

8840-496: The break with classical antiquity was not complete. 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 pagan Europe continued. The Franks , under

8970-407: The city of Byzantium as the newly renamed eastern capital, Constantinople . Diocletian's reforms strengthened the governmental bureaucracy, reformed taxation, and strengthened the army, which bought the empire time but did not resolve the problems it was facing: excessive taxation, a declining birthrate, and pressures on its frontiers, among others. Civil war between rival emperors became common in

9100-515: The compass point; and maximum is the upper (clockwise) angular limit of the compass point. Navigation texts dating from the Yuan , Ming , and Qing dynasties in China use a 24-pointed compass with named directions. These are based on the twelve Earthly Branches , which also form the basis of the Chinese zodiac. When a single direction is specified, it may be prefaced by the character 單 (meaning single) or 丹 . Headings mid-way in-between are compounds as in English. For instance, 癸子 refers to

9230-433: The compass with additional azimuths. Within European tradition, a fully defined compass has 32 "points" (and any finer subdivisions are described in fractions of points). Compass points or compass directions are valuable in that they allow a user to refer to a specific azimuth in a colloquial fashion, without having to compute or remember degrees. The names of the compass point directions follow these rules: In summary,

9360-599: The conquest of North Africa sundered maritime connections between those areas. Increasingly, the Byzantine Church differed in language, practices, and liturgy from the Western Church. The Eastern Church used Greek instead of the Western Latin. Theological and political differences emerged, and by the early and middle 8th century issues such as iconoclasm , clerical marriage , and state control of

9490-739: The construction of the Hagia Sophia in Constantinople and the reconquest of North Africa from the Vandals and Italy from the Ostrogoths, under Belisarius (d. 565). The conquest of Italy was not complete, as a deadly outbreak of plague in 542 led to the rest of Justinian's reign concentrating on defensive measures rather than further conquests. At the Emperor's death, the Byzantines had control of most of Italy , North Africa, and

9620-551: The control of kings. There were perhaps as many as 150 local kings in Ireland, of varying importance. The Carolingian dynasty , as the successors to Charles Martel are known, officially took control of the kingdoms of Austrasia and Neustria in a coup of 753 led by Pippin III (r. 752–768). A contemporary chronicle claims that Pippin sought, and gained, authority for this coup from Pope Stephen II (pope 752–757). Pippin's takeover

9750-638: The conversion of the Moravians , Bulgars , Bohemians , Poles , Magyars, and Slavic inhabitants of the Kievan Rus' . These conversions contributed to the founding of political states in the lands of those peoples—the states of Moravia , Bulgaria , Bohemia , Poland , Hungary, and the Kievan Rus'. Bulgaria, which was founded around 680, at its height reached from Budapest to the Black Sea and from

9880-753: The death of Louis the Child , and the selection of the unrelated Conrad I (r. 911–918) as king. The breakup of the Carolingian Empire was accompanied by invasions, migrations, and raids by external foes. The Atlantic and northern shores were harassed by the Vikings , who also raided the British Isles and settled there as well as in Iceland. In 911, the Viking chieftain Rollo (d. c. 931) received permission from

10010-401: The death of Queen Isabella I of Castile in 1504, or the conquest of Granada in 1492. Historians from Romance-speaking countries tend to divide the Middle Ages into two parts: an earlier "High" and later "Low" period. English-speaking historians, following their German counterparts, generally subdivide the Middle Ages into three intervals: "Early", "High", and "Late". In the 19th century,

10140-407: The direction halfway between point 子 and point 癸 , or 7 + 1 ⁄ 2 °. This technique is referred to as a double-needle ( 雙針 ) compass. Radius If an object does not have a center, the term may refer to its circumradius , the radius of its circumscribed circle or circumscribed sphere . In either case, the radius may be more than half the diameter, which is usually defined as

10270-578: The disorder, was killed fighting the Goths at the Battle of Adrianople on 9 August 378. In addition to the threat from such tribal confederacies in the north, internal divisions within the empire, especially within the Christian Church, caused problems. In 400, the Visigoths invaded the Western Roman Empire and, although briefly forced back from Italy, in 410 sacked the city of Rome . In 406

10400-442: The early Carolingian period, with a growing dominance of elite heavy cavalry. The use of militia-type levies of the free population declined over the Carolingian period. Although much of the Carolingian armies were mounted, a large proportion during the early period appear to have been mounted infantry , rather than true cavalry. One exception was Anglo-Saxon England, where the armies were still composed of regional levies, known as

