Fibonacci was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages". The name he is called, "Fibonacci", was made up in 1838 by the Franco-Italian historian Guillaume Libri and is short for filius Bonacci, he is known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano. Fibonacci popularized the Hindu–Arabic numeral system in the Western World through his composition in 1202 of Liber Abaci, he introduced Europe to the sequence of Fibonacci numbers, which he used as an example in Liber Abaci. Fibonacci was born around 1170 to an Italian merchant and customs official. Guglielmo directed a trading post in Algeria. Fibonacci travelled with him as a young boy, it was in Bugia that he learned about the Hindu–Arabic numeral system. Fibonacci travelled around the Mediterranean coast, meeting with many merchants and learning about their systems of doing arithmetic, he soon realised the many advantages of the Hindu-Arabic system which, unlike the Roman numerals used at the time, allowed easy calculation using a place-value system.
In 1202, he completed the Liber Abaci. Fibonacci became a guest of Emperor Frederick II. In 1240, the Republic of Pisa honored Fibonacci by granting him a salary in a decree that recognized him for the services that he had given to the city as an advisor on matters of accounting and instruction to citizens; the date of Fibonacci's death is not known, but it has been estimated to be between 1240 and 1250, most in Pisa. In the Liber Abaci, Fibonacci introduced the so-called modus Indorum, today known as the Hindu–Arabic numeral system; the book advocated numeration with the digits place value. The book showed the practical use and value of the new Hindu-Arabic numeral system by applying the numerals to commercial bookkeeping, converting weights and measures, calculation of interest, money-changing, other applications; the book had a profound impact on European thought. No copies of the 1202 edition are known to exist; the 1228 edition, first section introduces the Hindu-Arabic numeral system and compares the system with other systems, such as Roman numerals, methods to convert the other numeral systems into Hindu-Arabic numerals.
Replacing the Roman numeral system, its ancient Egyptian multiplication method, using an abacus for calculations, with a Hindu-Arabic numeral system was an advance in making business calculations easier and faster, which led to the growth of banking and accounting in Europe. The second section explains the uses of Hindu-Arabic numerals in business, for example converting different currencies, calculating profit and interest, which were important to the growing banking industry; the book discusses irrational numbers and prime numbers. Liber Abaci posed and solved a problem involving the growth of a population of rabbits based on idealized assumptions; the solution, generation by generation, was a sequence of numbers known as Fibonacci numbers. Although Fibonacci's Liber Abaci contains the earliest known description of the sequence outside of India, the sequence had been described by Indian mathematicians as early as the sixth century. In the Fibonacci sequence, each number is the sum of the previous two numbers.
Fibonacci omitted the "0" included today and began the sequence with 1, 1, 2.... He carried the calculation up to the thirteenth place, the value 233, though another manuscript carries it to the next place, the value 377. Fibonacci did not speak about the golden ratio as the limit of the ratio of consecutive numbers in this sequence. In the 19th century, a statue of Fibonacci was raised in Pisa. Today it is located in the western gallery of the Camposanto, historical cemetery on the Piazza dei Miracoli. There are many mathematical concepts named after Fibonacci because of a connection to the Fibonacci numbers. Examples include the Brahmagupta–Fibonacci identity, the Fibonacci search technique, the Pisano period. Beyond mathematics, namesakes of Fibonacci include the asteroid 6765 Fibonacci and the art rock band The Fibonaccis. Liber Abaci, a book on calculations Practica Geometriae, a compendium of techniques in surveying, the measurement and partition of areas and volumes, other topics in practical geometry.
