Calculus and Its Origins
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Newton.Indd | Sander Pinkse Boekproductie | 16-11-12 / 14:45 | Pag
omslag Newton.indd | Sander Pinkse Boekproductie | 16-11-12 / 14:45 | Pag. 1 e Dutch Republic proved ‘A new light on several to be extremely receptive to major gures involved in the groundbreaking ideas of Newton Isaac Newton (–). the reception of Newton’s Dutch scholars such as Willem work.’ and the Netherlands Jacob ’s Gravesande and Petrus Prof. Bert Theunissen, Newton the Netherlands and van Musschenbroek played a Utrecht University crucial role in the adaption and How Isaac Newton was Fashioned dissemination of Newton’s work, ‘is book provides an in the Dutch Republic not only in the Netherlands important contribution to but also in the rest of Europe. EDITED BY ERIC JORINK In the course of the eighteenth the study of the European AND AD MAAS century, Newton’s ideas (in Enlightenment with new dierent guises and interpre- insights in the circulation tations) became a veritable hype in Dutch society. In Newton of knowledge.’ and the Netherlands Newton’s Prof. Frans van Lunteren, sudden success is analyzed in Leiden University great depth and put into a new perspective. Ad Maas is curator at the Museum Boerhaave, Leiden, the Netherlands. Eric Jorink is researcher at the Huygens Institute for Netherlands History (Royal Dutch Academy of Arts and Sciences). / www.lup.nl LUP Newton and the Netherlands.indd | Sander Pinkse Boekproductie | 16-11-12 / 16:47 | Pag. 1 Newton and the Netherlands Newton and the Netherlands.indd | Sander Pinkse Boekproductie | 16-11-12 / 16:47 | Pag. 2 Newton and the Netherlands.indd | Sander Pinkse Boekproductie | 16-11-12 / 16:47 | Pag. -
A Study on University Education of Medieval European Mathematicians 1K
International Journal of Pure and Applied Mathematics Volume 116 No. 22 2017, 265-273 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu Special Issue ijpam.eu A Study on University Education of Medieval European Mathematicians 1K. Rejikumar and 2C.M. Indukala 1Deptment of Mathematics, N.S.S. College, Pandalam, Kerala, India. [email protected] 2University of Kerala, Palayam, Thiruvananthapuram, Kerala, India. [email protected] Abstract Higher educational institutions in a country play an important role in the cultural transformation of people. Its role in the coordination and strengthening of new knowledge and its proper dissemination in the community is an important factor in the development of any country. In this paper we compare the importance of role played by higher educational institutions in the development of Kerala School of Mathematics and European School of Mathematics. Key Words:Kerala school of mathematics, european school of mathematics, institutions of higher learning. 265 International Journal of Pure and Applied Mathematics Special Issue 1. Introduction The word university is originated from the Latin word “Universitas”, means the whole, the world or the universe. Before Universities were established, the main centers for education were monastic schools. Because of the increasing necessity for acquisition of knowledge, there happened the migration of cathedral schools to large cities. At the early stage Universities were consisted of a group of individuals assembled at some available spaces such as church or homes. Gradually Universities were established in secluded buildings and teachers were granted remuneration [1]. This paper deals with a cursory overview on the education details of eminent European scholars who made significant contributions in mathematics and other fields of interest during the period from 1300 to 1700. -
Calculation and Controversy
