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Dux ( /dʌks,dʊks/ ; plural: ducēs) is Latin for "leader" (from the noun dux, ducis, "leader, general") and later for duke and its variant forms (doge, duce, etc.). During the Roman Republic and for the first centuries of the Roman Empire, dux could refer to anyone who commanded troops, both Roman generals and foreign leaders, but was not a formal military rank.
Until the 3rd century, dux was not a formal expression of rank within the Roman military or administrative hierarchy. 
In the Roman army, a dux would be a general in charge of two or more legions. While the title of dux could refer to a consul or imperator, it usually refers to the Roman governor of the provinces. As the governor, the dux was both the highest civil official as well as the commander-in-chief of the legions garrisoned within the province.[ citation needed ]
In writing his commentaries on the Gallic Wars, Julius Caesar uses the term only for Celtic generals, with one exception for a Roman commander who held no official rank. 
By the mid-3rd century AD, it had acquired a more precise connotation defining the commander of an expeditionary force, usually made up of detachments (i.e., vexillationes ) from one or more of the regular military formations. Such appointments were made to deal with specific military situations when the threat to be countered seemed beyond the capabilities of the province-based military command structure that had characterised the Roman army of the High Empire. 
From the time of Gallienus onwards for more than a century were invariably Viri Perfectissimi, i.e., members of the second class of the equestrian order.  Thus, they would have out-ranked the commanders of provincial legions, who were usually Viri Egregii – equestrians of the third class. 
Duces differed from praesides who were the supreme civil as well as military authority within their provinces in that the function of the former was purely military. However, the military authority of a dux was not necessarily confined to a single province and they do not seem to have been subject to the authority of the governor of the province in which they happened to be operating. It was not until the end of the 3rd century that the term dux emerged as a regular military rank held by a senior officer of limitanei – i.e. frontier troops as opposed those attached to an Imperial field-army ( comitatenses ) – with a defined geographic area of responsibility. [note 1]
During the time of the Dominate, the powers of a dux were split from the role of the governor and were given to a new office called dux. The dux was now the highest military office within the province and commanded the legions, but the governor had to authorize the use of the dux's powers. However, once those powers were authorized, the dux could act independently from the governor and handle all military matters. The Dux Belgicae secundae ("commander of the second Belgic province") is an example of this office.
After Diocletian's Tetrarchy reform, the provinces were organized into dioceses with each dioceses administered by a vicarius. As with the governors, the vicarius was assisted by a dux. This dux was superior to all other duces within the dioceses—when the vicarius called the legions of the dioceses into action, all of the legions were at the command of the dux. The office of dux was, in turn, made subject to the magister militum of his respective praetorian prefecture, and above him to the emperor. The Dux per Gallias, dux of the diocese of Gaul, is an example of this office.
In the Byzantine era of the Roman Empire, the position of dux survived (Byzantine Greek: "δούξ", doux, plural "δούκες", doukes) as a rank equivalent to a general ( strategos ). In the late 10th and early 11th centuries, a doux or katepano was in charge of large circumscriptions consisting of several smaller themata and of the professional regiments ( tagmata ) of the Byzantine army (as opposed to the largely militia-like forces of most themata). In the Komnenian period, the title of doux replaced altogether the strategos in designating the military official in charge of a thema. In the Byzantine navy, doukes of the fleet appear in the 1070s, and the office of megas doux ("grand duke") was created in the 1090s as the commander-in-chief of the entire navy.
The title also gave rise to a family name, the aristocratic Doukas clan, which in the 9th–11th centuries provided several Byzantine emperors and generals, while later bearers of the name (maternally descended from the original family) founded the Despotate of Epirus in northwestern Greece.
King Arthur, in one of his earliest literary appearances, is described as dux bellorum ("dux of battles") among the kings of the Romano-Britons in their wars against the Anglo-Saxons. A chronicle from St Martin's monastery in Cologne states that the monastery had been pillaged by the Saxons in 778, but that it was rebuilt by an "Olgerus, dux Daniæ" (who may have been the historical person around whom the myth of Ogier the Dane formed), with the help of Charlemagne.
