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77-394: Charles Babbage KH FRS ( / ˈ b æ b ɪ dʒ / ; 26 December 1791 – 18 October 1871) was an English polymath . A mathematician, philosopher, inventor and mechanical engineer, Babbage originated the concept of a digital programmable computer. Babbage is considered by some to be " father of the computer ". He is credited with inventing the first mechanical computer ,
154-492: A Philosopher (1864), Babbage wrote a whole chapter on the topic of religion, where he identified three sources of divine knowledge: He stated, on the basis of the design argument , that studying the works of nature had been the more appealing evidence, and the one which led him to actively profess the existence of God . Advocating for natural theology, he wrote: In the works of the Creator ever open to our examination, we possess
231-543: A broader syllabus and more interest in applications; but William Whewell found the programme unacceptable. A controversy Babbage had with Richard Jones lasted for six years. He never did give a lecture. It was during this period that Babbage tried to enter politics. Simon Schaffer writes that his views of the 1830s included disestablishment of the Church of England , a broader political franchise , and inclusion of manufacturers as stakeholders. He twice stood for Parliament as
308-525: A candidate for the borough of Finsbury . In 1832 he came in third among five candidates, missing out by some 500 votes in the two-member constituency when two other reformist candidates, Thomas Wakley and Christopher Temple, split the vote. In his memoirs Babbage related how this election brought him the friendship of Samuel Rogers : his brother Henry Rogers wished to support Babbage again, but died within days. In 1834 Babbage finished last among four. In 1832, Babbage, Herschel and Ivory were appointed Knights of
385-698: A conventional resident don , and inattentive to his teaching responsibilities, he wrote three topical books during this period of his life. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1832. Babbage was out of sympathy with colleagues: George Biddell Airy , his predecessor as Lucasian Professor of Mathematics at Trinity College, Cambridge, thought an issue should be made of his lack of interest in lecturing. Babbage planned to lecture in 1831 on political economy . Babbage's reforming direction looked to see university education more inclusive, universities doing more for research,
462-513: A curve earlier studied and constructed by Pierre de Fermat and Guido Grandi . Agnesi described the curve as versiera in Italian, which is a synonym for the adjective versoria meaning "turning in every direction". At the same time versiera was used as a term for a "she-devil" or "witch", from Latin Adversarius , an alias for " devil " (Adversary of God). Future translations and publications of
539-534: A firm basis on which to raise the superstructure of an enlightened creed. The more man inquires into the laws which regulate the material universe, the more he is convinced that all its varied forms arise from the action of a few simple principles ... The works of the Creator, ever present to our senses, give a living and perpetual testimony of his power and goodness far surpassing any evidence transmitted through human testimony. The testimony of man becomes fainter at every stage of transmission, whilst each new inquiry into
616-632: A later visit to Piedmont . In April 1828 he was in Rome , and relying on Herschel to manage the difference engine project, when he heard that he had become a professor at Cambridge, a position he had three times failed to obtain (in 1820, 1823 and 1826). Babbage was instrumental in founding the Royal Astronomical Society in 1820, initially known as the Astronomical Society of London. Its original aims were to reduce astronomical calculations to
693-603: A life-threatening fever. For a short time, he attended King Edward VI Grammar School in Totnes , South Devon, but his health forced him back to private tutors for a time. Babbage then joined the 30-student Holmwood Academy , in Baker Street, Enfield , Middlesex , under the Reverend Stephen Freeman. The academy had a library that prompted Babbage's love of mathematics. He studied with two more private tutors after leaving
770-494: A meeting hosted by John Chapman to campaign against the Booksellers Association, still a cartel . It has been written that "what Arthur Young was to agriculture, Charles Babbage was to the factory visit and machinery". Babbage's theories are said to have influenced the layout of the 1851 Great Exhibition , and his views had a strong effect on his contemporary George Julius Poulett Scrope . Karl Marx argued that
847-399: A more standard form, and to circulate data. These directions were closely connected with Babbage's ideas on computation, and in 1824 he won its Gold Medal , cited "for his invention of an engine for calculating mathematical and astronomical tables ". Babbage's motivation to overcome errors in tables by mechanisation had been a commonplace since Dionysius Lardner wrote about it in 1834 in