calculation and controversy The young Newton owed his greatest intellectual debt to the French mathematician and natural philosopher, René Descartes. He was influ- enced by both English and Continental commentators on Descartes’ work. Problems derived from the writings of the Oxford mathematician, John Wallis, also featured strongly in Newton’s development as a mathe- matician capable of handling infinite series and the complexities of calcula- tions involving curved lines. The ‘Waste Book’ that Newton used for much of his mathematical working in the 1660s demonstrates how quickly his talents surpassed those of most of his contemporaries. Nevertheless, the evolution of Newton’s thought was only possible through consideration of what his immediate predecessors had already achieved. Once Newton had become a public figure, however, he became increasingly concerned to ensure proper recognition for his own ideas. In the quarrels that resulted with mathematicians like Gottfried Wilhelm Leibniz (1646–1716) or Johann Bernoulli (1667–1748), Newton supervised his disciples in the reconstruction of the historical record of his discoveries. One of those followers was William Jones, tutor to the future Earl of Macclesfield, who acquired or copied many letters and papers relating to Newton’s early career. These formed the heart of the Macclesfield Collection, which has recently been purchased by Cambridge University Library. 31 rené descartes, Geometria ed. and trans. frans van schooten 2 parts (Amsterdam, 1659–61) 4o: -2 4, a-3t4, g-3g4; π2, -2 4, a-f4 Trinity* * College, Cambridge,* shelfmark* nq 16/203 Newton acquired this book ‘a little before Christmas’ 1664, having read an earlier edition of Descartes’ Geometry by van Schooten earlier in the year. -
The Search for Longitude: Preliminary Insights from a 17Th Century Dutch Perspective
The search for longitude: Preliminary insights from a 17th Century Dutch perspective Richard de Grijs Kavli Institute for Astronomy & Astrophysics, Peking University, China Abstract. In the 17th Century, the Dutch Republic played an important role in the scientific revolution. Much of the correspondence among contemporary scientists and their associates is now digitally available through the ePistolarium webtool, allowing current scientists and historians unfettered access to transcriptions of some 20,000 letters from the Dutch Golden Age. This wealth of information offers unprece- dented insights in the involvement of 17th Century thinkers in the scientific issues of the day, including descriptions of their efforts in developing methods to accurately determine longitude at sea. Un- surprisingly, the body of correspondence referring to this latter aspect is largely dominated by letters involving Christiaan Huygens. However, in addition to the scientific achievements reported on, we also get an unparalleled and fascinating view of the personalities involved. 1. Scientific dissemination during the Dutch ‘Golden Age’ The 17th Century is regarded as the ‘Golden Age’ in the history of the Netherlands. The open, tolerant and transparent conditions in the 17th Century Dutch Republic – at the time known as the Republic of the Seven United Netherlands – allowed the nation to play a pivotal role in the international network of humanists and scholars before and during the ‘scientific revolution’. The country had just declared its independence from -
Johannes Hudde (1628-1704) the Person in Whom Science, Technology, and Governance Came Together
The Most Versatile Scientist, Regent, and VOC Director of the Dutch Golden Age: Johannes Hudde (1628-1704) The person in whom science, technology, and governance came together Michiel van Musscher, Painting of Johannes Hudde, Mayor of Amsterdam and mathematician, Amsterdam, Rijksmuseum (1686). Name: Theodorus M.A.M. de Jong Student number: 5936462 Number of words: 32,377 Date: 14-7-2018 E-mail address: [email protected] Supervisors: prof. dr. Rienk Vermij & dr. David Baneke Master: History and Philosophy of Science University: Utrecht University Table of Content blz. Introduction 4 1. Hudde as a student of the Cartesian philosopher Johannes de Raeij 10 The master as student 10 Descartes’ natural philosophy in De Raeij’s Clavis 12 2. Does the Earth move? 16 The pamphlet war between Hudde and Du Bois 16 3. The introduction of practical and ‘new’ mathematics at Leiden University 23 The Leiden engineering school: Duytsche Mathematique 24 Hudde’s improvement of Cartesian mathematics 25 Hudde’s method of solving high-degree equations and finding the extremes 27 4. The operation of microscopic lenses in theory and practice 30 Hudde’s theoretical treatise on spherical aberration, Specilla Circularia 30 Hudde’s alternative to lens grinding 31 5. Hudde’s question about the existence of only one God 35 Hudde’s correspondence with Spinoza 35 Hudde’s correspondence with Locke 40 6. From scholar to regent 47 Origin and background 47 The road to mayor 48 Hudde as an advisor to the States-General 50 The finances of the State of Holland 52 The two nephews: Hudde and Witsen 54 7. -
