David Gregory (mathematician)
David Gregory FRS was a Scottish mathematician and astronomer. He was professor of mathematics at the University of Edinburgh, Savilian Professor of Astronomy at the University of Oxford, a proponent of Isaac Newton's Principia; the fourth of the fifteen children of David Gregorie, a doctor from Kinnairdy and Jean Walker of Orchiston, David was born in Upper Kirkgate, Aberdeen. The nephew of astronomer and mathematician James Gregory, like his influential uncle before him, studied at Aberdeen Grammar School and Marischal College, from 1671 to 1675; the Gregorys left Scotland to escape religious discrimination. Young David visited several countries on the continent, including the Netherlands and France, did not return to Scotland until 1683. On 28 November 1683, Gregory graduated M. A. at University of Edinburgh, in October 1683 he became Chair of Mathematics at University of Edinburgh. He was "the first to teach the doctrines of the Principia, in a public seminary...in those days this was a daring innovation."Gregory decided to leave for England where, in 1691, he was elected Savilian Professor of Astronomy at the University of Oxford, due in large part to the influence of Isaac Newton.
The same year he was elected to be a Fellow of the Royal Society. In 1692, he was elected a Fellow of Oxford. Gregory spent several days with Isaac Newton in 1694, discussing revisions for a second edition of Newton's Principia. Gregory made notes of these discussions. In 1695 he published Catoptricae et dioptricae sphaericae elementa which addressed chromatic aberration and the possibility of its correction with achromatic lens. In 1705 Gregory became an Honorary Fellow of the Royal College of Physicians of Edinburgh. At the Union of 1707, he was given the responsibility of re-organising the Scottish Mint, he was an uncle of philosopher Thomas Reid. Gregory and his wife, Elizabeth Oliphant, had nine children. On his death in Maidenhead, Berkshire he was buried in Maidenhead churchyard. 1684: Exercitatio geometria dimensione curvarum 1695: Catoptricæ et dioptricæ sphæricæ elementa - digital facsimile from the Linda Hall Library 1702: Astronomiae physicae et geometricae elementa 1703: Euclides quae supersunt omnia 1745: Treatise of Practical Geometry via Internet Archive O'Connor, John J..
Lectures on Algebra ascribed to David Gregory, 18th century from Archives Hub by Jisc Papers of David Gregory from Archives Hub
Method of Fluxions
Method of Fluxions is a book by Isaac Newton. The book was completed in 1671, published in 1736. Fluxion is Newton's term for a derivative, he developed the method at Woolsthorpe Manor during the closing of Cambridge during the Great Plague of London from 1665 to 1667, but did not choose to make his findings known. Gottfried Leibniz developed his form of calculus independently around 1673, 7 years after Newton had developed the basis for differential calculus, as seen in surviving documents like “the method of fluxions and fluents..." from 1666. Leibniz however published his discovery of differential calculus in 1684, nine years before Newton formally published his fluxion notation form of calculus in part during 1693; the calculus notation in use today is that of Leibniz, although Newton's dot notation for differentiation x ˙ for denoting derivatives with respect to time is still in current use throughout mechanics and circuit analysis. Newton's Method of Fluxions was formally published posthumously, but following Leibniz's publication of the calculus a bitter rivalry erupted between the two mathematicians over who had developed the calculus first and so Newton no longer hid his knowledge of fluxions.