Flos, solutions to problems posed by Johannes of Palermo Liber quadratorum on Diophantine equations, dedicated to Emperor Frederick II. See in particular congruum and the Brahmagupta–Fibonacci identity. Di minor guisa Commentary on Book X of Euclid's Elements Fibonacci numbers in popular culture Republic of Pisa Adelard of Bath Footnotes Citations Devlin, Keith; the Man of Numbers: Fibonacci's Arithmetic Revolution. Walker Books. ISBN 978-0802779083. Goetzmann, William N. and Rouwenhorst, K. Geert, The Origins of Value: The Financial Innovations That Created Modern Capital Markets, ISBN 0-19-517571-9. Goetzmann, William N. Fibonacci and the Financial Revolution, Yale School of Management International Center for Finance Working Paper No. 03–28 Grimm, R. E. "The Autobiography of Leonardo Pisano", Fibonacci Quarterly, Vol. 11, No. 1, February 1973, pp. 99–104. Horadam, A. F. "Eight hundred years young," The Australian Mathematics Teacher 31 (1975
House of Wisdom
The House of Wisdom refers either to a major Abbasid public academy and intellectual center in Baghdad or to a large private library belonging to the Abbasid Caliphs during the Islamic Golden Age. The House of Wisdom is the subject of an active dispute over its functions and existence as a formal academy, an issue complicated by a lack of physical evidence following the collapse of the Abbasid Caliphate and a reliance on corroboration of literary sources to construct a narrative; the House of Wisdom was founded either as a library for the collections of the Caliph Harun al-Rashid in the late 8th century and turned into a public academy during the reign of Al-Ma'mun or was a private collection created by Al-Mansur to house rare books and collections of poetry in both Arabic and Persian. Regardless, the House of Wisdom existed as a part of the major Translation Movement taking place during the Abbasid Era, translating works from Greek and Syriac to Arabic, but it is unlikely that the House of Wisdom existed as the sole center of such work, as major translation efforts arose in Cairo and Damascus earlier than the proposed establishment of the House of Wisdom.
This translation movement lent momentum to a great deal of original research occurring in the Islamicate world, which had access to texts from Greek and Indian sources, as opposed to the "Bookshelf Thesis" that reduces the contributions of Islamicate scholars to mere translation and preservation of Greek texts. The House of Wisdom was made possible by the consistent flow of Arab and other scholars of the Islamicate world to Baghdad, owing to the city's position as capital of the Abbasid Caliphate; this is evidenced by the large number of scholars known to have studied in Baghdad between the 8th and 13th centuries, such as Al-Jahiz, Al-Kindi, Al-Ghazali among others, all of whom would have contributed to a vibrant academic community in Baghdad, producing a great number of notable works, regardless of the existence of a formal academy. The fields to which scholars associated with the House of Wisdom contributed include, but are not limited to philosophy, medicine and optics; the early name of the library, Khizanat al-Hikma, derives from its function as a place for the preservation of rare books and poetry, a primary function of the House of Wisdom until its destruction.
The House of Wisdom and its contents were destroyed in the Siege of Baghdad, leaving little in the way of archaeological evidence for the House of Wisdom, such that most knowledge about it is derived from the works of contemporary scholars of the era such as Al-Tabari and Ibn al-Nadim. Throughout the 4th to 7th centuries, scholarly work in the Arabic languages was either newly initiated, or carried on from the Hellenistic period. Centers of learning and of transmission of classical wisdom included colleges such as the School of Nisibis and the School of Edessa, the renowned hospital and medical academy of Jundishapur. During the Umayyad era, Muawiyah I started to gather a collection of books in Damascus, he formed a library that were referred to by the name of "Bayt al-Hikma". Books written in Greek and Persian in the fields of medicine, physics, mathematics and other disciplines were collected and translated by Muslim scholars at that time. Remarkably, the Umayyads appropriated paper-making techniques from the Chinese and joined many ancient intellectual centers under their rule, employed Christian and Persian scholars to both translate works into Arabic, to develop new knowledge.
These were fundamental elements that contributed directly to the flourishing of scholarship in the Arab world. In 750, the Abbasid dynasty replaced the Umayyad as the ruling dynasty of the Islamic Empire, and, in 762, the caliph al-Mansur built Baghdad and made it his capital, instead of Damascus. Baghdad's location and cosmopolitan population made the perfect location for a stable commercial and intellectual center; the Abbasid dynasty had a strong Persian bent, adopted many practices from the Sassanian Empire – among those, that of translating foreign works, except that now texts were translated into Arabic. For this purpose, al-Mansur founded a palace library, modeled after the Sassanian Imperial Library, provided economic and political support to the intellectuals working there, he invited delegations of scholars from India and other places to share their knowledge of mathematics and astronomy with the new Abbasid court. In the Abbasid Empire, many foreign works were translated into Arabic from Greek, Sanskrit and Syriac.