Dux is also the root of various high feudal noble titles of peerage rank, such as the English duke , the French duc, the Spanish and Portuguese duque, the Venetian doge , the Italian duca and duce , and the Byzantine Greek dukas or doukas (Gr. δούκας) (see Doukas).
Italian Fascist dictator Benito Mussolini used the title of dux (and duce in Italian) to represent his leadership. One fascist motto was "DVX MEA LVX", Latin for "[The] Duce [is] my light" or "[The] Leader [is] my light". 
In pre-revolutionary Russia, the Dux Factory built bicycles, automobiles and aircraft in Moscow. 
Duke is a male title either of a monarch ruling over a duchy, or of a member of royalty, or nobility. As rulers, dukes are ranked below emperors, kings, grand princes, grand dukes, and sovereign princes. As royalty or nobility, they are ranked below princes and grand dukes. The title comes from French duc, itself from the Latin dux, 'leader', a term used in republican Rome to refer to a military commander without an official rank, and later coming to mean the leading military commander of a province. In most countries, the word duchess is the female equivalent.
Grand duke is a European hereditary title, used either by certain monarchs or by members of certain monarchs' families. In status, a grand duke traditionally ranks in order of precedence below an emperor, as an approximate equal of king or archduke and above a sovereign prince or sovereign duke. The title is used in some current and former independent monarchies in Europe, particularly:
The themes or thémata were the main military/administrative divisions of the middle Byzantine Empire. They were established in the mid-7th century in the aftermath of the Slavic invasion of the Balkans and Muslim conquests of parts of Byzantine territory, and replaced the earlier provincial system established by Diocletian and Constantine the Great. In their origin, the first themes were created from the areas of encampment of the field armies of the East Roman army, and their names corresponded to the military units that had existed in those areas. The theme system reached its apogee in the 9th and 10th centuries, as older themes were split up and the conquest of territory resulted in the creation of new ones. The original theme system underwent significant changes in the 11th and 12th centuries, but the term remained in use as a provincial and financial circumscription until the very end of the Empire.
Through the 5th-century, Hellenistic political systems, philosophies and theocratic Christian-Eastern concepts had gained power in the eastern Greek-speaking Mediterranean due to the intervention of important religious figures there such as Eusebius of Caesarea and Origen of Alexandria who had been key to developing the constant Christianized worldview of late antiquity.
Vicarius is a Latin word, meaning substitute or deputy. It is the root of the English word "vicar".
A Roman governor was an official either elected or appointed to be the chief administrator of Roman law throughout one or more of the many provinces constituting the Roman Empire.
The megas doux was one of the highest positions in the hierarchy of the later Byzantine Empire, denoting the commander-in-chief of the Byzantine navy. It is sometimes also given in English by the half-Latinizations megaduke or megadux. The Greek word δούξ is the Hellenized form of the Latin term dux, meaning leader or commander.
The House of Doukas, Latinized as Ducas, from the Latin title dux, is the name of a Byzantine Greek noble family, whose branches provided several notable generals and rulers to the Byzantine Empire in the 9th–11th centuries. A maternally-descended line, the Komnenodoukai, founded the Despotate of Epirus in the 13th century, with another branch ruling over Thessaly.
In the Late Roman Empire, usually dated 284 AD to 602 AD, the regional governance district known as the Roman or civil diocese was made up of a grouping of provinces each headed by a Vicarius, who were the representatives of praetorian prefects. There were initially twelve dioceses, rising to fourteen by the end of the 4th century.