10530-531: The elites was richly embellished with jewels and gold. Lords and kings supported entourages of fighters who formed the backbone of the military forces. Family ties within the elites were important, as were the virtues of loyalty, courage, and honour. These ties led to the prevalence of the feud in aristocratic society, examples of which included those related by Gregory of Tours that took place in Merovingian Gaul. Most feuds seem to have ended quickly with

10660-591: The emergence of Islam in Arabia during the lifetime of Muhammad (d. 632). After his death, Islamic forces conquered much of the Eastern Roman Empire and Persia, starting with Syria in 634–635, continuing with Persia between 637 and 642, reaching Egypt in 640–641, North Africa in the later seventh century, and the Iberian Peninsula in 711. By 714, Islamic forces controlled much of

10790-403: The empire than tax-payers. The Emperor Diocletian (r. 284–305) split the empire into separately administered eastern and western halves in 286; the empire was not considered divided by its inhabitants or rulers, as legal and administrative promulgations in one division were considered valid in the other. In 330, after a period of civil war, Constantine the Great (r. 306–337) refounded

10920-573: The empire to Christianity , a gradual process that lasted from the 2nd to the 5th centuries. In 376, the Goths , fleeing from the Huns , received permission from Emperor Valens (r. 364–378) to settle in the Roman province of Thracia in the Balkans . The settlement did not go smoothly, and when Roman officials mishandled the situation, the Goths began to raid and plunder. Valens, attempting to put down

11050-447: The empire, including Egypt, Syria, and Anatolia until Heraclius' successful counterattack. In 628 the empire secured a peace treaty and recovered all of its lost territories. In Western Europe, some of the older Roman elite families died out while others became more involved with ecclesiastical than secular affairs. Values attached to Latin scholarship and education mostly disappeared, and while literacy remained important, it became

11180-486: The empire. Such movements were aided by the refusal of the Western Roman elites to support the army or pay the taxes that would have allowed the military to suppress the migration. The emperors of the 5th century were often controlled by military strongmen such as Stilicho (d. 408), Aetius (d. 454), Aspar (d. 471), Ricimer (d. 472), or Gundobad (d. 516), who were partly or fully of non-Roman background. When

11310-454: The entire Middle Ages were often referred to as the " Dark Ages ", but with the adoption of these subdivisions, use of this term was restricted to the Early Middle Ages, at least among historians. The Roman Empire reached its greatest territorial extent during the 2nd century AD; the following two centuries witnessed the slow decline of Roman control over its outlying territories. Economic issues, including inflation, and external pressure on

11440-635: The frontiers combined to create the Crisis of the Third Century , with emperors coming to the throne only to be rapidly replaced by new usurpers. Military expenses increased steadily during the 3rd century, mainly in response to the war with the Sasanian Empire , which revived in the middle of the 3rd century. The army doubled in size, and cavalry and smaller units replaced the Roman legion as

11570-523: The half- and quarter-point system increased the number of directions to include in the 'boxing'. Points remained the standard unit until switching to the three-figure degree method. These points were also used for relative measurement, so that an obstacle might be noted as 'two points off the starboard bow', meaning two points clockwise of straight ahead, 22 + 1 ⁄ 2 ° This relative measurement may still be used in shorthand on modern ships, especially for handoffs between outgoing and incoming helmsmen, as

11700-451: The imperial officials called missi dominici , who served as roving inspectors and troubleshooters. Charlemagne's court in Aachen was the centre of the cultural revival sometimes referred to as the " Carolingian Renaissance ". Literacy increased, as did development in the arts, architecture and jurisprudence, as well as liturgical and scriptural studies. The English monk Alcuin (d. 804)

11830-399: The initials T, G, L, S, O, L, P, and M on the main points. Portolan charts also colour-coded the compass winds: black for the eight principal winds, green for the eight half-winds, and red for the sixteen quarter-winds. Each half-wind name is simply a combination of the two principal winds that it bisects, with the shortest name usually placed first, for example: NNE is "Greco-Tramontana"; ENE

11960-415: The king of the united Austrasia and Neustria. Charles, more often known as Charles the Great or Charlemagne , embarked upon a programme of systematic expansion in 774 that unified a large portion of Europe, eventually controlling modern-day France, northern Italy, and Saxony . In the wars that lasted beyond 800, he rewarded allies with war booty and command over parcels of land. In 774, Charlemagne conquered