For a period of time encompassing Newton's working life, the discipline of analysis was a subject of controversy in the mathematical community. Although analytic techniques provided solutions to long-standing problems, including problems of quadrature and the finding of tangents, the proofs of these solutions were not known to be reducible to the synthetic rules of Euclidean geometry. Instead, analysts were forced to invoke infinitesimal, or "infinitely small", quantities to justify their algebraic manipulations; some of Newton's mathematical contemporaries, such as Isaac Barrow, were skeptical of such techniques, which had no clear geometric interpretation. Although in his early work Newton used infinitesimals in his derivations without justifying them, he developed something akin to the modern definition of limits in order to justify his work. Method of Fluxions at the Internet Archive
Sir Isaac Newton was an English mathematician, astronomer and author, recognised as one of the most influential scientists of all time, a key figure in the scientific revolution. His book Philosophiæ Naturalis Principia Mathematica, first published in 1687, laid the foundations of classical mechanics. Newton made seminal contributions to optics, shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus. In Principia, Newton formulated the laws of motion and universal gravitation that formed the dominant scientific viewpoint until it was superseded by the theory of relativity. Newton used his mathematical description of gravity to prove Kepler's laws of planetary motion, account for tides, the trajectories of comets, the precession of the equinoxes and other phenomena, eradicating doubt about the Solar System's heliocentricity, he demonstrated that the motion of objects on Earth and celestial bodies could be accounted for by the same principles. Newton's inference that the Earth is an oblate spheroid was confirmed by the geodetic measurements of Maupertuis, La Condamine, others, convincing most European scientists of the superiority of Newtonian mechanics over earlier systems.
Newton built the first practical reflecting telescope and developed a sophisticated theory of colour based on the observation that a prism separates white light into the colours of the visible spectrum. His work on light was collected in his influential book Opticks, published in 1704, he formulated an empirical law of cooling, made the first theoretical calculation of the speed of sound, introduced the notion of a Newtonian fluid. In addition to his work on calculus, as a mathematician Newton contributed to the study of power series, generalised the binomial theorem to non-integer exponents, developed a method for approximating the roots of a function, classified most of the cubic plane curves. Newton was a fellow of Trinity College and the second Lucasian Professor of Mathematics at the University of Cambridge, he was a devout but unorthodox Christian who rejected the doctrine of the Trinity. Unusually for a member of the Cambridge faculty of the day, he refused to take holy orders in the Church of England.
Beyond his work on the mathematical sciences, Newton dedicated much of his time to the study of alchemy and biblical chronology, but most of his work in those areas remained unpublished until long after his death. Politically and 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 spent the last three decades of his life in London, serving as Warden and Master of the Royal Mint, as well as president of the Royal Society. Isaac Newton was born on Christmas Day, 25 December 1642 "an hour or two after midnight", at Woolsthorpe Manor in Woolsthorpe-by-Colsterworth, a hamlet in the county of Lincolnshire, his father named Isaac Newton, had died three months before. Born prematurely, Newton was a small child; 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, Margery Ayscough.
Newton disliked his stepfather and maintained some enmity towards his mother for marrying him, as revealed by this entry in a list of sins committed up to the age of 19: "Threatening my father and mother Smith to burn them and the house over them." Newton's mother had three children from her second marriage. From the age of about twelve until he was seventeen, Newton was educated at The King's School, which taught Latin and Greek and imparted a significant foundation of mathematics, he was removed from school, returned to Woolsthorpe-by-Colsterworth by October 1659. His mother, widowed for the second time, attempted to make him an occupation he hated. Henry Stokes, master at The King's School, persuaded his mother to send him back to school. Motivated by a desire for revenge against a schoolyard bully, he became the top-ranked student, distinguishing himself by building sundials and models of windmills. In June 1661, he was admitted to Trinity College, Cambridge, on the recommendation of his uncle Rev William Ayscough, who had studied there.
He started as a subsizar—paying his way by performing valet's duties—until he was awarded a scholarship in 1664, guaranteeing him four more years until he could get his MA. At that time, the college's teachings were based on those of Aristotle, whom Newton supplemented with modern philosophers such as Descartes, astronomers such as Galileo and Thomas Street, through whom he learned of Kepler's work, he set down in his notebook a series of "Quaestiones" about mechanical philosophy. In 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that became calculus. Soon after Newton had obtained his BA degree in August 1665, the university temporarily closed as a precaution against the Great Plague. Although he had been undistinguished as a Cambridge student, Newton's private studies at his home in Woolsthorpe over the subsequent two years saw the development of his theories on calculus and the law of gravitation. In April 1667, he returned in October was elected as a fellow of Trinity.
Fellows were required to become ordained priests, although this was no
Physics is the natural science that studies matter, its motion, behavior through space and time, that studies the related entities of energy and force. Physics is one of the most fundamental scientific disciplines, its main goal is to understand how the universe behaves. Physics is one of the oldest academic disciplines and, through its inclusion of astronomy the oldest. Over much of the past two millennia, chemistry and certain branches of mathematics, were a part of natural philosophy, but during the scientific revolution in the 17th century these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, the boundaries of physics which are not rigidly defined. New ideas in physics explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics enable advances in new technologies.
