Analysis of Ideas Changing in the History of Mathematical Analysis

2021 ◽  
pp. 505-510
Author(s):  
Ming-Xing Hu ◽  
De-Peng Kong
Keyword(s):  
Mathematical Analysis ◽  
History Of Mathematics ◽  
Gottfried Wilhelm Leibniz ◽  
Central Field ◽  
Continuous Change ◽  
German Mathematician ◽  
Sir Isaac Newton ◽  
Isaac Newton ◽  
History Of ◽  
Modern Analysis

Analysis is a branch of mathematics that deals with continuous change and with certain general types of processes that have emerged from the study of continuous change, such as limits, differentiation, and integration. In the history of mathematics, analysis is the first subject became epidemic, the development of analysis originated from the British mathematician and physicist, the Sir Isaac Newton, and the German mathematician, Gottfried Wilhelm Leibniz, who developed the theory of Calculus, with hundred-years developing, the modern analysis is now very ample and has widely applications, it has grown into an enormous and central field of mathematical research, with applications throughout the sciences and in areas such as finance, economics, and sociology. In this paper, we investigated in some detail with the changing of the ideas in mathematical analysis. By numerating historical facts and the mathematical ideas, we concluded the result that the ideas changing is because of the changing of the studying objects, the conclusion are studied detailly in the paper.

“Did Hume Really Follow Berkeley”

Philosophy ◽  
1969 ◽  
Vol 44 (169) ◽  
pp. 238-242
Author(s):  
Grapham P. Conroy
Keyword(s):  
History Of Mathematics ◽  
George Berkeley ◽  
Sir Isaac Newton ◽  
Isaac Newton ◽  
History Of

The Bishop of Cloyne, George Berkeley, was the sort of philosopher who, although most genial himself, was quite apt to embroil opponents and critics of his time and of our own in long-lasting and sometimes unresolved controversies. In attacking the “infidel mathematicians”, the “minute philosophers” among the scientists, Berkeley initiated a controversy on behalf of religion by taking to task the theory of fluxions held by Sir Isaac Newton, his friends, and followers which, beginning with Berkeley's Analyst and replies to it by Jurin and Walton, was continued on over one hundred years by subsequent writers. Florian Cajori in his History of Mathematics, commenting on the affair has written:‘We must not neglect to express our appreciation of the fact that Berkeley withdrew from the controversy after he had said all that he had to say on his subject. Some of the debates that came later were almost interminable, because the participants continued writing even after they had nothing more to say.’

Newton and the Origin of Civilization

2012 ◽  
Author(s):  
Jed Z. Buchwald ◽  
Mordechai Feingold
Keyword(s):  
Good Reason ◽  
History Of Mathematics ◽  
Primary Sources ◽  
Ancient History ◽  
Isaac Newton ◽  
History Of ◽  
Ancient Civilizations ◽  
And Mathematics ◽  
One Year ◽  
Radical Ideas

Isaac Newton’s Chronology of Ancient Kingdoms Amended, published in 1728, one year after the great man’s death, unleashed a storm of controversy. And for good reason. The book presents a drastically revised timeline for ancient civilizations, contracting Greek history by five hundred years and Egypt’s by a millennium. This book tells the story of how one of the most celebrated figures in the history of mathematics, optics, and mechanics came to apply his unique ways of thinking to problems of history, theology, and mythology, and of how his radical ideas produced an uproar that reverberated in Europe’s learned circles throughout the eighteenth century and beyond. The book reveals the manner in which Newton strove for nearly half a century to rectify universal history by reading ancient texts through the lens of astronomy, and to create a tight theoretical system for interpreting the evolution of civilization on the basis of population dynamics. It was during Newton’s earliest years at Cambridge that he developed the core of his singular method for generating and working with trustworthy knowledge, which he applied to his study of the past with the same rigor he brought to his work in physics and mathematics. Drawing extensively on Newton’s unpublished papers and a host of other primary sources, the book reconciles Isaac Newton the rational scientist with Newton the natural philosopher, alchemist, theologian, and chronologist of ancient history.

scholarly journals Bibliography of recent books and articles dealing with the history of the Royal Society

1970 ◽  
Vol 25 (1) ◽  
pp. 127-133
Keyword(s):  
Royal Society ◽  
New Haven ◽  
Yale University ◽  
Sir Isaac Newton ◽  
Charles Town ◽  
Isaac Newton ◽  
James Cook ◽  
John Hunter ◽  
History Of ◽  
History Of Sciences