12090-679: The large brooches in fibula or penannular form that were a key piece of personal adornment for elites, including the Irish Tara Brooch . Highly decorated books were mostly Gospel Books and these have survived in larger numbers , including the Insular Book of Kells , the Book of Lindisfarne , and the imperial Codex Aureus of St. Emmeram , which is one of the few to retain its " treasure binding " of gold encrusted with jewels. Charlemagne's court seems to have been responsible for

12220-476: The letters, of Pope Gregory the Great (pope 590–604) survived, and of those more than 850 letters, the vast majority were concerned with affairs in Italy or Constantinople. The only part of Western Europe where the papacy had influence was Britain, where Gregory had sent the Gregorian mission in 597 to convert the Anglo-Saxons to Christianity. Irish missionaries were most active in Western Europe between

12350-417: The line of Western emperors ceased, many of the kings who replaced them were from the same background. Intermarriage between the new kings and the Roman elites was common. This led to a fusion of Roman culture with the customs of the invading tribes, including the popular assemblies that allowed free male tribal members more say in political matters than was common in the Roman state. Material artefacts left by

12480-408: The loss of granularity is less significant than the brevity and simplicity of the summary. The table below shows how each of the 128 directions are named. The first two columns give the number of points and degrees clockwise from north. The third gives the equivalent bearing to the nearest degree from north or south towards east or west. The "CW" column gives the fractional-point bearings increasing in

12610-517: The main and sometimes only outposts of education and literacy in a region. Many of the surviving manuscripts of the Latin classics were copied in monasteries in the Early Middle Ages. Monks were also the authors of new works, including history, theology, and other subjects, written by authors such as Bede (d. 735), a native of northern England who wrote in the late 7th and early 8th centuries. The Frankish kingdom in northern Gaul split into kingdoms called Austrasia , Neustria , and Burgundy during

12740-410: The main tactical unit. The need for revenue led to increased taxes and a decline in numbers of the curial , or landowning, class, and decreasing numbers of them willing to shoulder the burdens of holding office in their native towns. More bureaucrats were needed in the central administration to deal with the needs of the army, which led to complaints from civilians that there were more tax-collectors in

12870-402: The maximum distance between any two points of the figure. The inradius of a geometric figure is usually the radius of the largest circle or sphere contained in it. The inner radius of a ring, tube or other hollow object is the radius of its cavity. For regular polygons , the radius is the same as its circumradius. The inradius of a regular polygon is also called apothem . In graph theory ,

13000-467: The middle of the 4th century, diverting soldiers from the empire's frontier forces and allowing invaders to encroach. For much of the 4th century, Roman society stabilised in a new form that differed from the earlier classical period , with a widening gulf between the rich and poor, and a decline in the vitality of the smaller towns. Another change was the Christianisation , or conversion of

13130-543: The migrations of the Slavs added Slavic languages to Eastern Europe. As Western Europe witnessed the formation of new kingdoms, the Eastern Roman Empire remained intact and experienced an economic revival that lasted into the early 7th century. There were fewer invasions of the eastern section of the empire; most occurred in the Balkans. Peace with the Sasanian Empire , the traditional enemy of Rome, lasted throughout most of

13260-464: The military was the horseshoe , which allowed horses to be used in rocky terrain. The High Middle Ages was a period of tremendous expansion of population . The estimated population of Europe grew from 35 to 80 million between 1000 and 1347, although the exact causes remain unclear: improved agricultural techniques, the decline of slaveholding, a more clement climate and the lack of invasion have all been suggested. As much as 90 per cent of

13390-404: The name of one of the 32 points. Each of the 96 fractional points can be named in two ways, depending on which of the two adjoining whole points is used, for example, N ⁠ 3 / 4 ⁠ E is equivalent to NbE ⁠ 1 / 4 ⁠ N. Either form is easily understood, but alternative conventions as to correct usage developed in different countries and organisations. "It is the custom in

13520-849: The natives of Britannia  – modern-day Great Britain – settled in what is now Brittany . Other monarchies were established by the Visigothic Kingdom in the Iberian Peninsula , the Suebi in northwestern Iberia, and the Vandal Kingdom in North Africa . In the sixth century, the Lombards settled in Northern Italy , replacing the Ostrogothic kingdom with a grouping of duchies that occasionally selected

13650-545: The payment of some sort of compensation . Women took part in aristocratic society mainly in their roles as wives and mothers of men, with the role of mother of a ruler being especially prominent in Merovingian Gaul. In Anglo-Saxon society the lack of many child rulers meant a lesser role for women as queen mothers, but this was compensated for by the increased role played by abbesses of monasteries. Only in Italy does it appear that women were always considered under

