De analysi per aequationes numero terminorum infinitas: diferència entre les revisions

'''De analysi per aequationes numero terminorum infinitas''' (o sobre l'anàlisi per sèries infinites,<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> sobre l'anàlisi per equacions amb un nombre infinit de termes,<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> o sobre l'anàlisi mitjançant equacions d'un nombre infinit de termes, <ref>I. Grattan-Guinness 2005 – ''Landmark writings in Western mathematics 1640–1940'' – 1022 pages (Google eBook) [https://books.google.com/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> és una obra matemàtica d'[[Isaac Newton]].

Composta el 1669, probablement a mitjan aquell any, <ref>Endre Süli, David Francis Mayers 2003 – ''An introduction to numerical analysis'' – 433 pages [https://books.google.com/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> a partir d’idees que Newton havia adquirit durant el període 1665-1666. Newton va escriure:

{{cita|I qualsevol que siga l'anàlisi comú que es realitze mitjançant procediments d'equacions d'un nombre finit de termes (sempre que es puga fer), aquest nou mètode sempre pot realitzar el mateix mitjançant infinites equacions. De manera que no he fet cap pregunta sobre donar-li el mateix nom d'anàlisi. Perquè els raonaments en això no són menys segurs que en l’altre, ni les equacions menys exactes; tot i que els mortals els poders raonables dels quals estan confinats en límits estrets, no podem expressar ni concebre els termes d’aquestes equacions per saber exactament des d’allà les quantitats que volem. Per concloure, podem justament considerar que pertànyer a l '"Art analític", amb l'ajut del qual es poden determinar exactament i geomètricament les àrees i longituds, etc... de les corbes. ''Newton'' <ref name=" Boyer & Merzbach ">Carl B. Boyer, [[Uta Merzbach|Uta C. Merzbach]] {{cite book ref-llibre| url =https://archive.org/details/historyofmathema0003merz| url-access =registration| title títol= A History of Mathematics | year any=2011| publisher editorial= – 640 pages John Wiley and Sons, 11 November 2010| access-date = 27 Januarygener 2012 }} {{ISBN|0-470-63056-6}}</ref>}}

<math>\log(1 + x)</math>], que s’havia tornat a publicar a causa de [[Nicolaus Mercator]], o mitjançant l’impuls d’[[Isaac Barrow]] el 1669, per constatar el coneixement de l’autoria prèvia d’un mètode general de sèries infinites.<ref>B.B.Blank reviewing ''The Calculus Wars: Newton, Leibniz and the greatest mathematical clash of all time'' by J.S.Bardi [https://www.ams.org/notices/200905/rtx090500602p.pdf pdf] Retrieved 8 February 2012</ref><ref name="Britannica" /><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] {{Webarchive|url=https://web.archive.org/web/20180122130955/http://www.babson.edu/about-babson/at-a-glance/babsons-history/archives-and-collections/Pages/grace-k--babson-collection.aspx|date= 22 Januarygener 2018}} Retrieved 8 February 2012</ref> L'escriptura es va difondre entre els estudiosos com a manuscrit el 1669, inclòs [[John Collins]], un intel·ligent matemàtic per a un grup de matemàtics britànics i continentals.<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> per un grup de matemàtics britànics i continentals.<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> La seva relació amb Newton com a informador va resultar fonamental per aconseguir el reconeixement de Newton i el contacte amb John Wallis a la 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]] & [[Universitat de Bèrgam]] – 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 [https://books.google.com/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> Tant Cambridge University Press com la Royal Society van rebutjar el tractat de publicar-lo, publicant-lo a Londres el 1711 per William Jones, i de nou el 1744, com ''Methodus fluxionum et serierum infinitarum cum eisudem applicatione ad curvarum geometriam''' a <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> en Opuscula mathematica, philosophica et philologica per Marcum-Michaelem Bousquet en aquell temps editat per Johann Castillioneus.<ref name="Britannica" /><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'' [https://books.google.com/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><ref>Alexander Gelbukh, Eduardo F. Morales – MICAI 2008: advances in artificial intelligence : [[Conferència Internacional mexicana en Intel·ligència Artificial|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'' [https://books.google.com/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><ref>''Nicolas Bourbaki'' ([[Henri Cartan]], Claude Chevalley, Jean Dieudonné, [[André Weil]] ''et al'') – ''Functions of a real variable: elementary theory'' – 338 pages [https://books.google.com/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><ref>ISAACI NEWTONI – ''Opuscula'' [ [https://books.google.com/books?id=ZhcOAAAAQAAJ&printsec=frontcover#v=onepage&q&f=false apud Marcum-Michaelem Bousquet & socios, 1744] ] Retrieved 2012-01-27 originally from [[Ghent University]] digitalized on 26 October 2007</ref>