The Translation Movement gained great momentum during the reign of caliph al-Rashid, like his predecessor, was interested in scholarship and poetry. The texts concerned medicine and astronomy. Al-Rashid's library, direct predecessor to the House of Wisdom, was known as Bayt al-Hikma or, as the historian Al-Qifti called it, Khizanat Kutub al-Hikma. Under the sponsorship of caliph al-Ma'mun, economic support of the House of Wisdom and scholarship in general was increased. Furthermore, Abbasid society itself came to understand and appreciate the value of knowledge, support came from merchants and the military, it was easy for scholars and translators to make a living and an academic
Ancient Greece was a civilization belonging to a period of Greek history from the Greek Dark Ages of the 12th–9th centuries BC to the end of antiquity. Following this period was the beginning of the Early Middle Ages and the Byzantine era. Three centuries after the Late Bronze Age collapse of Mycenaean Greece, Greek urban poleis began to form in the 8th century BC, ushering in the Archaic period and colonization of the Mediterranean Basin; this was followed by the period of Classical Greece, an era that began with the Greco-Persian Wars, lasting from the 5th to 4th centuries BC. Due to the conquests by Alexander the Great of Macedon, Hellenistic civilization flourished from Central Asia to the western end of the Mediterranean Sea; the Hellenistic period came to an end with the conquests and annexations of the eastern Mediterranean world by the Roman Republic, which established the Roman province of Macedonia in Roman Greece, the province of Achaea during the Roman Empire. Classical Greek culture philosophy, had a powerful influence on ancient Rome, which carried a version of it to many parts of the Mediterranean Basin and Europe.
For this reason, Classical Greece is considered to be the seminal culture which provided the foundation of modern Western culture and is considered the cradle of Western civilization. Classical Greek culture gave great importance to knowledge. Science and religion were not separate and getting closer to the truth meant getting closer to the gods. In this context, they understood the importance of mathematics as an instrument for obtaining more reliable knowledge. Greek culture, in a few centuries and with a limited population, managed to explore and make progress in many fields of science, mathematics and knowledge in general. Classical antiquity in the Mediterranean region is considered to have begun in the 8th century BC and ended in the 6th century AD. Classical antiquity in Greece was preceded by the Greek Dark Ages, 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.
The Archaic Period saw early developments in Greek culture and society which formed the basis for the Classical Period. After the Archaic Period, the Classical Period in Greece is conventionally considered to have lasted from the Persian invasion of Greece in 480 until the death of Alexander the Great in 323; the period is characterized by a style, considered by observers to be exemplary, i.e. "classical", as shown in the Parthenon, for instance. 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 the Boeotian League and to the League of Corinth led by Macedon; this period saw the Greco-Persian Wars and the Rise of Macedon. Following the Classical period was the Hellenistic period, during which Greek culture and power expanded into the Near and Middle East; this period ends with the Roman conquest. Roman Greece is considered to be the period between Roman victory over the Corinthians at the Battle of Corinth in 146 BC and the establishment of Byzantium by Constantine as the capital of the Roman Empire in AD 330.
Late Antiquity refers to the period of Christianization during the 4th to early 6th centuries AD, sometimes taken to be complete with the closure of the Academy of Athens by Justinian I in 529. The historical period of ancient Greece is unique in world history as the first period attested directly in proper historiography, while earlier ancient history or proto-history is known by much more circumstantial evidence, such as annals or king lists, pragmatic epigraphy. Herodotus is 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 a century into the past, discussing 6th century historical figures such as Darius I of Persia, Cambyses II and Psamtik III, alluding to some 8th century ones such as Candaules. Herodotus was succeeded by authors such as Thucydides, Demosthenes and Aristotle. Most of these authors were either Athenian or pro-Athenian, why far more is known about the history and politics of Athens than those of many other cities.
Their scope is further limited by a focus on political and diplomatic history, ignoring economic and social history. In the 8th century BC, Greece began to emerge from the Dark Ages which followed the fall of the Mycenaean civilization. Literacy had been lost and Mycenaean script forgotten, but the Greeks adopted the Phoenician alphabet, modifying it to create the Greek alphabet. Objects with Phoenician writing on them may have been available in Greece from the 9th century BC, but the earliest evidence of Greek writing comes from graffiti on Greek pottery from the mid-8th century. Greece was divided into many small self-governing communities, a pattern dictated by Greek geography: every island and plain is cut off from its neighbors by the sea or mountain ranges; the Lelantine War is the earliest documented war of the ancient Greek period. It was fought between the important poleis of Chalcis and Eretria over the fertile Lelantine plain of Euboea. Both cities seem to have suffered a decline as result of the long war, though Chalcis was the nominal victor.