13780-587: The peninsula in a region they called Al-Andalus . The Islamic conquests reached their peak in the mid-eighth century. The defeat of Muslim forces at the Battle of Tours in 732 led to the reconquest of southern France by the Franks, but the main reason for the halt of Islamic growth in Europe was the overthrow of the Umayyad Caliphate and its replacement by the Abbasid Caliphate . The Abbasids moved their capital to Baghdad and were more concerned with

13910-408: The political and demographic nature of what had been the Western Roman Empire. By the end of the 5th century the western section of the empire was divided into smaller political units, ruled by the tribes that had invaded in the early part of the century. The deposition of the last emperor of the west, Romulus Augustulus , in 476 has traditionally marked the end of the Western Roman Empire. By 493

14040-532: The political power devolved to the local lords. Missionary efforts to Scandinavia during the 9th and 10th centuries helped strengthen the growth of kingdoms such as Sweden , Denmark , and Norway , which gained power and territory. Some kings converted to Christianity, although not all by 1000. Scandinavians also expanded and colonised throughout Europe. Besides the settlements in Ireland, England, and Normandy, further settlement took place in what became Russia and Iceland . Swedish traders and raiders ranged down

14170-419: The protection and control of a male relative. Peasant society is much less documented than the nobility. Most of the surviving information available to historians comes from archaeology ; few detailed written records documenting peasant life remain from before the 9th century. Most of the descriptions of the lower classes come from either law codes or writers from the upper classes. Landholding patterns in

14300-411: The reference plane is considered horizontal), longitudinal position , or axial position . In a spherical coordinate system, the radius describes the distance of a point from a fixed origin. Its position if further defined by the polar angle measured between the radial direction and a fixed zenith direction, and the azimuth angle, the angle between the orthogonal projection of the radial direction on

14430-525: The rivers of the Russian steppe, and even attempted to seize Constantinople in 860 and 907 . Christian Spain, initially driven into a small section of the peninsula in the north, expanded slowly south during the 9th and 10th centuries, establishing the kingdoms of Asturias and León . In Eastern Europe, Byzantium revived its fortunes under Emperor Basil I (r. 867–886) and his successors Leo VI (r. 886–912) and Constantine VII (r. 913–959), members of

14560-668: The slow infiltration of the Balkans by the Slavs added a further difficulty for Justinian's successors. It began gradually, but by the late 540s Slavic tribes were in Thrace and Illyrium , and had defeated an imperial army near Adrianople in 551. In the 560s the Avars began to expand from their base on the north bank of the Danube ; by the end of the 6th-century, they were the dominant power in Central Europe and routinely able to force

14690-697: The southern part of Great Britain. In northern Britain, Kenneth MacAlpin (d. c. 860) united the Picts and the Scots into the Kingdom of Alba . In the early 10th century, the Ottonian dynasty had established itself in Germany , and was engaged in driving back the Magyars. Its efforts culminated in the coronation in 962 of Otto I (r. 936–973) as Holy Roman Emperor . In 972, he secured recognition of his title by

14820-417: The system is the point where all three coordinates can be given as zero. This is the intersection between the reference plane and the axis. The axis is variously called the cylindrical or longitudinal axis, to differentiate it from the polar axis , which is the ray that lies in the reference plane, starting at the origin and pointing in the reference direction. The distance from the axis may be called

14950-412: The table. If s = 1 then these values are also the radii of the corresponding regular polygons. The radius of a d -dimensional hypercube with side s is The polar coordinate system is a two - dimensional coordinate system in which each point on a plane is determined by a distance from a fixed point and an angle from a fixed direction. The fixed point (analogous to the origin of

15080-497: The towns chosen as capitals. Although there had been Jewish communities in many Roman cities , the Jews suffered periods of persecution after the conversion of the empire to Christianity. Officially they were tolerated, if subject to conversion efforts, and at times were even encouraged to settle in new areas. Religious beliefs in the Eastern Roman Empire and Iran were in flux during the late sixth and early seventh centuries. Judaism

15210-645: The west, Byzantine control of most of the Western Empire could not be sustained; the reconquest of the Mediterranean periphery and the Italian Peninsula ( Gothic War ) in the reign of Justinian (r. 527–565) was the sole, and temporary, exception. The political structure of Western Europe changed with the end of the united Roman Empire. Although the movements of peoples during this period are usually described as "invasions", they were not just military expeditions but migrations of entire peoples into