For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have transformed modern-day society, such as television, domestic appliances, nuclear weapons. Astronomy is one of the oldest natural sciences. Early civilizations dating back to beyond 3000 BCE, such as the Sumerians, ancient Egyptians, the Indus Valley Civilization, had a predictive knowledge and a basic understanding of the motions of the Sun and stars; the stars and planets were worshipped, believed to represent gods. While the explanations for the observed positions of the stars were unscientific and lacking in evidence, these early observations laid the foundation for astronomy, as the stars were found to traverse great circles across the sky, which however did not explain the positions of the planets. According to Asger Aaboe, the origins of Western astronomy can be found in Mesopotamia, all Western efforts in the exact sciences are descended from late Babylonian astronomy.
Egyptian astronomers left monuments showing knowledge of the constellations and the motions of the celestial bodies, while Greek poet Homer wrote of various celestial objects in his Iliad and Odyssey. Natural philosophy has its origins in Greece during the Archaic period, when pre-Socratic philosophers like Thales rejected non-naturalistic explanations for natural phenomena and proclaimed that every event had a natural cause, they proposed ideas verified by reason and observation, many of their hypotheses proved successful in experiment. The Western Roman Empire fell in the fifth century, this resulted in a decline in intellectual pursuits in the western part of Europe. By contrast, the Eastern Roman Empire resisted the attacks from the barbarians, continued to advance various fields of learning, including physics. In the sixth century Isidore of Miletus created an important compilation of Archimedes' works that are copied in the Archimedes Palimpsest. In sixth century Europe John Philoponus, a Byzantine scholar, questioned Aristotle's teaching of physics and noting its flaws.
He introduced the theory of impetus. Aristotle's physics was not scrutinized until John Philoponus appeared, unlike Aristotle who based his physics on verbal argument, Philoponus relied on observation. On Aristotle's physics John Philoponus wrote: “But this is erroneous, our view may be corroborated by actual observation more than by any sort of verbal argument. For if you let fall from the same height two weights of which one is many times as heavy as the other, you will see that the ratio of the times required for the motion does not depend on the ratio of the weights, but that the difference in time is a small one, and so, if the difference in the weights is not considerable, that is, of one is, let us say, double the other, there will be no difference, or else an imperceptible difference, in time, though the difference in weight is by no means negligible, with one body weighing twice as much as the other”John Philoponus' criticism of Aristotelian principles of physics served as an inspiration for Galileo Galilei ten centuries during the Scientific Revolution.
Galileo cited Philoponus in his works when arguing that Aristotelian physics was flawed. In the 1300s Jean Buridan, a teacher in the faculty of arts at the University of Paris, developed the concept of impetus, it was a step toward the modern ideas of momentum. Islamic scholarship inherited Aristotelian physics from the Greeks and during the Islamic Golden Age developed it further placing emphasis on observation and a priori reasoning, developing early forms of the scientific method; the most notable innovations were in the field of optics and vision, which came from the works of many scientists like Ibn Sahl, Al-Kindi, Ibn al-Haytham, Al-Farisi and Avicenna. The most notable work was The Book of Optics, written by Ibn al-Haytham, in which he conclusively disproved the ancient Greek idea about vision, but came up with a new theory. In the book, he presented a study of the phenomenon of the camera obscura (his thousand-year-old
Savilian Professor of Astronomy
The position of Savilian Professor of Astronomy was established at the University of Oxford in 1619. It was founded by Sir Henry Savile, a mathematician and classical scholar, Warden of Merton College and Provost of Eton College, he appointed John Bainbridge as the first professor, who took up his duties in 1620 or 1621. There have been 21 astronomy professors in all. Past professors include Christopher Wren, architect of St Paul's Cathedral in London and the Sheldonian Theatre in Oxford. Three professors have been awarded the Gold Medal of the Royal Astronomical Society: Charles Pritchard, Harry Plaskett and Joseph Silk; the two Savilian chairs have been linked with professorial fellowships at New College, since the late 19th century. In the past, some of the professors were provided with an official residence, either near New College or at the Radcliffe Observatory, although this practice ended in the 19th century; the astronomy professor is a member of the Sub-Department of Astrophysics at Oxford.
