1.
Science and technology in Iran
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Iran has made considerable advances in science and technology through education and training, despite international sanctions in almost all aspects of research during the past 30 years. Irans university population swelled from 100,000 in 1979 to 2 million in 2006, 70% of its science and engineering students are women. Irans scientific progress is reported to be the fastest in the world, Iran has made great strides in different sectors, including aerospace, nuclear science, medical development, as well as stem cell and cloning research. Persia was a cradle of science in earlier times, contributing to medicine, mathematics, science, trying to revive the golden time of Persian science, Irans scientists now are cautiously reaching out to the world. Many individual Iranian scientists, along with the Iranian Academy of Medical Sciences, Science in Persia evolved in two main phases separated by the arrival and widespread adoption of Islam in the region. References to scientific subjects such as science and mathematics occur in books written in the Pahlavi languages. The Qanat originated in pre-Achaemenid Persia, the oldest and largest known qanat is in the Iranian city of Gonabad, which, after 2,700 years, still provides drinking and agricultural water to nearly 40,000 people. Persian philosophers and inventors may have created the first batteries in the Parthian or Sassanid eras, some have suggested that the batteries may have been used medicinally. Windwheels were developed by the Babylonians ca.1700 BC to pump water for irrigation, in the 7th century, Persian engineers in Greater Iran developed a more advanced wind-power machine, the windmill, building upon the basic model developed by the Babylonians. The 9th century mathematician Muhammad Ibn Musa-al-Kharazmi created the Logarithm table, developed algebra and his writings were translated into Latin by Gerard of Cremona under the title, De jebra et almucabola. Robert of Chester also translated it under the title Liber algebras et almucabala, the works of Kharazmi exercised a profound influence on the development of mathematical thought in the medieval West. The practice and study of medicine in Iran has a long, situated at the crossroads of the East and West, Persia was often involved in developments in ancient Greek and Indian medicine, pre- and post-Islamic Iran have been involved in medicine as well. For example, the first teaching hospital where medical students methodically practiced on patients under the supervision of physicians was the Academy of Gundishapur in the Persian Empire. Some experts go so far as to claim that, to a large extent. The idea of xenotransplantation dates to the days of Achaemenidae, as evidenced by engravings of many mythologic chimeras still present in Persepolis, several documents still exist from which the definitions and treatments of the headache in medieval Persia can be ascertained. These documents give detailed and precise information on the different types of headaches. The medieval physicians listed various signs and symptoms, apparent causes, the medieval writings are both accurate and vivid, and they provide long lists of substances used in the treatment of headaches. Many of the approaches of physicians in medieval Persia are accepted today, however, although largely mythical in content, the passage illustrates working knowledge of anesthesia in ancient Persia
2.
Nasir al-Din al-Tusi
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Khawaja Muhammad ibn Muhammad ibn al-Hasan al-Tūsī, better known as Nasīr al-Dīn Tūsī, was a Persian polymath, architect, philosopher, physician, scientist, theologian and Marja Taqleed. He was of the Twelver Shī‘ah Islamic belief, the Muslim scholar Ibn Khaldun considered Tusi to be the greatest of the later Persian scholars. Nasir al-Din Tusi was born in the city of Tus in medieval Khorasan in the year 1201, in Hamadan and Tus he studied the Quran, Hadith, Shia jurisprudence, logic, philosophy, mathematics, medicine and astronomy. He was apparently born into a Shī‘ah family and lost his father at a young age, at a young age he moved to Nishapur to study philosophy under Farid al-Din Damad and mathematics under Muhammad Hasib. He met also Farid al-Din Attar, the legendary Sufi master who was killed by Mongol invaders. In Mosul he studied mathematics and astronomy with Kamal al-Din Yunus and he was captured after the invasion of the Alamut castle by the Mongol forces. Tusi has about 150 works, of which 25 are in Persian and the remaining are in Arabic, here are some of his major works, Kitāb al-Shakl al-qattāʴ Book on the complete quadrilateral. A five volume summary of trigonometry, al-Tadhkirah fiilm al-hayah – A memoir on the science of astronomy. Many commentaries were written about this work called Sharh al-Tadhkirah - Commentaries were written by Abd al-Ali ibn Muhammad ibn al-Husayn al-Birjandi, akhlaq-i Nasiri – A work on ethics. Al-Risalah al-Asturlabiyah – A Treatise on astrolabe, Zij-i ilkhani – A major astronomical treatise, completed in 1272. Sharh al-isharat Awsaf al-Ashraf a short work in Persian Tajrīd al-iʿtiqād – A commentary on Shia doctrines. During his stay in Nishapur, Tusi established a reputation as an exceptional scholar, tusi’s prose writing, which number over 150 works, represent one of the largest collections by a single Islamic author. Writing in both Arabic and Persian, Nasir al-Din Tusi dealt with religious topics and non-religious or secular subjects. His works include the definitive Arabic versions of the works of Euclid, Archimedes, Ptolemy, Autolycus, Tusi convinced Hulegu Khan to construct an observatory for establishing accurate astronomical tables for better astrological predictions. Beginning in 1259, the Rasad Khaneh observatory was constructed in Azarbaijan, south of the river Aras, and to the west of Maragheh, the capital of the Ilkhanate Empire. Based on the observations in this for the time being most advanced observatory and this book contains astronomical tables for calculating the positions of the planets and the names of the stars. His model for the system is believed to be the most advanced of his time. Between Ptolemy and Copernicus, he is considered by many to be one of the most eminent astronomers of his time, for his planetary models, he invented a geometrical technique called a Tusi-couple, which generates linear motion from the sum of two circular motions
3.