A mercantile class arose in the first half of the 7th century BC, shown by the introduction of coinage in about 680 BC. This
The Byzantine Empire referred to as the Eastern Roman Empire or Byzantium, was the continuation of the Roman Empire in its eastern provinces during Late Antiquity and the Middle Ages, when its capital city was Constantinople. It survived the fragmentation and fall of the Western Roman Empire in the 5th century AD and continued to exist for an additional thousand years until it fell to the Ottoman Turks in 1453. During most of its existence, the empire was the most powerful economic and military force in Europe. Both the terms "Byzantine Empire" and "Eastern Roman Empire" are historiographical terms created after the end of the realm. Several signal events from the 4th to 6th centuries mark the period of transition during which the Roman Empire's Greek East and Latin West diverged. Constantine I reorganised the empire, made Constantinople the new capital, legalised Christianity. Under Theodosius I, Christianity became the Empire's official state religion and other religious practices were proscribed.
Under the reign of Heraclius, the Empire's military and administration were restructured and adopted Greek for official use in place of Latin. Thus, although the Roman state continued and its traditions were maintained, modern historians distinguish Byzantium from ancient Rome insofar as it was centred on Constantinople, oriented towards Greek rather than Latin culture, characterised by Eastern Orthodox Christianity; the borders of the empire evolved over its existence, as it went through several cycles of decline and recovery. During the reign of Justinian I, the empire reached its greatest extent after reconquering much of the Roman western Mediterranean coast, including North Africa and Rome itself, which it held for two more centuries; the Byzantine–Sasanian War of 602–628 exhausted the empire's resources and contributed to major territorial losses during the Early Muslim conquests of the 7th century, when it lost its richest provinces and Syria, to the Arab caliphate. During the Macedonian dynasty, the empire expanded again and experienced the two-century long Macedonian Renaissance, which came to an end with the loss of much of Asia Minor to the Seljuk Turks after the Battle of Manzikert in 1071.
This battle opened the way for the Turks to settle in Anatolia. The empire recovered during the Komnenian restoration, by the 12th century Constantinople was the largest and wealthiest European city. However, it was delivered a mortal blow during the Fourth Crusade, when Constantinople was sacked in 1204 and the territories that the empire governed were divided into competing Byzantine Greek and Latin realms. Despite the eventual recovery of Constantinople in 1261, the Byzantine Empire remained only one of several small rival states in the area for the final two centuries of its existence, its remaining territories were progressively annexed by the Ottomans over the 15th century. The Fall of Constantinople to the Ottoman Empire in 1453 ended the Byzantine Empire; the last of the imperial Byzantine successor states, the Empire of Trebizond, would be conquered by the Ottomans eight years in the 1461 Siege of Trebizond. The first use of the term "Byzantine" to label the years of the Roman Empire was in 1557, when the German historian Hieronymus Wolf published his work Corpus Historiæ Byzantinæ, a collection of historical sources.
The term comes from "Byzantium", the name of the city of Constantinople before it became Constantine's capital. This older name of the city would be used from this point onward except in historical or poetic contexts; the publication in 1648 of the Byzantine du Louvre, in 1680 of Du Cange's Historia Byzantina further popularised the use of "Byzantine" among French authors, such as Montesquieu. However, it was not until the mid-19th century that the term came into general use in the Western world; the Byzantine Empire was known to its inhabitants as the "Roman Empire", the "Empire of the Romans", "Romania", the "Roman Republic", as "Rhōmais". The inhabitants called themselves Romaioi and as late as the 19th century Greeks referred to Modern Greek as Romaiika "Romaic." After 1204 when the Byzantine Empire was confined to its purely Greek provinces the term'Hellenes' was used instead. While the Byzantine Empire had a multi-ethnic character during most of its history and preserved Romano-Hellenistic traditions, it became identified by its western and northern contemporaries with its predominant Greek element.