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#1732851908091924-505: A particularly strong influence on him. Later in life, Babbage concluded that "the true value of the Christian religion rested, not on speculative [theology] ... but ... upon those doctrines of kindness and benevolence which that religion claims and enforces, not merely in favour of man himself but of every creature susceptible of pain or of happiness." In his autobiography Passages from the Life of
1001-514: A prominent figure in the ideating of computing. Parts of his incomplete mechanisms are on display in the Science Museum in London. In 1991, a functioning difference engine was constructed from the original plans. Built to tolerances achievable in the 19th century, the success of the finished engine indicated that Babbage's machine would have worked. Babbage's birthplace is disputed, but according to
1078-508: A student, Babbage was also a member of other societies such as The Ghost Club , concerned with investigating supernatural phenomena, and the Extractors Club, dedicated to liberating its members from the madhouse, should any be committed to one. In 1812, Babbage transferred to Peterhouse, Cambridge . He was the top mathematician there, but did not graduate with honours. He instead received a degree without examination in 1814. He had defended
1155-427: A systematic illustration of the different results and theorems of infinitesimal calculus . The model for her treatise was Le calcul différentiel et intégral dans l’Analyse by Charles René Reyneau . In this treatise, she worked on integrating mathematical analysis with algebra . The first volume treats the analysis of finite quantities and the second of the analysis of infinitesimals . A French translation of
1232-554: A thesis that was considered blasphemous in the preliminary public disputation, but it is not known whether this fact is related to his not sitting the examination. Considering his reputation, Babbage quickly made progress. He lectured to the Royal Institution on astronomy in 1815, and was elected a Fellow of the Royal Society in 1816. After graduation, on the other hand, he applied for positions unsuccessfully, and had little in
1309-401: A translation from French of the lectures of Sylvestre Lacroix , which was then the state-of-the-art calculus textbook. Reference to Lagrange in calculus terms marks out the application of what are now called formal power series . British mathematicians had used them from about 1730 to 1760. As re-introduced, they were not simply applied as notations in differential calculus . They opened up
1386-852: A uniform rate that was put into effect with the introduction of the Uniform Fourpenny Post supplanted by the Uniform Penny Post in 1839 and 1840. Colby was another of the founding group of the Society. He was also in charge of the Survey of Ireland . Herschel and Babbage were present at a celebrated operation of that survey, the remeasuring of the Lough Foyle baseline. The Analytical Society had initially been no more than an undergraduate provocation. During this period it had some more substantial achievements. In 1816, Babbage, Herschel and Peacock published
1463-641: Is "considered to be the first woman in the Western world to have achieved a reputation in mathematics". The most valuable result of her labours was the Instituzioni analitiche ad uso della gioventù italiana , (Analytical Institutions for the Use of Italian Youth) which was published in Milan in 1748 and "was regarded as the best introduction extant to the works of Euler ". The goal of this work was, according to Agnesi herself, to give
1540-530: Is a Divine energy which overrides what we familiarly call the laws of nature." He alluded to the limits of human experience, expressing: "all that we see in a miracle is an effect which is new to our observation, and whose cause is concealed. The cause may be beyond the sphere of our observation, and would be thus beyond the familiar sphere of nature; but this does not make the event a violation of any law of nature. The limits of man's observation lie within very narrow boundaries, and it would be arrogance to suppose that
1617-492: Is that skilled workers typically spend parts of their time performing tasks that are below their skill level. If the labour process can be divided among several workers, labour costs may be cut by assigning only high-skill tasks to high-cost workers, restricting other tasks to lower-paid workers. He also pointed out that training or apprenticeship can be taken as fixed costs; but that returns to scale are available by his approach of standardisation of tasks, therefore again favouring
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#17328519080911694-462: The Edinburgh Review (under Babbage's guidance). The context of these developments is still debated. Babbage's own account of the origin of the difference engine begins with the Astronomical Society's wish to improve The Nautical Almanac . Babbage and Herschel were asked to oversee a trial project, to recalculate some part of those tables. With the results to hand, discrepancies were found. This
