Article ID: CBB001021368

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


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: (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.
Journal Electronique d'Histoire des Probabilités et de la Statistique
British Journal for the History of Mathematics
Historia Mathematica
Studies in History and Philosophy of Science
Notes and Records: The Royal Society Journal of the History of Science
Bollettino di Storia delle Scienze Matematiche
Johns Hopkins University Press
Probability and statistics
Probabilism (philosophy)
Bernoulli, Jakob
MacLaurin, Colin
Newton, Isaac
De Moivre, Abraham
Bernoulli, Nikolaus
Bernoulli, family
Time Periods
18th century
17th century
19th century
20th century
Great Britain
London (England)

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