A mathematician is someone who uses an extensive knowledge of mathematics in his or her work to solve mathematical problems. Mathematics is concerned with numbers, quantity, space and change. One of the earliest known mathematicians was Thales of Miletus, he is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number", it was the Pythagoreans who coined the term "mathematics", with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypatia of Alexandria, she succeeded her father as Librarian at the Great Library and wrote many works on applied mathematics. Because of a political dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked and scraping off her skin with clamshells.
Science and mathematics in the Islamic world during the Middle Ages followed various models and modes of funding varied based on scholars. It was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. Funding for translation of scientific texts in other languages was ongoing throughout the reign of certain caliphs, it turned out that certain scholars became experts in the works they translated and in turn received further support for continuing to develop certain sciences; as these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences. An example of a translator and mathematician who benefited from this type of support was al-Khawarizmi. A notable feature of many scholars working under Muslim rule in medieval times is that they were polymaths. Examples include the work on optics and astronomy of Ibn al-Haytham; the Renaissance brought an increased emphasis on science to Europe.
During this period of transition from a feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: Luca Pacioli. As time passed, many mathematicians gravitated towards universities. An emphasis on free thinking and experimentation had begun in Britain's oldest universities beginning in the seventeenth century at Oxford with the scientists Robert Hooke and Robert Boyle, at Cambridge where Isaac Newton was Lucasian Professor of Mathematics & Physics. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking.” In 1810, Humboldt convinced the King of Prussia to build a university in Berlin based on Friedrich Schleiermacher’s liberal ideas. Thus and laboratories started to evolve. British universities of this period adopted some approaches familiar to the Italian and German universities, but as they enjoyed substantial freedoms and autonomy the changes there had begun with the Age of Enlightenment, the same influences that inspired Humboldt.
The Universities of Oxford and Cambridge emphasized the importance of research, arguably more authentically implementing Humboldt’s idea of a university than German universities, which were subject to state authority. Overall, science became the focus of universities in the 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge; the German university system fostered professional, bureaucratically regulated scientific research performed in well-equipped laboratories, instead of the kind of research done by private and individual scholars in Great Britain and France. In fact, Rüegg asserts that the German system is responsible for the development of the modern research university because it focused on the idea of “freedom of scientific research and study.” Mathematicians cover a breadth of topics within mathematics in their undergraduate education, proceed to specialize in topics of their own choice at the graduate level.
In some universities, a qualifying exam serves to test both the breadth and depth of a student's understanding of mathematics. Mathematicians involved with solving problems with applications in real life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their specialized knowledge and professional methodology, approach many of the imposing problems presented in related scientific fields. With professional focus on a wide variety of problems, theoretical systems, localized constructs, applied mathematicians work in the study and formulation of mathematical models. Mathematicians and applied mathematicians are considered to be two of the STEM careers; the discipline of applied mathematics concerns
The Planisphaerium is a work by Ptolemy. The title can be translated as "celestial plane" or "star chart". In this work Ptolemy explored the mathematics of mapping figures inscribed in the celestial sphere onto a plane by what is now known as stereographic projection; this method of projection preserves the properties of circles. Written in Ancient Greek, Planisphaerium was one of many scientific works which survived from antiquity in Arabic translation. One reason why Planisphaerium attracted interest was that stereographic projection was the mathematical basis of the plane astrolabe, an instrument, used in the medieval Islamic world. In the 12th century the work was translated from Arabic into Latin by Herman of Carinthia, who translated commentaries by Maslamah Ibn Ahmad al-Majriti; the oldest known translation is in Arabic done by an unknown scholar as part of the Translation Movement in Baghdad. The word planisphere was used in the second century by Ptolemy to describe the representation of a spherical Earth by a map drawn in the plane.
Planisphere "Ptolemy on Astrolabes"
The Quran is the central religious text of Islam, which Muslims believe to be a revelation from God. It is regarded as the finest work in classical Arabic literature; the Quran is divided into chapters. Muslims believe that the Quran was orally revealed by God to the final Prophet, through the archangel Gabriel, incrementally over a period of some 23 years, beginning on 22 December 609 CE, when Muhammad was 40, concluding in 632, the year of his death. Muslims regard the Quran as Muhammad's most important miracle, a proof of his prophethood, the culmination of a series of divine messages starting with those revealed to Adam and ending with Muhammad; the word "Quran" occurs some 70 times in the Quran's text, other names and words are said to refer to the Quran. According to tradition, several of Muhammad's companions served as scribes and recorded the revelations. Shortly after his death, the Quran was compiled by the companions, who had written down or memorized parts of it; the codices showed differences that motivated Caliph Uthman to establish a standard version, now known as Uthman's codex, considered the archetype of the Quran known today.