The occasional use of the term "Empire of the Greeks" in the West to refer to the Eastern Roman Empire and of the Byzantine Emperor as Imperator Graecorum were used to separate it from the prestige of the Roman Empire within the new kingdoms of the West. No such distinction existed in the Islamic and Slavic worlds, where the Empire was more straightforwardly seen as the continuation of the Roman Empire. In the Islamic world, the Roman Empire was known as Rûm; the name millet-i Rûm, or "Roman nation," was used by the Ottomans through the 20th century to refer to the former subjects of the Byzantine Empire
Apollonius of Perga
Apollonius of Perga was a Greek geometer and astronomer known for his theories on the topic of conic sections. Beginning from the theories of Euclid and Archimedes on the topic, he brought them to the state they were in just before the invention of analytic geometry, his definitions of the terms ellipse and hyperbola are the ones in use today. Apollonius worked including astronomy. Most of the work has not survived except in fragmentary references in other authors, his hypothesis of eccentric orbits to explain the aberrant motion of the planets believed until the Middle Ages, was superseded during the Renaissance. For such an important contributor to the field of mathematics, scant biographical information remains; the 6th century Palestinian commentator, Eutocius of Ascalon, on Apollonius’ major work, states: “Apollonius, the geometrician... came from Perga in Pamphylia in the times of Ptolemy Euergetes, so records Herakleios the biographer of Archimedes....” Perga at the time was a Hellenized city of Pamphylia in Anatolia.
The ruins of the city yet stand. It was a center of Hellenistic culture. Euergetes, “benefactor,” identifies Ptolemy III Euergetes, third Greek dynast of Egypt in the diadochi succession, his “times” are his regnum, 246-222/221 BC. Times are always recorded by ruler or officiating magistrate, so that if Apollonius was born earlier than 246, it would have been the “times” of Euergetes’ father; the identity of Herakleios is uncertain. The approximate times of Apollonius are thus certain; the figure Specific birth and death years stated by the various scholars are only speculative. Eutocius appears to associate Perga with the Ptolemaic dynasty of Egypt. Never under Egypt, Perga in 246 BC belonged to the Seleucid Empire, an independent diadochi state ruled by the Seleucid dynasty. During the last half of the 3rd century BC, Perga changed hands a number of times, being alternatively under the Seleucids and under the Kingdom of Pergamon to the north, ruled by the Attalid dynasty. Someone designated "of Perga" might well be expected to have worked there.
To the contrary, if Apollonius was identified with Perga, it was not on the basis of his residence. The remaining autobiographical material implies that he lived and wrote in Alexandria. A letter by the Greek mathematician and astronomer Hypsicles was part of the supplement taken from Euclid's Book XIV, part of the thirteen books of Euclid's Elements. "Basilides of Tyre, O Protarchus, when he came to Alexandria and met my father, spent the greater part of his sojourn with him on account of the bond between them due to their common interest in mathematics. And on one occasion, when looking into the tract written by Apollonius about the comparison of the dodecahedron and icosahedron inscribed in one and the same sphere, to say, on the question what ratio they bear to one another, they came to the conclusion that Apollonius' treatment of it in this book was not correct, but I myself afterwards came across another book published by Apollonius, containing a demonstration of the matter in question, I was attracted by his investigation of the problem.
Now the book published by Apollonius is accessible to all. "For my part, I determined to dedicate to you what I deem to be necessary by way of commentary because you will be able, by reason of your proficiency in all mathematics and in geometry, to pass an expert judgment upon what I am about to write, because, on account of your intimacy with my father and your friendly feeling towards myself, you will lend a kindly ear to my disquisition. But it is time to have done with the preamble and to begin my treatise itself." Apollonius lived toward the end of a historical period now termed the Hellenistic Period, characterized by the superposition of Hellenic culture over extensive non-Hellenic regions to various depths, radical in some places, hardly at all in others. The change was initiated by Philip II of Macedon and his son, Alexander the Great, subjecting all of Greece is a series of stunning victories, went on to conquer the Persian Empire, which ruled territories from Egypt to Pakistan. Philip was assassinated in 336 BC.
Alexander went on to fulfill his plan by conquering the vast Persian empire. The material is located in the surviving false “Prefaces” of the books of his Conics; these are letters delivered to influential friends of Apollonius asking them to review the book enclosed with the letter. The Preface to Book I, addressed to one Eudemus, reminds him that Conics was requested by a house guest at Alexandria, the geometer, otherwise unknown to history. Naucrates had the first draft of all eight books in his hands by the end of the visit. Apollonius refers to them as being “without a thorough purgation”, he intended releasing each one as it was completed. Hearing of this plan from Apollonius himself on a subsequent visit of the latter to Pergamon, Eudemus had insisted Apollonius send him each book before release; the circumstances imply that at this stage Apollonius was a young geometer seeking the company and advice of established professionals. Pappus states. Euclid was long gone; this stay had been the final stage of Apollonius’ education.
