Tait equation: Difference between revisions
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== | {{EngvarB|date=September 2013}} | ||
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''' ''De analysi per aequationes numero terminorum infinitas'' ''' (On analysis by infinite series (<sub><ref>[[Mathematical Association of America|The Mathematical Association of America]] [http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=3803&bodyId=4071 .org] Retrieved 3 February 2012 & [http://www.newtonproject.sussex.ac.uk/prism.php?id=15 newtonproject] Retrieved 6 February 2012</ref></sub>) / On Analysis by Equations with an infinite number of terms (<sub><ref>[[Nicholls State University]] Thibodaux, Louisiana [https://docs.google.com/viewer?a=v&q=cache:ltcI46hBnZUJ:math.nicholls.edu/heck/teaching/573/573(Calc)Fa11/1.3.pdf+de+analysi+per+aequationes+numero+terminorum+infinitas&hl=en&gl=uk&pid=bl&srcid=ADGEESgck4DTNo0DVO2ywiuSP95LOZBd2b06M4HSyzcMf3ZaU6sAEu1jq0KiQ7PJDVIU7blkufyTbYsTFc-MJ-TASmrMdVIQh9N4lwVhmBOB11XHtm2oYJL4H5z4aPLyPStWKWZtA0CQ&sig=AHIEtbTs-SaOa6_CRe1im2Rks5z4DMa27Q .edu heck teaching ''573''] Retrieved 3 February 2012</ref></sub>) / On the Analysis by means of equations of an infinite number of terms (<sub><ref>I. Grattan-Guinness 2005 – ''Landmark writings in Western mathematics 1640–1940'' – 1022 pages (Google eBook) [http://books.google.co.uk/books?id=UdGBy8iLpocC&pg=PA62&lpg=PA62&dq=de+analysi+per+aequationes+numero+terminorum+infinitas&source=bl&ots=RWfD7aLBvf&sig=KdeZJkAntz5pcWDd4tJt_D_2Ndo&hl=en&sa=X&ei=ZasiT_iTOoKk0QW7v43OCg&ved=0CDwQ6AEwBjgU#v=onepage&q=de%20analysi%20per%20aequationes%20numero%20terminorum%20infinitas&f=false Elsevier, 20 May 2005] Retrieved 27 January 2012 ISBN 0-444-50871-6</ref></sub>) / About completely loosening infinity by way of number equalisations limits c.f. { ''[[Wikt:aequatio|aequatio]]'' (<sub><ref>[[Douglas Harper]] – [http://www.etymonline.com/index.php?allowed_in_frame=0&search=equation&searchmode=none etymonline] Retrieved 4 February 2012</ref></sub>) , ''[[Wikt:analysis|analysi]]'' = ἀναλύω (<sub><ref>[http://www.laparola.net/greco/parola.php?p=%E1%BC%80%CE%BD%CE%B1%CE%BB%E1%BD%BB%CF%89 LaParola] – ''unloose (for departure)'' – [http://concordances.org/greek/360.htm concordances.] – ''unloosen, undo'' – [http://www.perseus.tufts.edu/hopper/morph?l=a)nalu%2Fw&la=greek Tufts University]</ref></sub>) , ''[[Wikt:de#Latin|de]]'' } {<small><sub><ref>[[University of Notre Dame]] – [http://lysy2.archives.nd.edu/cgi-bin/words.exe?terminorum terminorum] – [http://archives.nd.edu/latgramm.htm archives] – [http://www.archives.nd.edu/cgi-bin/lookup.pl?stem=per&ending= per] – [http://catholic.archives.nd.edu/cgi-bin/lookup.pl?stem=de&ending= de] "DE ANALYSI per aequationes numero terminorum INFINITAS" [http://mathenexus.zum.de/html/analysis/numerische_verfahren/weiterfuehrendes/Newton-Geschichte-Verfahren.htm mathenexus] Retrieved 27 January 2012 to −02-04</ref></sub> <sub><ref>-''analysis''- [c.f. – Aristotle] [http://www.etymonline.com/index.php?allowed_in_frame=0&search=analysis&searchmode=none etymonline] Retrieved 4 February 2012</ref></sub></small>) is a mathematical work of [[Isaac Newton]]. | |||
==Creation== | |||