The Diocese of Pontus was a diocese of the later Roman Empire, incorporating the provinces of northern and northeastern Asia Minor up to the border with the Sassanid Empire in Armenia. The diocese was established after the reforms of Diocletian, and its vicarius, headquartered at Amaseia, was subordinate to the Praetorian prefecture of the East. Its military forces, facing the Sassanid threat, were commanded by the dux Ponti et Armeniae until the middle of the 5th century, and by two separate duces afterwards, until Justinian I instituted a new magister militum per Armeniam for the Armenian frontier. Justinian's reforms also abolished the diocese in 535, and its vicar was made into the governor of Galatia I. The results however were not satisfactory, and the diocese was reestablished in 548, continuing to function until replaced by the themata of Armeniakon and Opsikion in the later 7th century. On the north east shore of the Black Sea, the cities Nitike, Pitiyus, and Dioscurias were part of the diocese until the 7th century. The diocese included 12 provinces: Bithynia, Honorias, Paphlagonia, Helenopontus, Pontus Polemoniacus, Galatia I and Galatia II (Salutaris), Cappadocia I and Cappadocia II, Armenia I, Armenia II, Armenia Maior and the autonomous Armenian principalities (Satrapiae) in the area of Sophene. In 536, Armenia III and Armenia IV were created.
The Diocese of Egypt was a diocese of the later Roman Empire, incorporating the provinces of Egypt and Cyrenaica. Its capital was at Alexandria, and its governor had the unique title of praefectus augustalis instead of the ordinary vicarius. The diocese was initially part of the Diocese of the East, but in ca. 380, it became a separate entity, which lasted until its territories were overrun by the Muslim conquest of Egypt in the 640s.
Anthypatos is the translation in Greek of the Latin proconsul. In the Greek-speaking East, it was used to denote this office in Roman and early Byzantine times, surviving as an administrative office until the 9th century. Thereafter, and until the 11th century, it became a senior Byzantine court dignity.
In the late Byzantine Empire, the term kephale was used to denote local and provincial governors.
Mesopotamia was the name of a Byzantine theme located in what is today eastern Turkey. It should not be confused with the region of Mesopotamia or with the older Roman and early Byzantine province of Mesopotamia. The Byzantine theme was located between the rivers Arsanias and Çimisgezek.
The Theme of Dyrrhachium or Dyrrhachion was a Byzantine military-civilian province (theme), covering the Adriatic coast of modern Albania, and some coastal regions of modern Montenegro. It was established in the early 9th century and named after its capital, Dyrrhachium.
The island of Crete came under the rule of the Byzantine Empire in two periods: the first extends from the late antique period to the conquest of the island by Andalusian exiles in the late 820s, and the second from the island's reconquest in 961 to its capture by the competing forces of Genoa and Venice in 1205.
Subdivisions of the Byzantine Empire were administrative units of the Eastern Roman or Byzantine Empire (330–1453). The Empire had a developed administrative system, which can be divided into three major periods: the late Roman/early Byzantine, which was a continuation and evolution of the system begun by the emperors Diocletian and Constantine the Great, which gradually evolved into the middle Byzantine, where the theme system predominated alongside a restructured central bureaucracy, and the late Byzantine, where the structure was more varied and decentralized and where feudal elements appeared.
Lucius Aurelius Marcianus was a Roman soldier whose military career coincided with the period of crisis that characterized the middle decades of the Third Century AD – see Crisis of the Third Century. Probably of humble origins in one of the Illyrician provinces of the Empire he was one of the group of men from this region who chose a military career – or had it chosen for them – whose professional capabilities brought them to the fore of public life in those troubled times. Marcianus rose to the highest levels of the military hierarchy. The evidence suggests that he earned the trust of the Emperors Gallienus and Claudius II and, possibly, Marcus Aurelius Probus among their successors and that he was one of the principal commanders in the prolonged war against a coalition of what the late antique Greek writers called Scythian peoples whose incursions in that period seemed to threaten the very survival of the Roman state. These would refer to the major Germanic and Iranian peoples, among them the Goths and Roxolani, who invaded the Roman empire across the lower Danube River.