Eudemus was a senior figure in his earlier education at Pergamon.
Book of Ingenious Devices
The Book of Ingenious Devices was a large illustrated work on mechanical devices, including automata, published in 850 by the three Iraqi brothers of Persian descent, known as the Banu Musa working at the House of Wisdom in Baghdad, under the Abbasid Caliphate. The book how to use them; the book was commissioned by the Abbasid Caliph of Baghdad made by Al-Jazari, Abu Jafar al-Ma'mun ibn Harun, who instructed the Banu Musa to acquire all of the Hellenistic texts, preserved by monasteries and by scholars during the decline and fall of Roman civilization. The Banū Mūsā brothers invented a number of automata and mechanical devices, they described a hundred such devices in their Book of Ingenious Devices; some of the devices described in the Book of Ingenious Devices were inspired by the works of Hero of Alexandria and Philo of Byzantium, as well as ancient Persian and Indian engineering. Many of the other devices described in the book, were original inventions by the Banu Musa brothers. While they took Greek works as a starting point, the Banu Musa went "well beyond anything achieved by Hero or Philo."
Their preoccupation with automatic controls distinguishes them from their Greek predecessors, including the Banu Musa's "use of self-operating valves, timing devices, delay systems and other concepts of great ingenuity." Many of their innovations involved subtle combinations of aerostatics. The closest modern parallel to their work lies in pneumatic instrumentation. In turn, the Banu Musa's work was cited as an influence on the work of Al-Jazari, who produced a titled book in 1206. Given that the Book of Ingenious Devices was circulated across the Muslim world, some of its ideas may have reached Europe through Islamic Spain, such as the use of automatic controls in European machines or the use of conical valves in the work of Leonardo da Vinci; the Banu Musa brothers described a number of early automatic controls. Two-step level controls for fluids, an early form of discontinuous variable structure controls, was developed by the Banu Musa brothers, they described an early feedback controller.
Donald Routledge Hill wrote the following on the automatic controls underlying the mechanical trick devices described in the book: The trick vessels have a variety of different effects. For example, a single outlet pipe in a vessel might pour out first wine water and a mixture of the two. Although it cannot be claimed that the results are important, the means by which they were obtained are of great significance for the history of engineering; the Banu Musa were masters in the exploitation of small variations in aerostatic and hydrostatic pressures and in using conical valves as "in-line" components in flow systems, the first known use of conical valves as automatic controllers. The Banu Musa developed an early fail-safe system for use in their trick devices, as described by Hill: In several of these vessels, one can withdraw small quantities of liquid but if one withdraws a large quantity, no further extractions are possible. In modern terms, one would call the method used to achieve this result a fail-safe system.
The non-manual crank appears in several of the hydraulic devices described by the Banū Mūsā brothers in their Book of Ingenious Devices. These automatically operated cranks appear in several devices, two of which contain an action which approximates to that of a crankshaft, anticipating Al-Jazari's invention by several centuries and its first appearance in Europe by over five centuries. However, the automatic crank described by the Banu Musa would not have allowed a full rotation, but only a small modification was required to convert it to a crankshaft. A mechanism developed by the Banu Musa, of particular importance for future developments, was the conical valve, used in a variety of different applications; this includes using conical valves as "in-line" components in flow systems, the first known use of conical valves as automatic controllers. Some of the other valves they described include: Plug valve Float valve Tap The double-concentric siphon and the funnel with bent end for pouring in different liquids, neither of which appear in any earlier Greek works, were original inventions by the Banu Musa brothers.
Some of the other mechanisms they described include a float chamber and an early differential pressure sensor. The book describes the construction of various automatic fountains, an aspect, neglected in earlier Greek treatises on technology. In one of these fountains, the "water issues from the fountainhead in the shape of a shield, or like a lily-of-the-valley," i.e. "the shapes are discharged alternately—either a sheet of water concave downwards, or a spray." Another fountain "discharges a shield or a single jet," while a variation of this features double-action alternation, i.e. has two fountainheads, with one discharging a single jet and the other a shield, the two alternating repeatedly. Another variation features one main fountainhead and two or more subsidiary ones, such that when the main one ejects a single jet, the subsidiaries eject shields, with the two alternating; the Banu Musa brothers described the earliest known wind-powered fountain, described as, "operated by wind or water, it discharges a single jet or a lily-of-the-valley."