Ibn al-Haytham
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Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham, also known by the Latinization Alhazen or Alhacen, was an Arab Muslim scientist, mathematician, astronomer, and philosopher. Ibn al-Haytham made significant contributions to the principles of optics, astronomy, mathematics and he was the first to explain that vision occurs when light bounces on an object and then is directed to ones eyes. He spent most of his close to the court of the Fatimid Caliphate in Cairo and earned his living authoring various treatises. In medieval Europe, Ibn al-Haytham was honored as Ptolemaeus Secundus or simply called The Physicist and he is also sometimes called al-Baṣrī after his birthplace Basra in Iraq, or al-Miṣrī. Ibn al-Haytham was born c.965 in Basra, which was part of the Buyid emirate. Alhazen arrived in Cairo under the reign of Fatimid Caliph al-Hakim, Alhazen continued to live in Cairo, in the neighborhood of the famous University of al-Azhar, until his death in 1040. Legend has it that after deciding the scheme was impractical and fearing the caliphs anger, during this time, he wrote his influential Book of Optics and continued to write further treatises on astronomy, geometry, number theory, optics and natural philosophy. Among his students were Sorkhab, a Persian from Semnan who was his student for three years, and Abu al-Wafa Mubashir ibn Fatek, an Egyptian prince who learned mathematics from Alhazen. Alhazen made significant contributions to optics, number theory, geometry, astronomy, Alhazens work on optics is credited with contributing a new emphasis on experiment. In al-Andalus, it was used by the prince of the Banu Hud dynasty of Zaragossa and author of an important mathematical text. A Latin translation of the Kitab al-Manazir was made probably in the twelfth or early thirteenth century. His research in catoptrics centred on spherical and parabolic mirrors and spherical aberration and he made the observation that the ratio between the angle of incidence and refraction does not remain constant, and investigated the magnifying power of a lens. His work on catoptrics also contains the known as Alhazens problem. Alhazen wrote as many as 200 books, although only 55 have survived, some of his treatises on optics survived only through Latin translation. During the Middle Ages his books on cosmology were translated into Latin, Hebrew, the crater Alhazen on the Moon is named in his honour, as was the asteroid 59239 Alhazen. In honour of Alhazen, the Aga Khan University named its Ophthalmology endowed chair as The Ibn-e-Haitham Associate Professor, Alhazen, by the name Ibn al-Haytham, is featured on the obverse of the Iraqi 10, 000-dinar banknote issued in 2003, and on 10-dinar notes from 1982. The 2015 International Year of Light celebrated the 1000th anniversary of the works on optics by Ibn Al-Haytham, Alhazens most famous work is his seven-volume treatise on optics Kitab al-Manazir, written from 1011 to 1021. Optics was translated into Latin by a scholar at the end of the 12th century or the beginning of the 13th century
4.
