The doctrine of permutations and combinations, being an essential and fundamental part of the doctrine of chances; as it is delivered by Mr. James Bernoulli, in his excellent treatise on the doctrine of chances, intitled, Ars conjectandi, and by the celebrated Dr. John Wallis, of Oxford, in a tract intitled from the subject, and published at the end of his Treatise on algebra: in the former of which tracts is contained, a demonstration of Sir Isaac Newton's famous binomial theorem, in the cases of integral powers, and of the reciprocals of integral powers. Together with some other useful mathematical tracts / [by various authors] Published by Francis Maseres, esq.

Date:
1795
Catalogue details

Licence: Public Domain Mark

Credit: The doctrine of permutations and combinations, being an essential and fundamental part of the doctrine of chances; as it is delivered by Mr. James Bernoulli, in his excellent treatise on the doctrine of chances, intitled, Ars conjectandi, and by the celebrated Dr. John Wallis, of Oxford, in a tract intitled from the subject, and published at the end of his Treatise on algebra: in the former of which tracts is contained, a demonstration of Sir Isaac Newton's famous binomial theorem, in the cases of integral powers, and of the reciprocals of integral powers. Together with some other useful mathematical tracts / [by various authors] Published by Francis Maseres, esq. Source: Wellcome Collection.

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    «#« wuhoiit having much acquaintance'with the Latih language, J have, in order to render the contents of thefe three valu- able chapters acceflible to fiich perfons, tranllated thefe chapters into Englilh, and fubjoined the tranllation to the original text in Latin-, lb that the reader may chufe in which of the two languages he will perufe them. And in this tranflation I have expreffed myfelf in a fuller manner than Mr. Bernoulli had adopted in the originalj becaufe I had obferved that the great degree of brevity with which l\Ir. Bernoulli had expreffed himielf had rendered fome parts of the original rather obfeure. And 1 have likewife added a few notes both to the original and the tranflation, where the text feemed to me to require them. And further, in the latter part of the tranflation of thefe chapters, I have alfo done fometliing more than merely tranflate them. For, as I obferved that Mr. Bernoulli’s eonclufions concerning the properties of the Figurate num- bers, (which he had applied to the demonftration of the binomial theorem in the firft, or fimpleft, cafe of it, or when »2, or the index of the power of the binomial quan- tity a bf was an affirmative whole number^') might eafily be applied to the demonftration of the binomial theorem in another cafe of it, to wit, in that cafe of it in which m, or the index of the binomial quantity a b., ha negative whole number^ 1 drew up fonle additional articles, that are not contained in Mr. Bernoulli’s text, for this purpofe. Thele additional articles, (which contain a demontfration of the binomial theorem in the cafe of integral and negative powers, or in the cafe of the quantity a -h extend from page 123 to page 166 ; after which the tranflation of Mr. Bernoulli’s text is refumed, and continues to page 213. Thefe three chapters contain a moft accurate and diftineft explanation of the fundamental parts of the Dodtrine of Permutations and Combinations, and of the moft remark- able properties of the Figurate numbers, which, it is well known, are of the moft extenfive ufe in various branches a 2 of