Sir Henry Savile, the Warden of Merton College and Provost of Eton College, was saddened by what the 20th-century mathematician Ida Busbridge has described as "the wretched state of mathematical studies in England", so founded professorships in geometry and astronomy at the University of Oxford in 1619. He donated his books to the university's Bodleian Library, he required the professors to be men of good character, at least 26 years old, to have "imbibed the purer philosophy from the springs of Aristotle and Plato" before acquiring a thorough knowledge of science. The professors could come from any Christian country, but he specified that a professor from England should have a Master of Arts degree as a minimum, he wanted students to be educated in the works of the leading scientists of the ancient world. Tuition in trigonometry was to be shared by the two professors; as many students would have had little mathematical knowledge, the professors were permitted to provide instruction in basic mathematics in English.
He required the astronomy professor "to take astronomical observations as well by night as by day", to place in the library records of his discoveries. Savile prohibited the professors from practicing astrology or preparing horoscopes, stated that accepting any position as a priest or as an officer of the university or of a college would cause forfeiture of the professorship; each professor was required to lecture in public for 45 minutes twice weekly during the university terms and would be fined 10 shillings for every day missed. Students who were required to attend, but who failed to do without good cause, were to be fined sixpence. Savile provided that the rents from specified properties in Kent and Essex were to be divided between the professors, giving each £160 annually. Savile selected John Bainbridge to be the first astronomy professor. In the documents establishing the professorship, Savile reserved to himself the right to appoint the professors during his lifetime, although he died in 1622 before the position fell vacant.
He provided that after his death, vacancies should be filled by a majority of a group of "most distinguished persons": the Archbishop of Canterbury, the Lord Chancellor, the Chancellor of the university, the Bishop of London, the Secretary of State, the Chief Justice of the Common Pleas, the Chief Justice of the King's Bench, the Chief Baron of the Exchequer and the Dean of the Court of Arches. The Vice-Chancellor of the university was to inform the electors of any vacancy, could be summoned to advise them; the appointment could either be made straight away, or delayed for some months to see whether "any eminent mathematician can be allured" from abroad. As part of reforms of the university in the 19th century, the University of Oxford commissioners laid down new statutes for the chair in 1881, replacing Savile's original instructions and requirements; the 1881 statute provided that the professor was to "lecture and give instruction in theoretical and practical Astronomy", was to be a Fellow of New College.
The electors for the professorship were to be the Warden of New College, the Chancellor of the university, the President of the Royal Society, the Astronomer Royal, the Radcliffe Observer, a person nominated by the university council and one other nominated by New College. Changes to the university's internal legislation in the 20th and early 21st centuries abolished specific statutes for the duties of, rules for appointment to, individual chairs such as the Savilian professorships; the University Council is now empowered to make appropriate arrangements for appointments and conditions of service, with the college to which any professorship is allocated to have two representatives on the board of electors. The professorship is one of two permanent chairs attached to
Brook Taylor was an English mathematician, best known for Taylor's theorem and the Taylor series. Brook Taylor was born in Edmonton to John Taylor of Bifrons House in Patrixbourne and Olivia Tempest, daughter of Sir Nicholas Tempest, Bart. of Durham. He entered St John's College, Cambridge, as a fellow-commoner in 1701, took degrees of LL. B. and LL. D. in 1709 and 1714, respectively. Having studied mathematics under John Machin and John Keill, in 1708 he obtained a remarkable solution of the problem of the "centre of oscillation," which, remained unpublished until May 1714, when his claim to priority was disputed by Johann Bernoulli. Taylor's Methodus Incrementorum Directa et Inversa added a new branch to higher mathematics, now called the "calculus of finite differences". Among other ingenious applications, he used it to determine the form of movement of a vibrating string, by him first reduced to mechanical principles; the same work contained the celebrated formula known as Taylor's formula, the importance of which remained unrecognized until 1772, when J. L. Lagrange realized its powers and termed it "the main foundation of differential calculus".