1771-563: The Oxford Dictionary of National Biography he was most likely born at 44 Crosby Row, Walworth Road , London, England. A blue plaque on the junction of Larcom Street and Walworth Road commemorates the event. His date of birth was given in his obituary in The Times as 26 December 1792; but then a nephew wrote to say that Babbage was born one year earlier, in 1791. The parish register of St. Mary's , Newington , London, shows that Babbage
1848-527: The Difference Engine , that eventually led to more complex electronic designs, though all the essential ideas of modern computers are to be found in his Analytical Engine , programmed using a principle openly borrowed from the Jacquard loom . Babbage had a broad range of interests in addition to his work on computers covered in his 1832 book Economy of Manufactures and Machinery . He was an important figure in
1925-774: The House of Hanover was a branch. Since Hanover and the United Kingdom shared a monarch until 1837, the order was frequently bestowed upon British subjects . Until 1837 the order was frequently awarded to officers in the British Navy and Army , although it was still classed as a foreign order, with British members of the order not entitled to style themselves as "Sir" unless they were also created Knights Bachelor , as many were. The British link ended in 1837 when Hanover 's royal union with Great Britain ended, with Ernest Augustus becoming King of Hanover and Queen Victoria ascending
2002-457: The Instituzioni analitiche carried forward the former meaning either as a translation error or possibly as a pun. The curve has become known as the "Witch of Agnesi". Agnesi also wrote a commentary on the Traité analytique des sections coniques du marquis de l'Hôpital which, though highly praised by those who saw it in manuscript, was never published. In 1750, on the illness of her father, she
2079-681: The Royal Guelphic Order , however they were not subsequently made knights bachelor to entitle them to the prefix Sir , which often came with appointments to that foreign order (though Herschel was later created a baronet ). Babbage now emerged as a polemicist . One of his biographers notes that all his books contain a "campaigning element". His Reflections on the Decline of Science and some of its Causes (1830) stands out, however, for its sharp attacks. It aimed to improve British science, and more particularly to oust Davies Gilbert as President of
2156-672: The Statistical Society followed. Babbage was its public face, backed by Richard Jones and Robert Malthus . Babbage published On the Economy of Machinery and Manufactures (1832), on the organisation of industrial production . It was an influential early work of operational research . John Rennie the Younger in addressing the Institution of Civil Engineers on manufacturing in 1846 mentioned mostly surveys in encyclopaedias, and Babbage's book
2233-578: The Vector Analysis and the mathematics by which investigations in physical science are now conducted? In 1837, responding to the series of eight Bridgewater Treatises , Babbage published his Ninth Bridgewater Treatise , under the title On the Power, Wisdom and Goodness of God, as manifested in the Creation . In this work Babbage weighed in on the side of uniformitarianism in a current debate. He preferred
2310-480: The exponential map ). But via Herschel he was influenced by Arbogast's ideas in the matter of iteration , i.e. composing a function with itself, possibly many times. Writing in a major paper on functional equations in the Philosophical Transactions (1815/6), Babbage said his starting point was work of Gaspard Monge . From 1828 to 1839, Babbage was Lucasian Professor of Mathematics at Cambridge. Not
2387-440: The factory system . His view of human capital was restricted to minimising the time period for recovery of training costs. Another aspect of the work was its detailed breakdown of the cost structure of book publishing. Babbage took the unpopular line, from the publishers' perspective, of exposing the trade's profitability. He went as far as to name the organisers of the trade's restrictive practices. Twenty years later he attended
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2464-643: The British throne. When Hanover was annexed by the Kingdom of Prussia in 1866, the order continued as a house order to be awarded by the Royal House of Hanover. Today, its current Sovereign is the Hanoverian head of the house, Ernst August, Prince of Hanover . The insignia was based on the white horse on Hanover's arms. The Order includes two divisions, Civil and Military, the latter indicated by crossed swords on both
2541-582: The Royal Society, which Babbage wished to reform. It was written out of pique, when Babbage hoped to become the junior secretary of the Royal Society, as Herschel was the senior, but failed because of his antagonism to Humphry Davy . Michael Faraday had a reply written, by Gerrit Moll , as On the Alleged Decline of Science in England (1831). On the front of the Royal Society Babbage had no impact, with