Each number of Notes and Records contains a short bibliography of books and articles dealing with the history of the Royal Society or its Fellows which have been noted since the publication of the last number. If Fellows would be good enough to draw the Editor’s attention to omissions these would be added to the list in the next issue. Books Badash, L. (Editor). Rutherford and Boltwood: letters on radioactivity. (Yale studies in the History of Sciences and Medicine, Vol. 4.) New Haven: Yale University Press, 1969. $12.50. Begg, A. C. and Begg, N.C. James Cook and New Zealand . Wellington, N.Z.: A. R. Shearer, 1969. £ 2 5s. Berkeley, E. and Berkeley, Dorothy, S. Dr Alexander Gordon of Charles Town . University of North Carolina Press, 1969. $10.00. Bestcrman, T. Voltaire. London: Longmans, 1969. 8s. Bowden, D. K. Leibniz as a librarian and eighteenth-century librarians Germany . London: University College, 1969. 7s. 6d. Darwin, C. R. Questions about the breeding of animals . Facsim. repr. with an introduction by Sir Gavin Dc Beer. London: Society for the Bibliography of Natural History, 1969. £1 15s. Davis, N. P. Lawrence and Openhimer . London: Cape, 1969. 2s. Dobson, J. John Hunter. Edinburgh & London: E. & S. Livingstone, 1969. £ 2 10s. Eales, N. B. The Cole library of early medicine and zoology . Catalogue of books and pamphlets. Part 1. 1472 to 1800. Oxford: Aldcn Press for the Library, University of Reading, 1969. £$ 5s. Edleston, J. (Editor). Correspondence of Sir Isaac Newton and Professor Cotes . (1830.) (Cass Library of Science Classics. No. 12.) London: Frank Cass, 1969. £ 6 6s. Fothergill, B. Sir William Hamilton . Faber and Faber, 1969. £ 2 10s. French, R. K. Robert Whytt, the soul, and medicine . (Publications of the Wellcome Institute, No. 17.) London: Wellcome Institute of the History of Medicine, 1969. £ 2 5s.

The Libraries of Newton, Hooke and Boyle

1966 ◽  
Vol 21 (1) ◽  
pp. 42-55 ◽  
Keyword(s):  
Seventeenth Century ◽  
Scientific Literature ◽  
Scientific Theories ◽  
Robert Hooke ◽  
Sir Isaac Newton ◽  
Robert Boyle ◽  
Isaac Newton ◽  
The Past ◽  
The World ◽  
History Of

The demand and search for the scientific literature of the past has grown enormously in the last twenty years. In an age as conscious as ours of the significance of science to mankind, some scientists naturally turned their thoughts to the origins of science as we know it, how scientific theories grew and how discoveries were made. Both institutions and individual scientists partake in these interests and form collections of books necessary for their study. How did their predecessors fare in this respect? They, of course, formed their libraries at a time when books were easy to find—and cheap. But what did they select for their particular reading? For example, what did the libraries of the three greatest scientists of the seventeenth century, Sir Isaac Newton, Robert Hooke and Robert Boyle, look like? Fortunately in the case of Newton, the history of his books is now fairly clear, thanks to the devoted labours of Colonel R . de Villamil (i), but it is a sad reflection on our attitude to our great intellectual leaders that this library o f the greatest English scientist, whose work changed the world for hundreds of years, was not taken care of, was, in fact, forgotten and at times entirely neglected.

The Keynes Collection of the works of Sir Isaac Newton At King's College, Cambridge

1952 ◽  
Vol 10 (1) ◽  
pp. 40-50 ◽  
Keyword(s):  
Sir Isaac Newton ◽  
History Of Thought ◽  
Isaac Newton ◽  
Comprehensive Collection ◽  
King's College ◽  
Printed Books ◽  
Scientific Papers ◽  
History Of ◽  
Main Period ◽  
The University

WHEN John Maynard, 1st Baron Keynes of Tilton, died in 1946 he left, with other benefactions to King’s College, Cambridge, of which he had been a Fellow for thirty-seven years, his great collection of books and manuscripts. He had been a book collector all his life, but the main period of his activity in this field was during the final ten years. During this decade he worked tirelessly at assembling a comprehensive collection of first and early editions of works which illustrated the history of thought—pure philosophy, political theory and a careful selection of books which represented fundamental advances in the realm of natural science. The most important section of the library is the Newton Collection, which comprised at the time of Lord Keynes’s death some 130 manuscripts, many very extensive, and about the same number of printed books. It is the purpose of the present paper to make its contents better known to Newtonian scholars. The sale of the Portsmouth papers in 1936 The event which stimulated Keynes to his greatest effort in bookcollecting was the dispersal at Sotheby’s on 13 and 14 July 1936 of the Newton papers of Viscount Lymington, to whom they had descended from Catherine Conduitt, Viscountess Lymington, Newton’s great-niece. The relentless pressure of death-duties made it necessary to sell this great collection which had remained intact in the family of the Earls of Portsmouth until 1872, when the purely scientific papers were generously given to the University of Cambridge. The vast residue—manuscripts containing perhaps 3000000 words altogether—comprised all Newton’s alchemical, theological and chronological papers, much of his correspondence, all his Mint papers, and much material relating to his personal life, as well as that which Conduitt had gathered for his unwritten biography.