Persian people
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The Persians are an Iranian ethnic group that make up over half the population of Iran. They share a cultural system and are native speakers of the Persian language. The ancient Persians were originally a branch of the ancient Iranian population who entered modern-day Iran by the early 10th century BC. The English term Persian derives from Latin Persia, itself deriving from Greek Persís, in the Bible, it is referred to as Parás —sometimes Paras uMadai —within the books of Esther, Daniel, Ezra and Nehemya. Although Persis was originally one of the provinces of ancient Iran, varieties of this term were adopted through Greek sources, thus, in the Western world, the term Persian came to refer to all inhabitants of the country. 10th-century Iraqi historian Al-Masudi refers to Pahlavi, Dari and Azari as dialects of the Persian language, in 1333, medieval Moroccan traveler and scholar Ibn Battuta, referred to the people of Kabul as a specific sub-tribe of Persians. Lady Mary Sheil, in her observation of Iran during the Qajar era, describes Persians, Kurds and Leks to identify themselves as descendants of the ancient Persians. On March 21,1935, the king of Iran, Reza Shah Pahlavi, issued a decree asking the international community to use the term Iran. However, the term Persian is still used to designate the predominant population of the Iranian peoples living in the Iranian cultural continent. The earliest known written record attributed to the Persians is from the Black Obelisk of Shalmaneser III, the inscription mentions Parsua as a tribal chiefdom in modern-day western Iran. The ancient Persians were originally a branch of the Iranian population that, in the early 10th century BC. They were initially dominated by the Assyrians for much of the first three centuries after arriving in the region, however, they played a role in the downfall of the Neo-Assyrian Empire. The Medes, another branch of population, founded the unified empire of Media as the regions dominant cultural and political power in c.625 BC. Meanwhile, the Persian dynasty of the Achaemenids formed a state to the central Median power. In c.552 BC, the Achaemenids began a revolution which led to the conquest of the empire by Cyrus II in c.550 BC. They spread their influence to the rest of what is called the Iranian Plateau, at its greatest extent, the Achaemenid Empire stretched from parts of Eastern Europe in the west, to the Indus Valley in the east, making it the largest empire the world had yet seen. The Achaemenids developed the infrastructure to support their growing influence, including the creation of Pasargadae and its legacy and impact on the kingdom of Macedon was also notably huge, even for centuries after the withdrawal of the Persians from Europe following the Greco-Persian Wars. The empire collapsed in 330 BC following the conquests of Alexander the Great, until the Parthian era, the Iranian identity had an ethnic, linguistic, and religious value, however, it did not yet have a political import
5.
Optics
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Optics is the branch of physics which involves the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviolet, and infrared light, because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties. Most optical phenomena can be accounted for using the classical description of light. Complete electromagnetic descriptions of light are, however, often difficult to apply in practice, practical optics is usually done using simplified models. The most common of these, geometric optics, treats light as a collection of rays that travel in straight lines, physical optics is a more comprehensive model of light, which includes wave effects such as diffraction and interference that cannot be accounted for in geometric optics. Historically, the model of light was developed first, followed by the wave model of light. Progress in electromagnetic theory in the 19th century led to the discovery that waves were in fact electromagnetic radiation. Some phenomena depend on the fact that light has both wave-like and particle-like properties, explanation of these effects requires quantum mechanics. When considering lights particle-like properties, the light is modelled as a collection of particles called photons, quantum optics deals with the application of quantum mechanics to optical systems. Optical science is relevant to and studied in many related disciplines including astronomy, various engineering fields, photography, practical applications of optics are found in a variety of technologies and everyday objects, including mirrors, lenses, telescopes, microscopes, lasers, and fibre optics. Optics began with the development of lenses by the ancient Egyptians and Mesopotamians, the earliest known lenses, made from polished crystal, often quartz, date from as early as 700 BC for Assyrian lenses such as the Layard/Nimrud lens. The ancient Romans and Greeks filled glass spheres with water to make lenses, the word optics comes from the ancient Greek word ὀπτική, meaning appearance, look. Greek philosophy on optics broke down into two opposing theories on how vision worked, the theory and the emission theory. The intro-mission approach saw vision as coming from objects casting off copies of themselves that were captured by the eye, plato first articulated the emission theory, the idea that visual perception is accomplished by rays emitted by the eyes. He also commented on the parity reversal of mirrors in Timaeus, some hundred years later, Euclid wrote a treatise entitled Optics where he linked vision to geometry, creating geometrical optics. Ptolemy, in his treatise Optics, held a theory of vision, the rays from the eye formed a cone, the vertex being within the eye. The rays were sensitive, and conveyed back to the observer’s intellect about the distance. He summarised much of Euclid and went on to describe a way to measure the angle of refraction, during the Middle Ages, Greek ideas about optics were resurrected and extended by writers in the Muslim world
6.