2618-513: The Whitmore sisters. He made a home in Marylebone in London and established a large family. On his father's death in 1827, Babbage inherited a large estate (value around £100,000, equivalent to £10.9 million or $ 15 million today), making him independently wealthy. After his wife's death in the same year he spent time travelling. In Italy he met Leopold II, Grand Duke of Tuscany , foreshadowing
2695-667: The academy. The first was a clergyman near Cambridge ; through him Babbage encountered Charles Simeon and his evangelical followers, but the tuition was not what he needed. He was brought home, to study at the Totnes school: this was at age 16 or 17. The second was an Oxford tutor, under whom Babbage reached a level in Classics sufficient to be accepted by the University of Cambridge. Babbage arrived at Trinity College, Cambridge , in October 1810. He
2772-782: The actuarial tables of George Barrett , who died in 1821 leaving unpublished work, and surveyed the field in 1826 in Comparative View of the Various Institutions for the Assurance of Lives . This interest followed a project to set up an insurance company, prompted by Francis Baily and mooted in 1824, but not carried out. Babbage did calculate actuarial tables for that scheme, using Equitable Society mortality data from 1762 onwards. During this whole period, Babbage depended awkwardly on his father's support, given his father's attitude to his early marriage, of 1814: he and Edward Ryan wedded
2849-511: The badge and star. It originally had three classes, but with several reorganisations since 1841, as house order today it has four classes and an additional Cross of Merit. In descending order of seniority the classes are: Holders of the respective degrees of the order in Britain were entitled to be post-nominally addressed with the initials, which stand for Knight Grand Cross of Hanover, Knight Commander of Hanover and Knight of Hanover. The initial GCG
2926-462: The barb that both Babbage and Brewster had received public money. In the debate of the period on statistics ( qua data collection) and what is now statistical inference , the BAAS in its Statistical Section (which owed something also to Whewell ) opted for data collection. This Section was the sixth, established in 1833 with Babbage as chairman and John Elliot Drinkwater as secretary. The foundation of
3003-663: The bland election of the Duke of Sussex to succeed Gilbert the same year. As a broad manifesto, on the other hand, his Decline led promptly to the formation in 1831 of the British Association for the Advancement of Science (BAAS). The Mechanics' Magazine in 1831 identified as Declinarians the followers of Babbage. In an unsympathetic tone it pointed out David Brewster writing in the Quarterly Review as another leader; with
3080-467: The concept of a trade . John Ruskin went further, to oppose completely what manufacturing in Babbage's sense stood for. Babbage also affected the economic thinking of John Stuart Mill . George Holyoake saw Babbage's detailed discussion of profit sharing as substantive, in the tradition of Robert Owen and Charles Fourier , if requiring the attentions of a benevolent captain of industry , and ignored at
3157-452: The conception of creation in which a God-given natural law dominated, removing the need for continuous "contrivance". The book is a work of natural theology , and incorporates extracts from related correspondence of Herschel with Charles Lyell . Babbage put forward the thesis that God had the omnipotence and foresight to create as a divine legislator. In this book, Babbage dealt with relating interpretations between science and religion; on
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3234-599: The eldest of 21 children, including her half-siblings. Her father agreed with her that if she were to continue her mathematics research, then she would be permitted to do all the charity work she wanted. In addition to her performances and lessons, her responsibility was to teach her siblings. This task kept her from her own goal of entering a convent, as she had become strongly religious. Although her father refused to grant this wish, he agreed to let her live from that time on in an almost conventual semi-retirement, avoiding all interactions with society and devoting herself entirely to
3311-400: The excuse to retire from public life. She took over the management of the household. She was one of 21 children. Her family was recognized as one of the wealthiest in Milan. Maria was recognized early on as a child prodigy ; she could speak both Italian and French at five years of age. By her eleventh birthday, she had also learned Greek , Hebrew , Spanish , German , and Latin , and