A variation of this fountain incorporates a worm-and-pinion gear, while another variation features double-action alternation. The book describes a fountain with variable discharge; the book als
Claudius Ptolemy was a Greco-Roman mathematician, astronomer and astrologer. He lived in the city of Alexandria in the Roman province of Egypt, wrote in Koine Greek, held Roman citizenship; the 14th-century astronomer Theodore Meliteniotes gave his birthplace as the prominent Greek city Ptolemais Hermiou in the Thebaid. This attestation is quite late, and, according to Gerald Toomer, the translator of his Almagest into English, there is no reason to suppose he lived anywhere other than Alexandria, he died there around AD 168. Ptolemy wrote several scientific treatises, three of which were of importance to Byzantine and Western European science; the first is the astronomical treatise now known as the Almagest, although it was entitled the Mathematical Treatise and known as the Great Treatise. The second is the Geography, a thorough discussion of the geographic knowledge of the Greco-Roman world; the third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day.
This is sometimes known as the Apotelesmatika but more known as the Tetrabiblos from the Greek meaning "Four Books" or by the Latin Quadripartitum. Ptolemaeus is a Greek name, it occurs once in Greek mythology, is of Homeric form. It was common among the Macedonian upper class at the time of Alexander the Great, there were several of this name among Alexander's army, one of whom made himself pharaoh in 323 BC: Ptolemy I Soter, the first king of the Ptolemaic Kingdom. All male kings of Hellenistic Egypt, until Egypt became a Roman province in 30 BC ending the Macedonian family's rule, were Ptolemies; the name Claudius is a Roman nomen. It would have suited custom if the first of Ptolemy's family to become a citizen took the nomen from a Roman called Claudius, responsible for granting citizenship. If, as was common, this was the emperor, citizenship would have been granted between AD 41 and 68; the astronomer would have had a praenomen, which remains unknown. The ninth-century Persian astronomer Abu Maʿshar presents Ptolemy as a member of Egypt's royal lineage, stating that the descendants of Alexander's general Ptolemy I, who ruled Egypt, were wise "and included Ptolemy the Wise, who composed the book of the Almagest".
Abu Maʿshar recorded a belief that a different member of this royal line "composed the book on astrology and attributed it to Ptolemy". We can evidence historical confusion on this point from Abu Maʿshar's subsequent remark "It is sometimes said that the learned man who wrote the book of astrology wrote the book of the Almagest; the correct answer is not known." There is little evidence on the subject of Ptolemy's ancestry, apart from what can be drawn from the details of his name. Ptolemy can be shown to have utilized Babylonian astronomical data, he was a Roman citizen, but was ethnically either a Greek or a Hellenized Egyptian. He was known in Arabic sources as "the Upper Egyptian", suggesting he may have had origins in southern Egypt. Arabic astronomers and physicists referred to him by his name in Arabic: بَطْلُمْيوس Baṭlumyus. Ptolemy's Almagest is the only surviving comprehensive ancient treatise on astronomy. Babylonian astronomers had developed arithmetical techniques for calculating astronomical phenomena.
Ptolemy, claimed to have derived his geometrical models from selected astronomical observations by his predecessors spanning more than 800 years, though astronomers have for centuries suspected that his models' parameters were adopted independently of observations. Ptolemy presented his astronomical models in convenient tables, which could be used to compute the future or past position of the planets; the Almagest contains a star catalogue, a version of a catalogue created by Hipparchus. Its list of forty-eight constellations is ancestral to the modern system of constellations, but unlike the modern system they did not cover the whole sky. Across Europe, the Middle East and North Africa in the Medieval period, it was the authoritative text on astronomy, with its author becoming an mythical figure, called Ptolemy, King of Alexandria; the Almagest was preserved, in Arabic manuscripts. Because of its reputation, it was sought and was translated twice into Latin in the 12th century, once in Sicily and again in Spain.
Ptolemy's model, like those of his predecessors, was geocentric and was universally accepted until the appearance of simpler heliocentric models during the scientific revolution. His Planetary Hypotheses went beyond the mathematical model of the Almagest to present a physical realization of the universe as a set of nested spheres, in which he used the epicycles of his planetary model to compute the dimensions of the universe, he estimated the Sun was at an average dis