== | Composed in 1669,<ref name=" Boyer & Merzbach ">Carl B. Boyer, Uta C. Merzbach {{cite book | url =http://books.google.co.uk/books?id=BokVHiuIk9UC&printsec=frontcover#v=onepage&q&f=false| title = A History of Mathematics | publisher = – 640 pages John Wiley and Sons, 11 November 2010| accessdate = 27 January 2012 }} ISBN 0-470-63056-6</ref> during the mid-part of that year probably ,<ref>Endre Süli, David Francis Mayers 2003 – ''An introduction to numerical analysis'' – 433 pages [http://books.google.co.uk/books?id=hj9weaqJTbQC&pg=PA34&lpg=PA34&dq=de+analysi+per+aequationes+numero+terminorum+infinitas&source=bl&ots=sIXlfJIbCg&sig=v7DqDGDJnQL4oxuM86gHXqA55hM&hl=en&sa=X&ei=ZasiT_iTOoKk0QW7v43OCg&ved=0CEIQ6AEwCDgU#v=onepage&q=de%20analysi%20per%20aequationes%20numero%20terminorum%20infinitas&f=false Cambridge University Press, 28 Aug 2003 ] Retrieved 27 January 2012 ISBN 0-521-00794-1</ref> from ideas Newton had acquired during the period 1665–1666.<ref name="Boyer & Merzbach"/> Newton wrote | ||
{{cquote|And whatever the common Analysis performs by Means of Equations of a finite number of Terms (provided that can be done) this new method can always perform the same by means of infinite Equations. So that I have not made any Question of giving this the name of ''Analysis'' likewise. For the Reasonings in this are no less certain than in the other, nor the Equations less exact;albeit we Mortals whose reasoning Powers are confined within narrow Limits, can neither express, nor so conceive the Terms of these Equations as to know exactly from thence the Quantities we want. To conclude, we may justly reckon that to belong to the ''Analytic Art'' , by the help of which the Areas and Lengths, etc. of Curves may be exactly and geometrically determined. | |||
== | ''Newton''<ref name="Boyer & Merzbach"/> }} | ||
The explication was written to remedy apparent weaknesses in the ''logarithmic series''<ref name="Britannica"/> [infinite series for <math>\log(1 + x)</math>] ,<ref>B.B.Blank reviewing ''The Calculus Wars:Newton, Liebnitz and the greatest mathematical clash of all time'' by J.S.Bardi [http://www.ams.org/notices/200905/rtx090500602p.pdf pdf] Retrieved 8 February 2012</ref> that had become republished due to Nicolaus Mercator,<ref name="Britannica">Britannica Educational{{cite book | url =http://books.google.co.uk/books?id=ML5Uuo16D58C&pg=PA264&lpg=PA264&dq=de+analysi+per+aequationes+numero+terminorum+infinitas&source=bl&ots=duy4nR4LGV&sig=WultfQ2c05OXOXb6WOsymBo7r7I&hl=en&sa=X&ei=H5giT_TnGIK_0QWzsYTOCg&sqi=2&ved=0CGwQ6AEwCQ#v=onepage&q=de%20analysi%20per%20aequationes%20numero%20terminorum%20infinitas&f=false | title = The Britannica Guide to Analysis and Calculus | publisher = – 288 pages The Rosen Publishing Group, 1 July 2010 | accessdate = 27 January 2012 }} ISBN 1-61530-220-4</ref><ref>Babson College [http://www.babson.edu/about-babson/at-a-glance/babsons-history/archives-and-collections/Pages/grace-k--babson-collection.aspx archives-and-collections] Retrieved 8 February 2012</ref> or through the encouragement of Isaac Barrow in 1669, to ascertain the knowing of the prior authorship of a general method of ''infinite series''. The writing was circulated amongst scholars as a manuscript in 1669,<ref name="Britannica"/><ref>King's College London [http://kingscollections.org/exhibitions/specialcollections/to-scrutinize-nature/newton-and-his-champions-i/isaac-barrow © 2010 – 2012 King's College London] Retrieved 27 January 