Number theory
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Number theory or, in older usage, arithmetic is a branch of pure mathematics devoted primarily to the study of the integers. It is sometimes called The Queen of Mathematics because of its place in the discipline. Number theorists study prime numbers as well as the properties of objects out of integers or defined as generalizations of the integers. Integers can be considered either in themselves or as solutions to equations, questions in number theory are often best understood through the study of analytical objects that encode properties of the integers, primes or other number-theoretic objects in some fashion. One may also study real numbers in relation to rational numbers, the older term for number theory is arithmetic. By the early century, it had been superseded by number theory. The use of the arithmetic for number theory regained some ground in the second half of the 20th century. In particular, arithmetical is preferred as an adjective to number-theoretic. The first historical find of a nature is a fragment of a table. The triples are too many and too large to have been obtained by brute force, the heading over the first column reads, The takiltum of the diagonal which has been subtracted such that the width. The tables layout suggests that it was constructed by means of what amounts, in language, to the identity 2 +1 =2. If some other method was used, the triples were first constructed and then reordered by c / a, presumably for use as a table. It is not known what these applications may have been, or whether there could have any, Babylonian astronomy, for example. It has been suggested instead that the table was a source of examples for school problems. While Babylonian number theory—or what survives of Babylonian mathematics that can be called thus—consists of this single, striking fragment, late Neoplatonic sources state that Pythagoras learned mathematics from the Babylonians. Much earlier sources state that Thales and Pythagoras traveled and studied in Egypt, Euclid IX 21—34 is very probably Pythagorean, it is very simple material, but it is all that is needed to prove that 2 is irrational. Pythagorean mystics gave great importance to the odd and the even, the discovery that 2 is irrational is credited to the early Pythagoreans. This forced a distinction between numbers, on the one hand, and lengths and proportions, on the other hand, the Pythagorean tradition spoke also of so-called polygonal or figurate numbers
7.
Avicenna
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Avicenna or Ibn Sīnā was a Persian polymath who is regarded as one of the most significant thinkers and writers of the Islamic Golden Age. Of the 450 works he is known to have written, around 240 have survived, in 1973, Avicennas Canon Of Medicine was reprinted in New York. Besides philosophy and medicine, Avicennas corpus includes writings on astronomy, alchemy, geography and geology, psychology, Islamic theology, logic, mathematics, physics and poetry. Avicenna is a Latin corruption of the Arabic patronym Ibn Sīnā, meaning Son of Sina, however, Avicenna was not the son, but the great-great-grandson of a man named Sina. His full name was Abū ʿAlī al-Ḥusayn ibn ʿAbd Allāh ibn al-Ḥasan ibn ʿAlī ibn Sīnā, Ibn Sina created an extensive corpus of works during what is commonly known as the Islamic Golden Age, in which the translations of Greco-Roman, Persian, and Indian texts were studied extensively. Under the Samanids, Bukhara rivaled Baghdad as a capital of the Islamic world. The study of the Quran and the Hadith thrived in such a scholarly atmosphere, philosophy, Fiqh and theology were further developed, most noticeably by Avicenna and his opponents. Al-Razi and Al-Farabi had provided methodology and knowledge in medicine and philosophy, Avicenna had access to the great libraries of Balkh, Khwarezm, Gorgan, Rey, Isfahan and Hamadan. Various texts show that he debated philosophical points with the greatest scholars of the time, aruzi Samarqandi describes how before Avicenna left Khwarezm he had met Al-Biruni, Abu Nasr Iraqi, Abu Sahl Masihi and Abu al-Khayr Khammar. Avicenna was born c. 980 in Afshana, a village near Bukhara, the capital of the Samanids, a Persian dynasty in Central Asia and Greater Khorasan. His mother, named Setareh, was from Bukhara, his father, Abdullah, was a respected Ismaili scholar from Balkh and his father worked in the government of Samanid in the village Kharmasain, a Sunni regional power. After five years, his brother, Mahmoud, was born. Avicenna first began to learn the Quran and literature in such a way that when he was ten years old he had learned all of them. According to his autobiography, Avicenna had memorised the entire Quran by the age of 10 and he learned Indian arithmetic from an Indian greengrocer, ءMahmoud Massahi and he began to learn more from a wandering scholar who gained a livelihood by curing the sick and teaching the young. He also studied Fiqh under the Sunni Hanafi scholar Ismail al-Zahid, Avicenna was taught some extent of philosophy books such as Introduction s Porphyry, Euclids Elements, Ptolemys Almagest by an unpopular philosopher, Abu Abdullah Nateli, who claimed philosophizing. As a teenager, he was troubled by the Metaphysics of Aristotle. For the next year and a half, he studied philosophy, in such moments of baffled inquiry, he would leave his books, perform the requisite ablutions, then go to the mosque, and continue in prayer till light broke on his difficulties. Deep into the night, he would continue his studies, and even in his dreams problems would pursue him and work out their solution
8.