3388-460: The fields of functional equations (including the difference equations fundamental to the difference engine) and operator ( D-module ) methods for differential equations . The analogy of difference and differential equations was notationally changing Δ to D, as a "finite" difference becomes "infinitesimal". These symbolic directions became popular, as operational calculus , and pushed to the point of diminishing returns. The Cauchy concept of limit
3465-573: The first part of the book. The second part considered the "domestic and political economy" of manufactures. The book sold well, and quickly went to a fourth edition (1836). Babbage represented his work as largely a result of actual observations in factories, British and abroad. It was not, in its first edition, intended to address deeper questions of political economy; the second (late 1832) did, with three further chapters including one on piece rate . The book also contained ideas on rational design in factories, and profit sharing . In Economy of Machinery
3542-423: The gift of a diamond ring, a personal letter, and a diamond and crystal case. Many others praised her work, including Pope Benedict XIV , who wrote her a complimentary letter and sent her a gold wreath and a gold medal. In writing this work, Agnesi was advised and helped by two distinguished mathematicians: her former teacher Ramiro Rampinelli and Jacopo Riccati . In Instituzioni analitiche , Agnesi discussed
3619-407: The last four decades of her life to studying theology (especially patristics ) and to charitable work and serving the poor. She was a devout Catholic and wrote extensively on the marriage between intellectual pursuit and mystical contemplation, most notably in her essay Il cielo mistico (The Mystic Heaven). She saw the rational contemplation of God as a complement to prayer and contemplation of
3696-612: The life, death and resurrection of Jesus Christ. Maria Teresa Agnesi Pinottini , harpsichordist and composer , was her sister. Maria Gaetana Agnesi was born in Milan , to a wealthy and literate family. Her father Pietro Agnesi, a wealthy silk merchant, wanted to elevate his family into the Milanese nobility. In order to achieve his goal, he married Anna Fortunato Brivio of the Brivius de Brokles family in 1717. Her mother's death provided her
3773-519: The one hand, he insisted that "there exists no fatal collision between the words of Scripture and the facts of nature;" on the other hand, he wrote that the Book of Genesis was not meant to be read literally in relation to scientific terms. Against those who said these were in conflict, he wrote "that the contradiction they have imagined can have no real existence, and that whilst the testimony of Moses remains unimpeached, we may also be permitted to confide in
3850-510: The peculiar conception of the nature of miracle which underlies Babbage's ideas of Singular Points on Curves (Chap, viii) – from European Theology or Hindu Metaphysic? Oh! how the English clergy of that day hated Babbage's book! Babbage was raised in the Protestant form of the Christian faith, his family having inculcated in him an orthodox form of worship. He explained: My excellent mother taught me
3927-445: The post went to William Wallace . With Herschel, Babbage worked on the electrodynamics of Arago's rotations , publishing in 1825. Their explanations were only transitional, being picked up and broadened by Michael Faraday . The phenomena are now part of the theory of eddy currents , and Babbage and Herschel missed some of the clues to unification of electromagnetic theory , staying close to Ampère's force law . Babbage purchased
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#17328519080914004-623: The reach of man's power is to form the limits of the natural world." Knight of the Royal Guelphic Order The Royal Guelphic Order ( German : Königlicher Guelphen-Orden ), sometimes referred to as the Hanoverian Guelphic Order , is a Hanoverian order of chivalry instituted on 28 April 1815 by the Prince Regent (later King George IV ). It takes its name from the House of Guelph , of which
4081-541: The same year by Gottfried Friedenberg. The French engineer and writer on industrial organisation Léon Lalanne was influenced by Babbage, but also by the economist Claude Lucien Bergery , in reducing the issues to "technology". William Jevons connected Babbage's "economy of labour" with his own labour experiments of 1870. The Babbage principle is an inherent assumption in Frederick Winslow Taylor 's scientific management . Mary Everest Boole claimed that there
4158-550: The second volume by P. T. d'Antelmy , with additions by Charles Bossut (1730–1814), was published in Paris in 1775; and Analytical Institutions , an English translation of the whole work by John Colson (1680–1760), the Lucasian Professor of Mathematics at Cambridge , "inspected" by John Hellins , was published in 1801 at the expense of Baron Maseres . The work was dedicated to Empress Maria Theresa , who thanked Agnesi with
4235-414: The social scene in London, and is credited with importing the "scientific soirée" from France with his well-attended Saturday evening soirées . His varied work in other fields has led him to be described as "pre-eminent" among the many polymaths of his century. Babbage, who died before the complete successful engineering of many of his designs, including his Difference Engine and Analytical Engine, remained