2012</ref> including [[John Collins (mathematician)|John Collins]] a mathematics ''[[Wikt:intelligencer|intelligencer]]''<ref>Birch, History of Royal Society, ''et al'' (Richard S. Westfall ed.) [[Rice University]] [http://galileo.rice.edu/Catalog/NewFiles/collins.html galileo.edu] Retrieved 8 February 2012</ref> for a group of British and continental mathematicians. His relationship with Newton in the capacity of informant proved instrumental in securing Newton recognition and contact with [[John Wallis]] at the Royal Society.<ref>D.Harper – [http://www.etymonline.com/index.php?allowed_in_frame=0&search=informant&searchmode=none index] Retrieved 8 February 2012</ref><ref>Niccolò Guicciardini & [[University of Bergamo]] – Isaac Newton on mathematical certainty and method, Issue 4 – 422 pages ISBN 0-262-01317-7 Transformations: Studies in the History of Science and Technology [http://books.google.co.uk/books?id=U4I82SJKqAIC&pg=PA12&lpg=PA12&dq=Newton+Project+De+analysi+per+aequationes+numero+terminorum+infinitas&source=bl&ots=LZchbHixvc&sig=FPtC_csirdMnnCBjenTGjYjMLaY&hl=en&sa=X&ei=PuMyT9muCejA0QWpkZHABw&ved=0CGAQ6AEwCQ#v=onepage&q=Newton%20Project%20De%20analysi%20per%20aequationes%20numero%20terminorum%20infinitas&f=false MIT Press, 30 Oct 2009] & ''John Wallis as editor of Newton's mathematical work'' [http://rsnr.royalsocietypublishing.org/content/early/2011/11/08/rsnr.2011.0051.abstract The Royal Society 2012] Retrieved 8 February 2012</ref> | |||
Both Cambridge University Press and Royal Society rejected the treatise from publication,<ref name="Britannica"/> being instead published in London in 1711<ref>Anders Hald 2003 – ''A history of probability and statistics and their applications before 1750'' – 586 pages ''Volume 501 of Wiley series in probability and statistics'' [http://books.google.co.uk/books?id=pOQy6-qnVx8C&pg=PA563&lpg=PA563&dq=de+analysi+per+aequationes+numero+terminorum+infinitas&source=bl&ots=GSuOWdev_q&sig=oEPpGMF9tpwGZRXnGF2WclkSzN8&hl=en&sa=X&ei=bJgiT-f_HKiP0AWcrPTNCg&ved=0CDkQ6AEwBTgU#v=onepage&q=de%20analysi%20per%20aequationes%20numero%20terminorum%20infinitas&f=false Wiley-IEEE, 2003] Retrieved 27 January 2012 ISBN 0-471-47129-1</ref> by William Jones,<ref>Alexander Gelbukh, Eduardo F. Morales – MICAI 2008: advances in artificial intelligence : 7th Mexican International Conference on Artificial Intelligence, Atizapán de Zaragoza, Mexico, 27–31 October 2008 : proceedings (Google eBook) – 1034 pages ''Volume 5317 of Lecture Notes in Artificial Intelligence'' [http://books.google.co.uk/books?id=NVpZqnGDf5oC&pg=PA517&lpg=PA517&dq=De+analysi+per+aequationes+numero+terminorum+infinitas&source=bl&ots=3JUxC9iZ9Q&sig=3uP-4Qvn_Oc6W06Zz8uU8nosTXE&hl=en&sa=X&ei=v6YiT4WNDaTI0QWN4MXOCg&ved=0CCIQ6AEwADgK#v=onepage&q=De%20analysi%20per%20aequationes%20numero%20terminorum%20infinitas&f=false Springer, 2008] Retrieved 27 January 2012 ISBN 3-540-88635-4</ref> and again in 1744,<ref>''Nicolas Bourbaki'' (Henri Cartan, Claude Chevalley, Jean Dieudonné, André Weil ''et al'') – ''Functions of a real variable: elementary theory'' – 338 pages [http://books.google.co.uk/books?id=dtYLvM02cRYC&pg=PA161&lpg=PA161&dq=de+analysi+per+aequationes+numero+terminorum+infinitas&source=bl&ots=bs51LDS3nI&sig=NTI2cCRxNEok1xUfIDoa2e4vTJo&hl=en&sa=X&ei=bJgiT-f_HKiP0AWcrPTNCg&ved=0CDYQ6AEwBDgU#v=onepage&q=de%20analysi%20per%20aequationes%20numero%20terminorum%20infinitas&f=false