In his 1715 essay Linear Perspective, Taylor set forth the true principles of the art in an original and more general form than any of his predecessors. Taylor was elected a fellow of the Royal Society early in 1712, in the same year sat on the committee for adjudicating the claims of Sir Isaac Newton and Gottfried Leibniz, acted as secretary to the society from 13 January 1714 to 21 October 1718. From 1715 his studies took a religious bent, he corresponded in that year with the Comte de Montmort on the subject of Nicolas Malebranche's tenets. Unfinished treatises, On the Jewish Sacrifices and On the Lawfulness of Eating Blood, written on his return from Aix-la-Chapelle in 1719, were afterwards found among his papers, his marriage in 1721 with Miss Brydges of Wallington, led to an estrangement from his father, which ended in 1723 after her death in giving birth to a son, who died. He spent the next two years with his family at Bifrons, in 1725 he married—this time with his father's approval—Sabetta Sawbridge of Olantigh, who died in childbirth in 1730.
By the date of his father's death in 1729 he had inherited the Bifrons estate. As a mathematician, he was the only Englishman after Sir Isaac Newton and Roger Cotes capable of holding his own with the Bernoullis, but a great part of the effect of his demonstrations was lost through his failure to express his ideas and clearly. Taylor's fragile health gave way, he was buried in London on 2 December 1731, near his first wife, in the churchyard of St Anne's, Soho. A posthumous work entitled Contemplatio Philosophica was printed for private circulation in 1793 by Taylor's grandson, Sir William Young, prefaced by a life of the author, with an appendix containing letters addressed to him by Bolingbroke and others. Several short papers by Taylor were published in Phil. Trans. Vols. xxvii to xxxii, including accounts of some interesting experiments in magnetism and capillary attraction. In 1719 he issued an improved version of his work on perspective, with the title New Principles of Linear Perspective, revised by John Colson in 1749, printed again, with portrait and life of the author, in 1811.
A French translation was published in 1757. In Methodus Incrementorum, Taylor gave the first satisfactory investigation of astronomical refraction. Taylor, Methodus Incrementorum Directa et Inversa, London: William Innys. Annotated English translation by Ian Bruce Taylor, Linear Perspective: Or, a New Method of Representing Justly All Manner of Objects as They Appear to the Eye in All Situations, London: R. Knaplock, archived from the original on 2016-04-11. Taylor is an impact crater located on the Moon, named in honour of Brook Taylor. Andersen, Kirsti. Brook Taylor’s Work on Linear Perspective. Springer Science & Business Media. ISBN 978-1-4612-0935-5. Anderson, Marlow. Sherlock Holmes in Babylon: And Other Tales of Mathematical History. Mathematical Association of America. P. 309. ISBN 978-0-88385-546-1. Carlyle, Edward Irving. "Taylor, Brook". In Lee, Sidney. Dictionary of National Biography. 55. London: Smith, Elder & Co. Feigenbaum, Lenore. "Brook Taylor and the Method of Increments". Archive for History of Exact Sciences.
34: 1–140. Doi:10.1007/BF00329903. O'Connor, John J.. "Brook Taylor", MacTutor History of Mathematics archive, University of St Andrews. Beningbrough Hall has a painting by John Closterman of Taylor aged about 12 with his brothers and sisters. See NPG 5320: The Children of John Taylor of Bifrons Park Brook Taylor's pedigree Taylor, a crater on the Moon named after Brook Taylor
Edinburgh is the capital city of Scotland and one of its 32 council areas. Part of the county of Midlothian, it is located in Lothian on the Firth of Forth's southern shore. Recognised as the capital of Scotland since at least the 15th century, Edinburgh is the seat of the Scottish Government, the Scottish Parliament and the supreme courts of Scotland; the city's Palace of Holyroodhouse is the official residence of the monarch in Scotland. The city has long been a centre of education in the fields of medicine, Scots law, philosophy, the sciences and engineering, it is the second largest financial centre in the United Kingdom and the city's historical and cultural attractions have made it the United Kingdom's second most popular tourist destination, attracting over one million overseas visitors each year. Edinburgh is Scotland's second most populous city and the seventh most populous in the United Kingdom; the official population estimates are 488,050 for the Locality of Edinburgh, 513,210 for the City of Edinburgh, 1,339,380 for the city region.