4312-414: The source of the productivity of the factory system was exactly the combination of the division of labour with machinery, building on Adam Smith , Babbage and Ure. Where Marx picked up on Babbage and disagreed with Smith was on the motivation for division of labour by the manufacturer: as Babbage did, he wrote that it was for the sake of profitability , rather than productivity, and identified an impact on
4389-518: The study of theology , and especially of the Fathers and devoted herself to the poor, homeless, and sick, giving away the gifts she had received and begging for money to continue her work with the poor. In 1783, she founded and became the director of the Opera Pia Trivulzio , a home for Milan's elderly, where she lived as the nuns of the institution did. On 9 January 1799, Maria Agnesi died poor and
4466-479: The study of mathematics. After having read in 1739 the Traité analytique des sections coniques of the Marquis Guillaume de l'Hôpital , she was fully introduced into the field in 1740 by Ramiro Rampinelli , an Olivetan monk who was one of the most notable Italian mathematicians of that time. During that time, Maria studied with him both differential and integral calculus. According to Britannica, she
4543-612: The testimony of our senses." The Ninth Bridgewater Treatise was quoted extensively in Vestiges of the Natural History of Creation . The parallel with Babbage's computing machines is made explicit, as allowing plausibility to the theory that transmutation of species could be pre-programmed. Jonar Ganeri, author of Indian Logic , believes Babbage may have been influenced by Indian thought; one possible route would be through Henry Thomas Colebrooke . Mary Everest Boole argues that Babbage
4620-514: The time. Charles Babbage's Saturday night soirées , held from 1828 into the 1840s, were important gathering places for prominent scientists, authors and aristocracy. Babbage is credited with importing the "scientific soirée" from France with his well-attended Saturday evening soirées . Works by Babbage and Ure were published in French translation in 1830; On the Economy of Machinery was translated in 1833 into French by Édouard Biot , and into German
4697-591: The usual forms of my daily and nightly prayer; and neither in my father nor my mother was there any mixture of bigotry and intolerance on the one hand, nor on the other of that unbecoming and familiar mode of addressing the Almighty which afterwards so much disgusted me in my youthful years. Rejecting the Athanasian Creed as a "direct contradiction in terms", in his youth he looked to Samuel Clarke 's works on religion, of which Being and Attributes of God (1704) exerted
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#17328519080914774-542: The way of a career. In 1816 he was a candidate for a teaching job at Haileybury College ; he had recommendations from James Ivory and John Playfair , but lost out to Henry Walter . In 1819, Babbage and Herschel visited Paris and the Society of Arcueil , meeting leading French mathematicians and physicists. That year Babbage applied to be professor at the University of Edinburgh , with the recommendation of Pierre Simon Laplace ;
4851-431: The works of the Almighty gives to us more exalted views of his wisdom, his goodness, and his power. Like Samuel Vince , Babbage also wrote a defence of the belief in divine miracles . Against objections previously posed by David Hume , Babbage advocated for the belief of divine agency, stating "we must not measure the credibility or incredibility of an event by the narrow sphere of our own experience, nor forget that there
4928-564: Was baptised on 6 January 1792, supporting a birth year of 1791. Babbage was one of four children of Benjamin Babbage and Betsy Plumleigh Teape. His father was a banking partner of William Praed in founding Praed's & Co. of Fleet Street , London, in 1801. In 1808, the Babbage family moved into the old Rowdens house in East Teignmouth . Around the age of eight, Babbage was sent to a country school in Alphington near Exeter to recover from
5005-469: Was already self-taught in some parts of contemporary mathematics; he had read Robert Woodhouse , Joseph Louis Lagrange , and Maria Gaetana Agnesi . As a result, he was disappointed in the standard mathematical instruction available at the university. Babbage, John Herschel , George Peacock , and several other friends formed the Analytical Society in 1812; they were also close to Edward Ryan . As
5082-980: Was also used, and was cited in the original statutes of the order. Gold and silver medals were attached to the order, for award to those not eligible for the order itself, including non commissioned officers and royal servants. The Order has six officers: the Chancellor, the Vice-Chancellor, the Registrar, the King of Arms , the Genealogist, and the Secretary. The first six officers were: Maria Gaetana Agnesi Maria Gaetana Agnesi ( UK : / æ n ˈ j eɪ z i / an- YAY -zee , US : / ɑː n ˈ -/ ahn- , Italian: [maˈriːa ɡaeˈtaːna aɲˈɲeːzi, -ɲɛːz-] ; 16 May 1718 – 9 January 1799)