There are, variant readings, with minor differences in meaning. The Quran assumes familiarity with major narratives recounted in the Biblical scriptures, it summarizes some, dwells at length on others and, in some cases, presents alternative accounts and interpretations of events. The Quran describes itself as a book of guidance for mankind 2:185, it sometimes offers detailed accounts of specific historical events, it emphasizes the moral significance of an event over its narrative sequence. Hadith are additional written traditions supplementing the Quran. In most denominations of Islam, the Quran is used together with hadith to interpret sharia law. During prayers, the Quran is recited only in Arabic. Someone who has memorized the entire Quran is called a hafiz. Quranic verse is sometimes recited with a special kind of elocution reserved for this purpose, called tajwid. During the month of Ramadan, Muslims complete the recitation of the whole Quran during tarawih prayers. In order to extrapolate the meaning of a particular Quranic verse, most Muslims rely on exegesis, or tafsir.
The word qurʼān appears assuming various meanings. It is a verbal noun of the Arabic verb qaraʼa, meaning "he read" or "he recited"; the Syriac equivalent is qeryānā, which refers to "scripture reading" or "lesson". While some Western scholars consider the word to be derived from the Syriac, the majority of Muslim authorities hold the origin of the word is qaraʼa itself. Regardless, it had become an Arabic term by Muhammad's lifetime. An important meaning of the word is the "act of reciting", as reflected in an early Quranic passage: "It is for Us to collect it and to recite it."In other verses, the word refers to "an individual passage recited ". Its liturgical context is seen in a number of passages, for example: "So when al-qurʼān is recited, listen to it and keep silent." The word may assume the meaning of a codified scripture when mentioned with other scriptures such as the Torah and Gospel. The term has related synonyms that are employed throughout the Quran; each synonym possesses its own distinct meaning, but its use may converge with that of qurʼān in certain contexts.
Such terms include kitāb. The latter two terms denote units of revelation. In the large majority of contexts with a definite article, the word is referred to as the "revelation", that, "sent down" at intervals. Other related words are: dhikr, used to refer to the Quran in the sense of a reminder and warning, ḥikmah, sometimes referring to the revelation or part of it; the Quran describes itself as "the discernment", "the mother book", "the guide", "the wisdom", "the remembrance" and "the revelation". Another term is al-kitāb, though it is used in the Arabic language for other scriptures, such as the Torah and the Gospels; the term mus'haf is used to refer to particular Quranic manuscripts but is used in the Quran to identify earlier revealed books. Islamic tradition relates that Muhammad received his first revelation in the Cave of Hira during one of his isolated retreats to the mountains. Thereafter, he received revelations over a period of 23 years. According to hadith and Muslim history, after Muhammad immigrated to Medina and formed an independent Muslim community, he ordered many of his companions to recite the Quran and to learn and teach the laws, which were revealed daily.
It is related that some of the Quraysh who were taken prisoners at the Battle of Badr regained their freedom after they had taught some of the Muslims the simple writing of the time. Thus a group of Muslims became literate; as it was spoken, the Quran was recorded on tablets and the wide, flat ends of date palm fronds. Most suras were in use amongst early Mu
The Benedictines the Order of Saint Benedict, are a monastic Catholic religious order of monks and nuns that follow the Rule of Saint Benedict. They are sometimes called the Black Monks, in reference to the colour of the members' religious habits. Despite being called an order, the Benedictines do not operate under a single hierarchy but are instead organised as a collection of independent monastic communities, with each community within the order maintaining its own autonomy. Unlike other religious orders, the Benedictines do not have a superior general or motherhouse with universal jurisdiction. Instead, the order is represented internationally by the Benedictine Confederation, an organisation, set up in 1893 to represent the order's shared interests; the monastery at Subiaco in Italy, established by Saint Benedict of Nursia c. 529, was the first of the dozen monasteries he founded. He founded the Abbey of Monte Cassino. There is no evidence, that he intended to found an order and the Rule of Saint Benedict presupposes the autonomy of each community.