Edinburgh lies at the heart of the Edinburgh and South East Scotland city region comprising East Lothian, Fife, Scottish Borders and West Lothian. The city is the annual venue of the General Assembly of the Church of Scotland, it is home to national institutions such as the National Museum of Scotland, the National Library of Scotland and the Scottish National Gallery. The University of Edinburgh, founded in 1582 and now one of four in the city, is placed 18th in the QS World University Rankings for 2019; the city is famous for the Edinburgh International Festival and the Fringe, the latter being the world's largest annual international arts festival. Historic sites in Edinburgh include Edinburgh Castle, the Palace of Holyroodhouse, the churches of St. Giles and the Canongate, the extensive Georgian New Town, built in the 18th/19th centuries. Edinburgh's Old Town and New Town together are listed as a UNESCO World Heritage site, managed by Edinburgh World Heritage since 1999. "Edin", the root of the city's name, derives from Eidyn, the name for this region in Cumbric, the Brittonic Celtic language spoken there.
The name's meaning is unknown. The district of Eidyn centred on the dun or hillfort of Eidyn; this stronghold is believed to have been located at Castle Rock, now the site of Edinburgh Castle. Eidyn was conquered by the Angles of Bernicia in the 7th century and by the Scots in the 10th century; as the language shifted to Old English, subsequently to modern English and Scots, The Brittonic din in Din Eidyn was replaced by burh, producing Edinburgh. Din became dùn in Scottish Gaelic, producing Dùn Èideann; the city is affectionately nicknamed Auld Reekie, Scots for Old Smoky, for the views from the country of the smoke-covered Old Town. Allan Ramsay said. A name the country people give Edinburgh from the cloud of smoke or reek, always impending over it."Thomas Carlyle said, "Smoke cloud hangs over old Edinburgh,—for since Aeneas Silvius's time and earlier, the people have the art strange to Aeneas, of burning a certain sort of black stones, Edinburgh with its chimneys is called'Auld Reekie' by the country people."A character in Walter Scott's The Abbot says "... yonder stands Auld Reekie--you may see the smoke hover over her at twenty miles' distance."Robert Chambers who said that the sobriquet could not be traced before the reign of Charles II attributed the name to a Fife laird, Durham of Largo, who regulated the bedtime of his children by the smoke rising above Edinburgh from the fires of the tenements.
"It's time now bairns, to tak' the beuks, gang to our beds, for yonder's Auld Reekie, I see, putting on her nicht -cap!"Some have called Edinburgh the Athens of the North for a variety of reasons. The earliest comparison between the two cities showed that they had a similar topography, with the Castle Rock of Edinburgh performing a similar role to the Athenian Acropolis. Both of them had fertile agricultural land sloping down to a port several miles away. Although this arrangement is common in Southern Europe, it is rare in Northern Europe; the 18th-century intellectual life, referred to as the Scottish Enlightenment, was a key influence in gaining the name. Such luminaries as David Hume and Adam Smith shone during this period. Having lost most of its political importance after the Union, some hoped that Edinburgh could gain a similar influence on London as Athens had on Rome. A contributing factor was the neoclassical architecture that of William Henry Playfair, the National Monument. Tom Stoppard's character Archie, of Jumpers, said playing on Reykjavík meaning "smoky bay", that the "Reykjavík of the South" would be more appropriate.
The city has been known by several Latin names, such as Aneda or Edina. The adjectival form of the latter, can be seen inscribed on educational buildings; the Scots poets Robert Fergusson and Robert Burns used Edina in their poems. Ben Jonson described it as "Britaine's other eye", Sir Walter Scott referred to it as "yon Empress of the North". Robert Louis Stevenson a son of the city, wrote, "Edinburgh is what Paris ought to be"; the colloquial pronunciation "Embra" or "Embro" has been used, as in Robert Garioch's Embro to the Ploy. The earliest known human habitation in the Edinburgh area was at Cramond, where evidence was found of a Mesolithi