5159-421: Was an Italian mathematician , philosopher , theologian , and humanitarian . She was the first woman to write a mathematics handbook and the first woman appointed as a mathematics professor at a university. She is credited with writing the first book discussing both differential and integral calculus and was a member of the faculty at the University of Bologna , although she never served. She devoted
5236-423: Was appointed by Pope Benedict XIV to the chair of mathematics and natural philosophy and physics at Bologna , though she never served. She was the second woman ever to be granted a professorship at a university, Laura Bassi being the first. In 1751, she became ill again and was told not to study by her doctors. After the death of her father in 1752 she carried out a long-cherished purpose by giving herself to
5313-431: Was described what is now called the "Babbage principle". It pointed out commercial advantages available with more careful division of labour . As Babbage himself noted, it had already appeared in the work of Melchiorre Gioia in 1815. The term was introduced in 1974 by Harry Braverman . Related formulations are the "principle of multiples" of Philip Sargant Florence , and the "balance of processes". What Babbage remarked
5390-543: Was fifteen, her father began to regularly gather in his house a circle of the most learned men in Bologna , before whom she read and maintained a series of theses on the most abstruse philosophical questions. Records of these meetings are given in Charles de Brosses ' Lettres sur l'Italie and in the Propositiones Philosophicae , which her father had published in 1738 as an account of her final performance, where she defended 190 philosophical theses. Her father remarried twice after Maria's mother died, and Maria Agnesi ended up
5467-489: Was first an article in the Encyclopædia Metropolitana , the form in which Rennie noted it, in the company of related works by John Farey Jr. , Peter Barlow and Andrew Ure . From An essay on the general principles which regulate the application of machinery to manufactures and the mechanical arts (1827), which became the Encyclopædia Metropolitana article of 1829, Babbage developed the schematic classification of machines that, combined with discussion of factories, made up
5544-474: Was in 1821 or 1822, and was the occasion on which Babbage formulated his idea for mechanical computation. The issue of the Nautical Almanac is now described as a legacy of a polarisation in British science caused by attitudes to Sir Joseph Banks , who had died in 1820. Babbage studied the requirements to establish a modern postal system , with his friend Thomas Frederick Colby , concluding there should be
5621-430: Was introduced to Indian thought in the 1820s by her uncle George Everest: Some time about 1825, [Everest] came to England for two or three years, and made a fast and lifelong friendship with Herschel and with Babbage, who was then quite young. I would ask any fair-minded mathematician to read Babbage's Ninth Bridgewater Treatise and compare it with the works of his contemporaries in England; and then ask himself whence came
5698-435: Was kept at bay. Woodhouse had already founded this second "British Lagrangian School" with its treatment of Taylor series as formal. In this context function composition is complicated to express, because the chain rule is not simply applied to second and higher derivatives. This matter was known to Woodhouse by 1803, who took from Louis François Antoine Arbogast what is now called Faà di Bruno's formula . In essence it
5775-404: Was known to Abraham De Moivre (1697). Herschel found the method impressive, Babbage knew of it, and it was later noted by Ada Lovelace as compatible with the analytical engine. In the period to 1820 Babbage worked intensively on functional equations in general, and resisted both conventional finite differences and Arbogast's approach (in which Δ and D were related by the simple additive case of
5852-401: Was profound influence – via her uncle George Everest – of Indian thought in general and Indian logic , in particular, on Babbage and on her husband George Boole , as well as on Augustus De Morgan : Think what must have been the effect of the intense Hinduizing of three such men as Babbage, De Morgan, and George Boole on the mathematical atmosphere of 1830–65. What share had it in generating
5929-427: Was referred to as the "Seven-Tongued Orator". Agnesi suffered a mysterious illness at the age of twelve that was attributed to her excessive studying and reading, so she was prescribed vigorous dancing and horseback riding. This treatment did not work; she began to experience extreme convulsions, after which she was encouraged to pursue moderation. By age fourteen, she was studying ballistics and geometry . When she
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