When Monte Cassino was sacked by the Lombards about the year 580, the monks fled to Rome, it seems probable that this constituted an important factor in the diffusion of a knowledge of Benedictine monasticism. It was from the monastery of St. Andrew in Rome that Augustine, the prior, his forty companions set forth in 595 on their mission for the evangelization of England. At various stopping places during the journey, the monks left behind them traditions concerning their rule and form of life, also some copies of the Rule. Lérins Abbey, for instance, founded by Honoratus in 375 received its first knowledge of the Benedictine Rule from the visit of St. Augustine and his companions in 596. Gregory of Tours says that at Ainay Abbey, in the sixth century, the monks "followed the rules of Basil, Cassian and other fathers and using whatever seemed proper to the conditions of time and place", doubtless the same liberty was taken with the Benedictine Rule when it reached them. In Gaul and Switzerland, it supplemented the much stricter Irish or Celtic Rule introduced by Columbanus and others.
In many monasteries it entirely displaced the earlier codes. By the ninth century, the Benedictine had become the standard form of monastic life throughout the whole of Western Europe, excepting Scotland and Ireland, where the Celtic observance still prevailed for another century or two. Through the work of Benedict of Aniane, it became the rule of choice for monasteries throughout the Carolingian empire. Monastic scriptoria flourished from the ninth through the twelfth centuries. Sacred Scripture was always at the heart of every monastic scriptorium; as a general rule those of the monks who possessed skill as writers made this their chief, if not their sole active work. An anonymous writer of the ninth or tenth century speaks of six hours a day as the usual task of a scribe, which would absorb all the time available for active work in the day of a medieval monk. In the Middle Ages monasteries were founded by the nobility. Cluny Abbey was founded by William I, Duke of Aquitaine in 910; the abbey was noted for its strict adherence to the Rule of St. Benedict.
The abbot of Cluny was the superior of all the daughter houses, through appointed priors. One of the earliest reforms of Benedictine practice was that initiated in 980 by Romuald, who founded the Camaldolese community; the dominance of the Benedictine monastic way of life began to decline towards the end of the twelfth century, which saw the rise of the Franciscans and Dominicans. Benedictines took a fourth vow of "stability". Not being bound by location, the mendicants were better able to respond to an "urban" environment; this decline was further exacerbated by the practice of appointing a commendatory abbot, a lay person, appointed by a noble to oversee and to protect the goods of the monastery. Oftentimes, this resulted in the appropriation of the assets of monasteries at the expense of the community which they were intended to support; the English Benedictine Congregation is the oldest of the nineteen Benedictine congregations. Augustine of Canterbury and his monks established the first English Benedictine monastery at Canterbury soon after their arrival in 597.
Other foundations followed. Through the influence of Wilfrid, Benedict Biscop, Dunstan, the Benedictine Rule spread with extraordinary rapidity, in the North it was adopted in most of the monasteries, founded by the Celtic missionaries from Iona. Many of the episcopal sees of England were founded and governed by the Benedictines, no fewer than nine of the old cathedrals were served by the black monks of the priories attached to them. Monasteries served as places of refuge for the weak and homeless; the monks studied the healing properties of plants and minerals to alleviate the sufferings of the sick. Germany was evangelized by English Benedictines. Willibrord and Boniface preached there in the seventh and eighth centuries and founded several abbeys. In the English Reformation, all monasteries were dissolved and their lands confiscated by the Crown, forcing their Catholic members to flee into exile on the Continent. During the 19th century they were able to return to England, including to Selby Abbey in Yorkshire, one of the few great monastic churches to survive the Dissolution.
St. Mildred's Priory, on the Isle of Thanet, was built in 1027 on the site of an abbey founded in 670 by the daughter of the first Christian King of Kent; the priory is home to a community of Benedictine nuns. Five of
Time is the indefinite continued progress of existence and events that occur in irreversible succession through the past, in the present, the future. Time is a component quantity of various measurements used to sequence events, to compare the duration of events or the intervals between them, to quantify rates of change of quantities in material reality or in the conscious experience. Time is referred to as a fourth dimension, along with three spatial dimensions. Time has long been an important subject of study in religion and science, but defining it in a manner applicable to all fields without circularity has eluded scholars. Diverse fields such as business, sports, the sciences, the performing arts all incorporate some notion of time into their respective measuring systems. Time in physics is unambiguously operationally defined as "what a clock reads". See Units of Time. Time is one of the seven fundamental physical quantities in both the International System of Units and International System of Quantities.