Lecture 1. Education and Math in the Medieval Europe
Lecture 1. Education and Math in the Medieval Europe Historical context: Early Middle Ages or Dark Ages refer to the period of 5th – 10th centuries 5th century: Fall of the Western Roman Empire in 410-476, decline in population, deurbanization, loss of culture 6th century: Justinian I published Code of Civil Law and retakes Rome from Ostrogoths 7th century: Arab army capture new territories 8th century: Carolingian Renaissance: monastic and cathedral schools were established everywhere to train men of civil service, Palace School at Aahen (in Abbasside Caliphate: Islamic Golden Age, “House of Wisdom”) Barbarian invasions: the Viking Age 793-1066, raids of Magyars (Hungarians) 795-1001, invasions of Saracens (Arabs, Berbers, Moors and Turks) first occupation in 8th century, continued in 9th-11th. Great Schism 1054 separation between the East Orthodox and the West Catholic Churches Boethius (480-524) noble Roman, Christian philosopher, “last of the Romans and the first of Scholastics” Magister officiorum (head of government and court services) of Theodoric, king of Italy and of Goths, who later imprisoned and executed Boethius in charges of conspiracy Consolation of Philosophy philosophical treatise composed in jail: on Weal of fortune, evil and death, etc., one of the most popular and influential works of the Middle Ages Translated many books from Greek to Latin: philosophy (Aristotle, Plato), Math (“Arithmetic” of Nicomachus, geometry books, etc.) were textbooks for quadrivium in the Middle Ages. Cassiodorus (485-585) Roman statesman and writer, was Magister officiorum after Boethius Established a system of monastery education (School at Vivarium) based on 7 Liberal Arts Through Early Middle Ages, schools at some monasteries and cathedrals were the only centers to get a minimal education based on Trivium and aimed for religious needs. -
Mapping the Dutch World Overseas in the Seventeenth Century Kees Zandvliet
46 • Mapping the Dutch World Overseas in the Seventeenth Century Kees Zandvliet In 1602, the Verenigde Oostindische Compagnie (VOC, Monumenta Cartographica intended to demonstrate, or Dutch East India Company) was chartered by the through reproduction and description of the most impor- States General of the Netherlands (the state assembly) to tant maps manufactured by the Dutch, the role these conduct a monopoly in trade east of the Cape of Good maps played in exploration.2 Therefore it concentrates Hope and west of the Strait of Magellan. Seventeen years primarily on maps from the period of the great Dutch later, in 1619, the Company acquired a privilege from the voyages of discovery in the first half of the seventeenth States General relating to maps.1 The privilege stipulated century. This work made the manuscript maps and plans that to publish any geographical information about the in the atlas of the collector Laurens van der Hem and the chartered area of the Company, the express permission of important watercolors of Joannes Vingboons available to the board of directors of the Company, the Heren XVII a much wider audience. Interest in maps and charts re- (the seventeen gentlemen), was required. In their request lated to maritime history, the history of discoveries, and for this privilege, the directors emphasized the impor- bibliographical history remains strong, as is clear from tance of the geographical knowledge acquired by the more recent studies by such scholars as Keuning, Koe- VOC’s employees on a daily basis: to map seas, straits, man, and Schilder.3 Study of the cartography of the Com- and coastlines and to compile treatises on the areas with panies has often been limited to the production of mar- which the VOC traded. -
List of Figures