Rainbow
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A rainbow is a meteorological phenomenon that is caused by reflection, refraction and dispersion of light in water droplets resulting in a spectrum of light appearing in the sky. It takes the form of a multicoloured arc, Rainbows caused by sunlight always appear in the section of sky directly opposite the sun. However, the observer sees only an arc formed by illuminated droplets above the ground. In a primary rainbow, the arc shows red on the outer part and this rainbow is caused by light being refracted when entering a droplet of water, then reflected inside on the back of the droplet and refracted again when leaving it. In a double rainbow, an arc is seen outside the primary arc. A rainbow is not located at a distance from the observer. Thus, a rainbow is not an object and cannot be physically approached, indeed, it is impossible for an observer to see a rainbow from water droplets at any angle other than the customary one of 42 degrees from the direction opposite the light source. Even if an observer sees another observer who seems under or at the end of a rainbow, Rainbows span a continuous spectrum of colours. Rainbows can be caused by many forms of airborne water and these include not only rain, but also mist, spray, and airborne dew. Rainbows can be observed there are water drops in the air. Because of this, rainbows are seen in the western sky during the morning. The most spectacular rainbow displays happen when half the sky is dark with raining clouds. The result is a rainbow that contrasts with the darkened background. During such good visibility conditions, the larger but fainter secondary rainbow is often visible and it appears about 10° outside of the primary rainbow, with inverse order of colours. The rainbow effect is commonly seen near waterfalls or fountains. In addition, the effect can be created by dispersing water droplets into the air during a sunny day. Rarely, a moonbow, lunar rainbow or nighttime rainbow, can be seen on strongly moonlit nights, as human visual perception for colour is poor in low light, moonbows are often perceived to be white. It is difficult to photograph the complete semicircle of a rainbow in one frame, for a 35 mm camera, a wide-angle lens with a focal length of 19 mm or less would be required
9.
Camera obscura
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The surroundings of the projected image have to be relatively dark for the image to be clear, so many historical camera obscura experiments were performed in dark rooms. The term camera obscura also refers to constructions or devices that use of the principle within a box. Camerae obscurae with a lens in the opening have been used since the second half of the 16th century, before the term camera obscura was first used in 1604, many other expressions were used including cubiculum obscurum, cubiculum tenebricosum, conclave obscurum and locus obscurus. Rays of light travel in straight lines and change when they are reflected and partly absorbed by an object, retaining information about the color, lit objects reflect rays of light in all directions. The human eye itself works much like a camera obscura with an opening, a biconvex lens, a camera obscura device consists of a box, tent or room with a small hole in one side. Light from a scene passes through the hole and strikes a surface inside, where the scene is reproduced, inverted and reversed. The image can be projected onto paper, and can then be traced to produce an accurate representation. In order to produce a reasonably clear projected image, the aperture has to be about 1/100th the distance to the screen, many camerae obscurae use a lens rather than a pinhole because it allows a larger aperture, giving a usable brightness while maintaining focus. As the pinhole is made smaller, the image gets sharper, with too small a pinhole, however, the sharpness worsens, due to diffraction. Using mirrors, as in an 18th-century overhead version, it is possible to project a right-side-up image, another more portable type is a box with an angled mirror projecting onto tracing paper placed on the glass top, the image being upright as viewed from the back. There are theories that occurrences of camera obscura effects inspired paleolithic cave paintings and it is also suggested that camera obscura projections could have played a role in Neolithic structures. Perforated gnomons projecting an image of the sun were described in the Chinese Zhoubi Suanjing writings. The location of the circle can be measured to tell the time of day. In Arab and European cultures its invention was later attributed to Egyptian astronomer. Some ancient sightings of gods and spirits, especially in worship, are thought to possibly have been conjured up by means of camera obscura projections. In these writings it is explained how the image in a collecting-point or treasure house is inverted by an intersecting point that collected the light. Light coming from the foot of a person would partly be hidden below. Rays from the head would partly be hidden above and partly form the part of the image
10.