Time is used to define other quantities – such as velocity – so defining time in terms of such quantities would result in circularity of definition. An operational definition of time, wherein one says that observing a certain number of repetitions of one or another standard cyclical event constitutes one standard unit such as the second, is useful in the conduct of both advanced experiments and everyday affairs of life; the operational definition leaves aside the question whether there is something called time, apart from the counting activity just mentioned, that flows and that can be measured. Investigations of a single continuum called spacetime bring questions about space into questions about time, questions that have their roots in the works of early students of natural philosophy. Temporal measurement has occupied scientists and technologists, was a prime motivation in navigation and astronomy. Periodic events and periodic motion have long served as standards for units of time. Examples include the apparent motion of the sun across the sky, the phases of the moon, the swing of a pendulum, the beat of a heart.
The international unit of time, the second, is defined by measuring the electronic transition frequency of caesium atoms. Time is of significant social importance, having economic value as well as personal value, due to an awareness of the limited time in each day and in human life spans. Speaking, methods of temporal measurement, or chronometry, take two distinct forms: the calendar, a mathematical tool for organising intervals of time, the clock, a physical mechanism that counts the passage of time. In day-to-day life, the clock is consulted for periods less than a day whereas the calendar is consulted for periods longer than a day. Personal electronic devices display both calendars and clocks simultaneously; the number that marks the occurrence of a specified event as to hour or date is obtained by counting from a fiducial epoch – a central reference point. Artifacts from the Paleolithic suggest that the moon was used to reckon time as early as 6,000 years ago. Lunar calendars were among the first to appear, with years of either 13 lunar months.
Without intercalation to add days or months to some years, seasons drift in a calendar based on twelve lunar months. Lunisolar calendars have a thirteenth month added to some years to make up for the difference between a full year and a year of just twelve lunar months; the numbers twelve and thirteen came to feature prominently in many cultures, at least due to this relationship of months to years. Other early forms of calendars originated in Mesoamerica in ancient Mayan civilization; these calendars were religiously and astronomically based, with 18 months in a year and 20 days in a month, plus five epagomenal days at the end of the year. The reforms of Julius Caesar in 45 BC put the Roman world on a solar calendar; this Julian calendar was faulty in that its intercalation still allowed the astronomical solstices and equinoxes to advance against it by about 11 minutes per year. Pope Gregory XIII introduced a correction in 1582. During the French Revolution, a new clock and calendar were invented in attempt to de-Christianize time and create a more rational system in order to replace the Gregorian calendar.
The French Republican Calendar's days consisted of ten hours of a hundred minutes of a hundred seconds, which marked a deviation from the 12-based duodecimal system used in many other devices by many cultures. The system was abolished in 1806. A large variety of devices have been invented to measure time; the study of these devices is called horology. An Egyptian device that dates to c. 1500 BC, similar in shape to a bent T-square, measured the passage of time from the shadow cast by its crossbar on a nonlinear rule. The T was oriented eastward in the mornings. At noon, the device was turned around so. A sundial uses a gnomon to cast a shadow on a set of markings calibrated to the hour; the position of the shadow marks the hour in local time. The idea to separate the day into smaller parts is credited to Egyptians because of their sundials, which operated on a duodecimal system; the importance of the number 12 is due to the number of lunar cycles in a year and the number of stars used to count the passage of night.
The most precise timekeeping device of the ancient
Chartres is a commune and capital of the Eure-et-Loir department in France. It is located about 90 km southwest of Paris. Chartres is famous world-wide for its cathedral. Constructed between 1193 and 1250, this Gothic cathedral is in an exceptional state of preservation; the majority of the original stained glass windows survive intact, while the architecture has seen only minor changes since the early 13th century. Much of the old town, including the library associated with the School of Chartres, was destroyed by bombs in 1944. Chartres was in Gaul one of the principal towns of a Celtic tribe. In the Gallo-Roman period, it was called Autricum, name derived from the river Autura, afterwards civitas Carnutum, "city of the Carnutes", from which Chartres got its name; the city was burned by the Normans in 858, unsuccessfully besieged by them in 911. During the Middle Ages, it was the most important town of the Beauce, it gave its name to a county, held by the counts of Blois, the counts of Champagne, afterwards by the House of Châtillon, a member of which sold it to the Crown in 1286.