Springer, 2004] Retrieved 27 January 2012</ref> as ''Methodus fluxionum et serierum infinitarum cum eisudem applicatione ad curvarum geometriam''<ref>Department of Mathematics (''Dipartimento di Matematico'') "Ulisse Dini" [http://web.math.unifi.it/archimede/archimede_NEW_inglese/mostra_calcolo/pannelli/3.html html] Retrieved 27 January 2012</ref> in ''[[Magnum opus|Opuscula mathematica, philosophica et philologica]]'' by Marcum-Michaelem Bousquet at that time edited by Johann Castillioneus.<ref>ISAACI NEWTONI – ''Opuscula'' [ [http://books.google.co.uk/books?id=ZhcOAAAAQAAJ&printsec=frontcover#v=onepage&q&f=false apud Marcum-Michaelem Bousquet & socios, 1744] ] Retrieved 2012-01-27 originally from [[Ghent University]] digitailized on the 26th of October 2007</ref> | |||
==Content== | |||
The exponential series, i.e. tending toward infinity, was discovered by Newton and is contained within the ''Analysis''. The treatise contains also the sine series and cosine series and arc series, the logarithmic series and the binomial series.<ref>[http://www.washjeff.edu/professors/woltermann-michael-l M. Woltermann] [[Washington & Jefferson College]][https://docs.google.com/viewer?a=v&q=cache:tm5zLSUmjPYJ:www.washjeff.edu/users/mwoltermann/Dorrie/13.pdf+De+analysi+per+aequationes+numero+terminorum+infinitas&hl=en&gl=uk&pid=bl&srcid=ADGEESjE--jnLHjHNEP2yYB6CczTNAQPVeWJcN2vNLv6CD1RmESo7jOEPKhCD_CcPVSYGL_JHgn1zT2bkaQFrzHnMLbUAo42gQvgPTpkDQyrfCKpuSpf1W4gghG6_mv1vJPtGMerg9wj&sig=AHIEtbR8h7TcM7s8RcbkRLX9vcYCfkAZ6A .edu] Retrieved 8 February 2012</ref> | |||
''==See also== | |||
[[Newton's Method]] | |||
'' | |||
==References== | |||
{{reflist}} | |||
[[Category:Latin texts]] | |||
[[Category:Works by Isaac Newton]] | |||
[[Category:Infinity]] |
Latest revision as of 21:22, 17 October 2012
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Creation
Composed in 1669,[8] during the mid-part of that year probably ,[9] from ideas Newton had acquired during the period 1665–1666.[8] Newton wrote
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The explication was written to remedy apparent weaknesses in the logarithmic series[10] [infinite series for ] ,[11] that had become republished due to Nicolaus Mercator,[10][12] or through the encouragement of Isaac Barrow in 1669, to ascertain the knowing of the prior authorship of a general method of infinite series. The writing was circulated amongst scholars as a manuscript in 1669,[10][13] including John Collins a mathematics intelligencer[14] for a group of British and continental mathematicians. His relationship with Newton in the capacity of informant proved instrumental in securing Newton recognition and contact with John Wallis at the Royal Society.[15][16]
Both Cambridge University Press and Royal Society rejected the treatise from publication,[10] being instead published in London in 1711[17] by William Jones,[18] and again in 1744,[19] as Methodus fluxionum et serierum infinitarum cum eisudem applicatione ad curvarum geometriam[20] in Opuscula mathematica, philosophica et philologica by Marcum-Michaelem Bousquet at that time edited by Johann Castillioneus.[21]
Content
The exponential series, i.e. tending toward infinity, was discovered by Newton and is contained within the Analysis. The treatise contains also the sine series and cosine series and arc series, the logarithmic series and the binomial series.[22]