scholarly journals On a point connected with the dispute about the invention of fluxions

1851 ◽  
Vol 5 ◽  
pp. 599-600
Keyword(s):  
Royal Society ◽  
Sir Isaac Newton ◽  
Isaac Newton ◽  
History Of

An assertion made by Sir Isaac Newton in a letter to Conti, published in Raphson’s History of Fluxions, that the materials of the Commercium Epistolicum were “ collected and published by a numerous Committee of gentlemen of different nations , appointed by the Royal Society for that purpose,” appeared to be at variance with the list of the Committee as it was appointed on the 6th of March, 1711- 12, and which only contains the names of Arbuthnot, Hill, Halley, Jones, Machin and Burnet, who were all English. But on further search of the records of the Society with the aid of Mr. Weld, the Assistant Secretary, the author ascertained that other members were subsequently added to the Committee, among whom were Bonet, the Prussian minister, and De Moivre, both of whom were foreigners ; thus showing that the imputations which might have been cast on Newton’s veracity are groundless.

scholarly journals IX. On the laws which regulate the polarisation of light by reflexion from transparent bodies. By David Brewster, LL. D. F. R. S. Edin. and F. S. A. Edin. In a letter addressed to Right Hon. Sir Joseph Banks, Bart. K. B. P. R. S

1815 ◽  
Vol 105 ◽  
pp. 125-159 ◽  
Keyword(s):  
The Other ◽  
Angle Of Incidence ◽  
Double Refraction ◽  
Sir Isaac Newton ◽  
Isaac Newton ◽  
Refractive Power ◽  
Polarised Light ◽  
History Of ◽  
History Of Optics ◽  
General Fact

Dear Sir, The discovery of the polarisation of light by reflexion, con­stitutes a memorable epoch in the history of optics; and the name of Malus, who first made known this remarkable pro­perty of bodies, will be for ever associated with a branch of science which he had the sole merit of creating. By a few brilliant and comprehensive experiments he established the general fact, that light acquired the same property as one of the pencils formed by double refraction, when it was reflected at a particular angle from the surfaces of all transparent bodies: he found that the angle of incidence at which this property was communicated, was greater in bodies of a high refractive power, and he measured, with considerable accuracy, the polarising angles for glass and water. In order to discover the law which regulated the phenomena, he com­pared these angles with the refractive and dispersive powers of glass and water, and finding that there was no relation be­tween these properties of transparent bodies, he draws the following general conclusion. “The polarising angle neither“ follows the order of the refractive powers, nor that of the “dispersive forces. It is a property of bodies independent“ of the other modes of action which they exercise upon “light.“ This premature generalisation of a few imperfectly ascer­tained facts, is perhaps equalled only by the mistake of Sir Isaac Newton, who pronounced the construction of an achromatic telescope to be incompatible with the known principles of optics. Like Newton, too, Malus himself aban­doned the enquiry; and even his learned associates in the Institute, to whom he bequeathed the prosecution of his views, have sought for fame in the investigation of other properties of polarised light.

scholarly journals XIII. Demonstration of the Fundamental Property of the Lever

1812 ◽  
Vol 6 ◽  
pp. 397-403
Author(s):  
David Brewster
Keyword(s):  
History Of Science ◽  
Mathematical Reasoning ◽  
Fundamental Property ◽  
Sir Isaac Newton ◽  
Physical Body ◽  
Isaac Newton ◽  
History Of

It is a singular fact in the history of science, that, after all the attempts of the most eminent modern mathematicians, to obtain a simple and satisfactory demonstration of the fundamental property of the lever, the solution of this problem given by Archimedes, should still be considered as the most legitimate and elementary. Galileo, Huygens, De la Hire, Sir Isaac Newton, Maclaurin, Landen, and Hamilton, have directed their attention to this important part of mechanics; but their demonstrations are in general either tedious and abstruse, or founded on assumptions too arbitrary to be recognised as a proper basis for mathematical reasoning. Even the demonstration given by Archimedes is not free from objections, and is applicable only to the lever, considered as a physical body.

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