In 1417, during the Hundred Years' War, Chartres fell into the hands of the English, from whom it was recovered in 1432. In 1528, it was raised to the rank of a duchy by Francis I. In 1568, during the Wars of Religion, Chartres was unsuccessfully besieged by the Huguenot leader, the Prince of Condé, it was taken by the royal troops of Henry IV on 19 April 1591. On Sunday, 27 February 1594, the cathedral of Chartres was the site of the coronation of Henry IV after he converted to the Catholic faith, the only king of France whose coronation ceremony was not performed in Reims. In 1674, Louis XIV raised Chartres from a duchy to a duchy peerage in favor of his nephew, Duke Philippe II of Orléans; the title of Duke of Chartres was hereditary in the House of Orléans, given to the eldest son of the Duke of Orléans. In the 1870-1871 Franco-Prussian War, Chartres was seized by the Germans on 2 October 1870, continued during the rest of the war to be an important centre of operations. In World War II, the city suffered heavy damage by bombing and during the battle of Chartres in August 1944, but its cathedral was spared by an American Army officer who challenged the order to destroy it.
On 16 August 1944, Colonel Welborn Barton Griffith, Jr. questioned the necessity of destroying the cathedral and volunteered to go behind enemy lines to find out whether the Germans were using it as an observation post. With his driver, Griffith proceeded to the cathedral and, after searching it all the way up its bell tower, confirmed to Headquarters that it was empty of Germans; the order to destroy the cathedral was withdrawn. Colonel Griffith was killed in action on that day in the town of Lèves, 3.5 kilometres north of Chartres. For his heroic action both at Chartres and Lèves, Colonel Griffith received, several decorations awarded by the President of the United States and the U. S. Military, from the French government. Following deep reconnaissance missions in the region by the 3rd Cavalry Group and units of the 1139 Engineer Combat Group, after heavy fighting in and around the city, Chartres was liberated, on 18 August 1944, by the U. S. 5th Infantry and 7th Armored Divisions belonging to the XX Corps of the U.
S. Third Army commanded by General George S. Patton. Chartres is built on a hill on the left bank of the Eure River, its renowned medieval cathedral is at the top of the hill, its two spires are visible from miles away across the flat surrounding lands. To the southeast stretches the fertile plain of Beauce, the "granary of France", of which the town is the commercial centre. Chartres is best known for its cathedral, the Cathédrale Notre-Dame de Chartres, considered one of the finest and best preserved Gothic cathedrals in France and in Europe, its historical and cultural importance has been recognized by its inclusion on the UNESCO list of World Heritage Sites. It was built on the site of the former Chartres cathedral of Romanesque architecture, destroyed by fire in 1194. Begun in 1205, the construction of Notre-Dame de Chartres was completed 66 years later; the stained glass windows of the cathedral were financed by guilds of merchants and craftsmen, by wealthy noblemen, whose names appear at the bottom.
It is not known how the famous and unique blue, bleu de Chartres, of the glass was created, it has been impossible to replicate it. The French author Michel Pastoureau, says that it could be called bleu de Saint-Denis; the Église Saint-Pierre de Chartres, was the church of the Benedictine Abbaye Saint-Père-en-Vallée, founded in the 7th century by queen Balthild. At time of its construction, the abbey was outside the walls of the city, it contains fine stained glass and twelve representations of the apostles in enamel, created about 1547 by Léonard Limosin, which now can be seen in the Fine arts museum. Other noteworthy churches of Chartres are Saint-Aignan, Saint-Martin-au-Val, inside the Saint-Brice hospital. Musée des Beaux-Arts, Fine arts museum, housed in the former episcopal palace adjacent to the cathedral. Le Centre international du vitrail, a workshop-museum and cultural center devoted to stained glass art, located 50 metres from the cathedral. Conservatoire du machinisme et des pratiques agricoles, an agricultural museum.
Musée le grenier de l'histoire, history museum specializing in military uniforms and accoutrements, in Lèves, a suburb of Chartres. Muséum des sciences naturelles et de la préhistoire, Natural Science and Prehistory Museum (clo
An astrolabe is an elaborate inclinometer used by astronomers and navigators to measure the altitude above the horizon of a celestial body, day or night. It can be used to identify stars or planets, to determine local latitude given local time, to survey, or to triangulate, it was used in classical antiquity, the Islamic Golden Age, the European Middle Ages and the Age of Discovery for all these purposes. The astrolabe's importance not only comes from the early development of astronomy, but is effective for determining latitude on land or calm seas. Although it is less reliable on the heaving deck of a ship in rough seas, the mariner's astrolabe was developed to solve that problem. OED gives the translation "star-taker" for the English word astrolabe and traces it through medieval Latin to the Greek word astrolabos, from astron "star" and lambanein "to take". In the medieval Islamic world the Arabic word "al-Asturlāb" was given various etymologies. In Arabic texts, the word is translated as "ākhdhu al-Nujuum", a direct translation of the Greek word.