15340-438: Was a trend throughout the old Roman lands that happened in the Early Middle Ages. This was especially marked in the lands that did not lie on the Mediterranean, such as northern Gaul or Britain. Non-local goods appearing in the archaeological record are usually luxury goods. In the northern parts of Europe, not only were the trade networks local, but the goods carried were simple, with little pottery or other complex products. Around

15470-469: Was an active proselytising faith, and at least one Arab political leader converted to it. In addition Jewish theologians wrote polemics defending their religion against Christian and Islamic influences. Christianity had active missions competing with the Persians' Zoroastrianism in seeking converts, especially among residents of the Arabian Peninsula . All these strands came together with

15600-438: Was an important feature of the 5th-century Roman military. The various invading tribes had differing emphases on types of soldiers—ranging from the primarily infantry Anglo-Saxon invaders of Britain to the Vandals and Visigoths who had a high proportion of cavalry in their armies. During the early invasion period, the stirrup had not been introduced into warfare, which limited the usefulness of cavalry as shock troops because it

15730-474: Was dominated by efforts to regain the dignity and classicism of imperial Roman and Byzantine art , but was also influenced by the Insular art of the British Isles. Insular art integrated the energy of Irish Celtic and Anglo-Saxon Germanic styles of ornament with Mediterranean forms such as the book, and established many characteristics of art for the rest of the medieval period. Surviving religious works from

15860-408: Was invited to Aachen and brought the education available in the monasteries of Northumbria. Charlemagne's chancery —or writing office—made use of a new script today known as Carolingian minuscule , allowing a common writing style that advanced communication across much of Europe. Charlemagne sponsored changes in church liturgy , imposing the Roman form of church service on his domains, as well as

15990-493: Was less need for large tax revenues and so the taxation systems decayed. Warfare was common between and within the kingdoms. Slavery declined as the supply weakened, and society became more rural. Between the 5th and 8th centuries, new peoples and individuals filled the political void left by Roman centralised government. The Ostrogoths , a Gothic tribe, settled in Roman Italy in the late fifth century under Theoderic

16120-555: Was marked by scholasticism , a philosophy that emphasised joining faith to reason, and by the founding of universities . The theology of Thomas Aquinas , the paintings of Giotto , the poetry of Dante and Chaucer , the travels of Marco Polo , and the Gothic architecture of cathedrals such as Chartres are among the outstanding achievements toward the end of this period and into the Late Middle Ages. The Late Middle Ages

16250-656: Was marked by difficulties and calamities including famine, plague, and war, which significantly diminished the population of Europe; between 1347 and 1350, the Black Death killed about a third of Europeans. Controversy, heresy , and the Western Schism within the Catholic Church paralleled the interstate conflict, civil strife, and peasant revolts that occurred in the kingdoms. Cultural and technological developments transformed European society, concluding

16380-439: Was marked by numerous divisions of the empire among his sons and, after 829, civil wars between various alliances of father and sons over the control of various parts of the empire. Eventually, Louis recognised his eldest son Lothair I (d. 855) as emperor and gave him Italy. Louis divided the rest of the empire between Lothair and Charles the Bald (d. 877), his youngest son. Lothair took East Francia , comprising both banks of

16510-549: Was not possible to put the full force of the horse and rider behind blows struck by the rider. The greatest change in military affairs during the invasion period was the adoption of the Hunnic composite bow in place of the earlier, and weaker, Scythian composite bow. Another development was the increasing use of longswords and the progressive replacement of scale armour by mail armour and lamellar armour . The importance of infantry and light cavalry began to decline during

16640-503: Was reinforced with propaganda that portrayed the Merovingians as inept or cruel rulers, exalted the accomplishments of Charles Martel, and circulated stories of the family's great piety. At the time of his death in 768, Pippin left his kingdom in the hands of his two sons, Charles (r. 768–814) and Carloman (r. 768–771). When Carloman died of natural causes, Charles blocked the succession of Carloman's young son and installed himself as

16770-533: Was the denarius or denier , while the Anglo-Saxon version was called a penny . From these areas, the denier or penny spread throughout Europe from 700 to 1000 AD. Copper or bronze coins were not struck, nor were gold except in Southern Europe. No silver coins denominated in multiple units were minted. Christianity was a major unifying factor between Eastern and Western Europe before the Arab conquests, but

16900-409: Was with the British Isles and Scandinavia, in contrast to the older Roman Empire with its trading networks centred on the Mediterranean. The empire was administered by an itinerant court that travelled with the emperor, as well as approximately 300 imperial officials called counts , who administered the counties the empire had been divided into. Clergy and local bishops served as officials, as well as

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