==See also== Newton's Method
References
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- ↑ The Mathematical Association of America .org Retrieved 3 February 2012 & newtonproject Retrieved 6 February 2012
- ↑ Nicholls State University Thibodaux, Louisiana .edu heck teaching 573 Retrieved 3 February 2012
- ↑ I. Grattan-Guinness 2005 – Landmark writings in Western mathematics 1640–1940 – 1022 pages (Google eBook) Elsevier, 20 May 2005 Retrieved 27 January 2012 ISBN 0-444-50871-6
- ↑ Douglas Harper – etymonline Retrieved 4 February 2012
- ↑ LaParola – unloose (for departure) – concordances. – unloosen, undo – Tufts University
- ↑ University of Notre Dame – terminorum – archives – per – de "DE ANALYSI per aequationes numero terminorum INFINITAS" mathenexus Retrieved 27 January 2012 to −02-04
- ↑ -analysis- [c.f. – Aristotle] etymonline Retrieved 4 February 2012
- ↑ 8.0 8.1 Carl B. Boyer, Uta C. Merzbach 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 ISBN 0-470-63056-6 - ↑ Endre Süli, David Francis Mayers 2003 – An introduction to numerical analysis – 433 pages Cambridge University Press, 28 Aug 2003 Retrieved 27 January 2012 ISBN 0-521-00794-1
- ↑ 10.0 10.1 10.2 10.3 Britannica Educational20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 ISBN 1-61530-220-4 - ↑ B.B.Blank reviewing The Calculus Wars:Newton, Liebnitz and the greatest mathematical clash of all time by J.S.Bardi pdf Retrieved 8 February 2012
- ↑ Babson College archives-and-collections Retrieved 8 February 2012
- ↑ King's College London © 2010 – 2012 King's College London Retrieved 27 January 2012
- ↑ Birch, History of Royal Society, et al (Richard S. Westfall ed.) Rice University galileo.edu Retrieved 8 February 2012
- ↑ D.Harper – index Retrieved 8 February 2012
- ↑ Niccolò Guicciardini & University of Bergamo – Isaac Newton on mathematical certainty and method, Issue 4 – 422 pages ISBN 0-262-01317-7 Transformations: Studies in the History of Science and Technology MIT Press, 30 Oct 2009 & John Wallis as editor of Newton's mathematical work The Royal Society 2012 Retrieved 8 February 2012
- ↑ Anders Hald 2003 – A history of probability and statistics and their applications before 1750 – 586 pages Volume 501 of Wiley series in probability and statistics Wiley-IEEE, 2003 Retrieved 27 January 2012 ISBN 0-471-47129-1
- ↑ Alexander Gelbukh, Eduardo F. Morales – MICAI 2008: advances in artificial intelligence : 7th Mexican International Conference on Artificial Intelligence, Atizapán de Zaragoza, Mexico, 27–31 October 2008 : proceedings (Google eBook) – 1034 pages Volume 5317 of Lecture Notes in Artificial Intelligence Springer, 2008 Retrieved 27 January 2012 ISBN 3-540-88635-4
- ↑ Nicolas Bourbaki (Henri Cartan, Claude Chevalley, Jean Dieudonné, André Weil et al) – Functions of a real variable: elementary theory – 338 pages Springer, 2004 Retrieved 27 January 2012
- ↑ Department of Mathematics (Dipartimento di Matematico) "Ulisse Dini" html Retrieved 27 January 2012
- ↑ ISAACI NEWTONI – Opuscula [ apud Marcum-Michaelem Bousquet & socios, 1744 ] Retrieved 2012-01-27 originally from Ghent University digitailized on the 26th of October 2007
- ↑ M. Woltermann Washington & Jefferson College.edu Retrieved 8 February 2012