Al-Biruni quotes and criticizes medieval scientist Hamzah al-Isfahani who stated: "asturlab is an arabization of this Persian phrase". In medieval Islamic sources, there is a folk etymology of the word as "lines of lab", where "Lab" refers to a certain son of Idris; this etymology is mentioned by a 10th-century scientist rejected by al-Khwarizmi. An early astrolabe was invented in the Hellenistic civilization by Apollonius of Perga between 220 and 150 BC attributed to Hipparchus; the astrolabe was a marriage of the planisphere and dioptra an analog calculator capable of working out several different kinds of problems in astronomy. Theon of Alexandria wrote a detailed treatise on the astrolabe, Lewis argues that Ptolemy used an astrolabe to make the astronomical observations recorded in the Tetrabiblos; the invention of the plane astrolabe is sometimes wrongly attributed to Theon's daughter Hypatia, but it is, in fact, known to have been in use at least 500 years before Hypatia was born. The misattribution comes from a misinterpretation of a statement in a letter written by Hypatia's pupil Synesius, which mentions that Hypatia had taught him how to construct a plane astrolabe, but does not state anything about her having invented it herself.
Astrolabes continued in use in the Greek-speaking world throughout the Byzantine period. About 550 AD, Christian philosopher John Philoponus wrote a treatise on the astrolabe in Greek, the earliest extant treatise on the instrument. Mesopotamian bishop Severus Sebokht wrote a treatise on the astrolabe in the Syriac language in the mid-7th century. Sebokht refers to the astrolabe as being made of brass in the introduction of his treatise, indicating that metal astrolabes were known in the Christian East well before they were developed in the Islamic world or in the Latin West. Astrolabes were further developed in the medieval Islamic world, where Muslim astronomers introduced angular scales to the design, adding circles indicating azimuths on the horizon, it was used throughout the Muslim world, chiefly as an aid to navigation and as a way of finding the Qibla, the direction of Mecca. Eighth-century mathematician Muhammad al-Fazari is the first person credited with building the astrolabe in the Islamic world.
The mathematical background was established by Muslim astronomer Albatenius in his treatise Kitab az-Zij, translated into Latin by Plato Tiburtinus. The earliest surviving astrolabe is dated AH 315. In the Islamic world, astrolabes were used to find the times of sunrise and the rising of fixed stars, to help schedule morning prayers. In the 10th century, al-Sufi first described over 1,000 different uses of an astrolabe, in areas as diverse as astronomy, navigation, timekeeping, Salat, etc; the spherical astrolabe was a variation of both the astrolabe and the armillary sphere, invented during the Middle Ages by astronomers and inventors in the Islamic world. The earliest description of the spherical astrolabe dates back to Al-Nayrizi. In the 12th century, Sharaf al-Dīn al-Tūsī invented the linear astrolabe, sometimes called the "staff of al-Tusi", "a simple wooden rod with graduated markings but without sights, it was furnished with a plumb line and a double chord for making angular measurements and bore a perforated pointer".
The geared mechanical astrolabe was invented by Abi Bakr of Isfahan in 1235. Herman Contractus, the abbot of Reichman Abbey, examined the use of the astrolabe in Mensura Astrolai during the 11th century. Peter of Maricourt wrote a treatise on the construction and use of a universal astrolabe in the last half of the 13th century entitled Nova compositio astrolabii particularis. Universal astrolabes can be found at the History of Science Museum in Oxford. English author Geoffrey Chaucer compiled A Treatise on the Astrolabe for his son based on a work by Messahalla or Ibn al-Saffar; the same source was translated by others. The first printed book on the astrolabe was Composition and Use of Astrolabe by Christian of Prachatice using Messahalla, but original. In 1370, the first Indian treatise on the astrolabe was written by the Jain astronomer Mahendra Suri. A simplified astrolabe, known as a balesilha, was used by sailors to get an accurate reading of latitude while out to sea; the use of