List of figures Figure 1 Huygens: sketch of 6 August 1679 Figure 2 Spherical aberration Figure 3 Cartesian oval. Figure 4 Huygens: focal distance of a bi-convex lens Figure 5 Huygens: punctum concursus Figure 6 Huygens: refraction at the anterior side of a bi-convex lens Figure 7 Huygens: refraction at the posterior side of a bi-convex lens. Figure 8 Huygens: focal distance of a bi-convex lens Figure 9 Huygens: extended image. Figure 10 Huygens: magnification by a convex lens. Figure 11 Huygens: four of the cases of magnification by telescopes. Figure 12 Huygens: analysis of Keplerian telescope with erector lens. Figure 13 Diagram for Keplerian telescope with erector lens. Figure 14 Kepler’s solution to the pinhole problem Figure 15 Kepler: focal distance of a plano-convex lens Figure 16 Kepler: image formation by a lens Figure 17 Della Porta: image of a near object Figure 18 Della Porta: image of distant object Figure 19 Della Porta: image by a telescope Figure 20 Barrow’s analysis of image formation in refraction. Figure 21 Huygens: observations of Saturn with the 12- and a 23-foot telescope. Figure 22 Huygens: beam to facilitate lens grinding. Figure 23 Daza’s scale Figure 24 Huygens’ eyepiece. Figure 25 Diagram for Huygens’ eyepiece. Figure 26 Huygens: spherical aberration of a plano-convex lens. Figure 27 Huygens: spherical aberration of a bi-convex lens Figure 28 Hudde’s calculation of spherical aberration Figure 29 Huygens: Galilean configuration in which spherical aberration is neutralized. Figure 30 Huygens: ‘Circle’ of aberration. Figure 31 Huygens: Aberration produced by a Keplerian configuration. -
Correspondence
Correspondence Baruch Spinoza Copyright © Jonathan Bennett 2017. All rights reserved [Brackets] enclose editorial explanations. Small ·dots· enclose material that has been added, but can be read as though it were part of the original text. Occasional •bullets, and also indenting of passages that are not quotations, are meant as aids to grasping the structure of a sentence or a thought. Every four-point ellipsis . indicates the omission of a brief passage that seems to present more difficulty than it is worth. Longer omissions are reported between brackets in normal-sized type.—Many of the letters have somewhat ornate salutations (e.g. ‘Most excellent Sir, and dearest friend’) and/or signings-off (e.g. ‘Farewell, special friend, and remember me, who am your most devoted. ’); these are omitted except when there’s a special reason not to.—For a helpful and thoughtful presentation of the letters, see Edwin Curley (ed), The Collected Works of Spinoza, vol. 1 for letters 1–28, vol. 2 for letters 29–84. The editorial notes in the present version derive mostly from those two volumes, the material in vol. 2 having been generously made available by Curley, in advance of its publication, to the preparer of the version. First launched: May 2014 Correspondence Baruch Spinoza Contents letters 1–16: written in 1661–1663 1 1. from Oldenburg, 26.viii.1661:....................................................1 2. to Oldenburg, ix.1661:........................................................1 3. from Oldenburg, 27.ix.1661:....................................................3 4. to Oldenburg, x.1661:........................................................4 5. from Oldenburg, 21.x.1661:....................................................5 6. to Oldenburg, iv.1662:.......................................................5 7. from Oldenburg, vii.1662:.....................................................9 8. -
' E Miracle of Our Time'
Newton and the Netherlands.indd | Sander Pinkse Boekproductie | 28-09-12 / 11:43 | Pag. 13 ‘e Miracle of Our Time’ How Isaac Newton was fashioned in the Netherlands ERIC JORINK AND HUIB ZUIDERVAART Introduction 13 It has more or less become a truism that the Dutch Republic played an ‘T HE M important, not to say a crucial role, in the spread of ‘Newtonianism’ in I Europe during the early eighteenth century. As Klaas van Berkel has OF RACLE written: O It is partly or even mainly thanks to intellectual circles in the UR TIME’ Dutch Republic that Newton’s ideas were after all accepted in the rest of Europe; Dutch scientists and Dutch manuals were responsible for the spread of Newtonianism through Europe. For once, the Netherlands was indeed the pivot of intellectual Europe. It is well known that in Herman Boerhaave (–), by far the most famous professor of the Dutch Republic, was