Article ID: CBB001021368

Influences of Jakob's Bernoulli's Ars Conjectandi in 18th-c. Great Britain (2006)

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Schneider, Ivo H. (Author)


Journal Electronique d'Histoire des Probabilités et de la Statistique
Volume: 2, no. 1a
Issue: 1a


Publication Date: 2006
Edition Details: http://www.jehps.net/Juin2006/Schneider.pdf (Accessed on November 18, 2010). Part of a special issue, “Bernoulli's Art of Conjecture”
Language: English

TheArsConjectandiinfluencedBritishmathematiciansinthreedifferentways.Bythesecondbook,BernoullishowedhimselfasapioneerofcombinatorialmethodswhoseworkwaseventuallytranslatedintoEnglishin1795.JakobBernoulli'stractoninfiniteseries,whichwasappendedtotheArsConjectandiwasquotedbymathematiciansconcernedwiththeinfinitesimalcalculus,themostimportantbeingColinMaclaurin.TheArsConjectandihadthegreatestimpactthroughitsfirstandfourthbookandhereespeciallyononeauthor,AbrahamdeMoivre.ThisisvisibleinthetransitionfromthebasicconceptofoddsusedindeMoivre'sMensuraSortistotheconceptofprobabilityinTheDoctrineofChancs,forwhichdeMoivreoffersafirst,albeitmodest,theory.DeMoivre'sgreatestachievementinthenewtheoryofprobabilitycreatedbyJakobBernoulliandhimselfwasaformofthecentrallimittheorem.ItwasinspiredbyBernoulli'slawoflargenumbers.Usinganasymptoticseriesforn!,whichhehaddevelopedtogetherwithJamesStirling,andJakobBernoulli'sformulaforsumsofpowersofintegerscontainedinthesecondbookoftheArsConjectandi,deMoivrewasabletoapproximatethebinomialdistribution,asdevelopedinthefirstbookoftheArsConjectandi,bythenormaldistribution.AsimilardeductionbyThomasSimpson,whofollowedcloselythemodelofdeMoivre,canbeattributedtotheindirectinfluenceoftheArsConjectandi.TheproblemsarisingfromdeMoivre'sfindingandhisinterpretation of it eventually led to Thomas Bayes' Essay and the discussion of its theological implications.

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Authors & Contributors
Grabiner, Judith V.
Bruneau, Olivier
Wess, Jane A.
Serrano, David Teira
Santos Del Cerro, Jesús
Renouf, E. M.
Concepts
Mathematics
Probability and statistics
Probabilism (philosophy)
Calculus
Philosophy
Biographies
Time Periods
18th century
17th century
19th century
Enlightenment
20th century
Places
Scotland
Great Britain
London (England)
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