Isaac Newton
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His book Philosophiæ Naturalis Principia Mathematica, first published in 1687, laid the foundations of classical mechanics. Newton also made contributions to optics, and he shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus. Newtons Principia formulated the laws of motion and universal gravitation that dominated scientists view of the universe for the next three centuries. Newtons work on light was collected in his influential book Opticks. He also formulated a law of cooling, made the first theoretical calculation of the speed of sound. Newton was a fellow of Trinity College and the second Lucasian Professor of Mathematics at the University of Cambridge, politically and personally tied to the Whig party, Newton served two brief terms as Member of Parliament for the University of Cambridge, in 1689–90 and 1701–02. He was knighted by Queen Anne in 1705 and he spent the last three decades of his life in London, serving as Warden and Master of the Royal Mint and his father, also named Isaac Newton, had died three months before. Born prematurely, he was a child, his mother Hannah Ayscough reportedly said that he could have fit inside a quart mug. When Newton was three, his mother remarried and went to live with her new husband, the Reverend Barnabas Smith, leaving her son in the care of his maternal grandmother, Newtons mother had three children from her second marriage. From the age of twelve until he was seventeen, Newton was educated at The Kings School, Grantham which taught Latin and Greek. He was removed from school, and by October 1659, he was to be found at Woolsthorpe-by-Colsterworth, Henry Stokes, master at the Kings School, persuaded his mother to send him back to school so that he might complete his education. Motivated partly by a desire for revenge against a bully, he became the top-ranked student. In June 1661, he was admitted to Trinity College, Cambridge and he started as a subsizar—paying his way by performing valets duties—until he was awarded a scholarship in 1664, which guaranteed him four more years until he would get his M. A. He set down in his notebook a series of Quaestiones about mechanical philosophy as he found it, in 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that later became calculus. Soon after Newton had obtained his B. A. degree in August 1665, in April 1667, he returned to Cambridge and in October was elected as a fellow of Trinity. Fellows were required to become ordained priests, although this was not enforced in the restoration years, however, by 1675 the issue could not be avoided and by then his unconventional views stood in the way. Nevertheless, Newton managed to avoid it by means of a special permission from Charles II. A and he was elected a Fellow of the Royal Society in 1672. Newtons work has been said to distinctly advance every branch of mathematics then studied and his work on the subject usually referred to as fluxions or calculus, seen in a manuscript of October 1666, is now published among Newtons mathematical papers
11.
Euclid
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Euclid, sometimes called Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the father of geometry. He was active in Alexandria during the reign of Ptolemy I, in the Elements, Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, Euclid is the anglicized version of the Greek name Εὐκλείδης, which means renowned, glorious. Very few original references to Euclid survive, so little is known about his life, the date, place and circumstances of both his birth and death are unknown and may only be estimated roughly relative to other people mentioned with him. He is rarely mentioned by name by other Greek mathematicians from Archimedes onward, the few historical references to Euclid were written centuries after he lived by Proclus c.450 AD and Pappus of Alexandria c.320 AD. Proclus introduces Euclid only briefly in his Commentary on the Elements, Proclus later retells a story that, when Ptolemy I asked if there was a shorter path to learning geometry than Euclids Elements, Euclid replied there is no royal road to geometry. This anecdote is questionable since it is similar to a story told about Menaechmus, a detailed biography of Euclid is given by Arabian authors, mentioning, for example, a birth town of Tyre. This biography is generally believed to be completely fictitious, however, this hypothesis is not well accepted by scholars and there is little evidence in its favor. The only reference that historians rely on of Euclid having written the Elements was from Proclus, although best known for its geometric results, the Elements also includes number theory. The geometrical system described in the Elements was long known simply as geometry, today, however, that system is often referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries that mathematicians discovered in the 19th century. In addition to the Elements, at least five works of Euclid have survived to the present day and they follow the same logical structure as Elements, with definitions and proved propositions. Data deals with the nature and implications of information in geometrical problems. On Divisions of Figures, which only partially in Arabic translation. It is similar to a first-century AD work by Heron of Alexandria, catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors. The attribution is held to be anachronistic however by J J OConnor, phaenomena, a treatise on spherical astronomy, survives in Greek, it is quite similar to On the Moving Sphere by Autolycus of Pitane, who flourished around 310 BC. Optics is the earliest surviving Greek treatise on perspective, in its definitions Euclid follows the Platonic tradition that vision is caused by discrete rays which emanate from the eye. One important definition is the fourth, Things seen under a greater angle appear greater, proposition 45 is interesting, proving that for any two unequal magnitudes, there is a point from which the two appear equal. Other works are attributed to Euclid, but have been lost