the rst academic to speak in public strongly in favour of Newton, calling him ‘the mir- acle of our time’ and ‘the Prince of Geometricians’. In the very same year, the mathematician and burgomaster Bernard Nieuwentijt (– ) published his Het regt gebruik der wereldbeschouwing (e Reli- gious Philosopher: Or, the Right Use of Contemplating the Works of the Creator), a work which would become extremely popular, both in the Netherlands and abroad, and which made important references to Newton. Het regt gebruik contributed much to the popularity of the experimental natural philosophy, so characteristic of eighteenth-cen- tury Dutch culture. Moreover, in a young journalist and lawyer Newton and the Netherlands.indd | Sander Pinkse Boekproductie | 28-09-12 / 11:43 | Pag. -
The Dutch Mathematical Landscape
The Dutch mathematical landscape The 16th and 17th centuries The Dutch mathematical landscape took shape in the 16th century. The first university in the Netherlands was Leiden (1575), followed by Franeker (1585), Groningen (1614), Amsterdam (1632), and Utrecht (1636). All were places of mathematics teaching and research, as was the University of Leuven (founded in 1425 as the oldest university in the Low Countries, with a mathematical Chair established in 1563). Teaching was still based on the quadrivium: arithmetic and geometry were seen as mathematica pura, whilst astronomy, and music belonged to mathematica mixta, i.e. applied mathematics. The latter also included fields like mechanics, (mathematical) optics, cartography, etc. Outside the universities (where the written language was Latin), everyday use of mathematics - like calculating with fractions - by practical people like merchants was promoted through books written in Dutch, like Die maniere om te leeren cyffren na die rechte consten Algorismi. Int gheheele ende int ghebroken (1508) by the well-known publisher Thomas van der Noot (1475-1525) in Brussels. The following brief history will concentrate on the Netherlands, but in any case, with a few exceptions like Newton!s distinguished predecessor René- François de Sluse (1622-1685), Belgian mathematics went into decline already at the end of the16th century, about a hundred years before a similar fate befell Dutch mathematics. The well-known marxist historian of mathematics Dirk Jan Struik (1894-2000) characterized the Dutch mathematical landscape of the 16th century as follows: “In this period mathematics appeared mainly as an applied science useful for the many and growing needs of the new economic and political system. -
The Rijksmuseum Bulletin
the rijksmuseum bulletin 42 the rijks the restorationa ofquestion womanmuseum ofin framingblue reading a letter bulletin An Amsterdam Couple Reunited Michiel van Musscher’s Portraits of Johannes Hudde and Debora Blaeuw • jonathan bikker • common type of seventeenth- Detail of fig. 1 is a bookcase and a shelf with three A century Dutch portrait is the globes. The painting belongs to the pendant pair showing a married couple genre of the scholar’s portrait – a genre on two identical canvases or panels. that usually did not accommodate In most cases, the husband is meant female pendants, even if the scholar to hang to the left and the wife to the in question was married. Even more right, often with the two individuals than the genre to which it belongs and set on diagonals that converge in the the portrait’s provenance, Hudde’s centre. Sometimes such portrait pairs orientation in the painting, which would become separated and art historians necessitate a reversal of the usual left/ can engage in one of their favourite right hanging of companion pieces, has sports, the reunification of estranged never given cause to search for a missing couples. Of course not all seventeenth- pendant. This being the case, it came as century Dutch portraits were conceived a great surprise to discover that a female as pairs, and when there is no reason to pendant to Van Musscher’s Portrait of suspect that a portrait had a pendant, Johannes Hudde does exist. why go looking for one? This was the The painting in question is in a Dutch case with Michiel van Musscher’s 1686 private collection and has never been Portrait of Johannes Hudde (1628-1704), published before (fig.