An Introduction to the Method of Increments, Expressed by a New Form of Notation: Shewing More Intimately Its Relation to the Fluxional Analysis |
Common terms and phrases
1+2 multipliers 3xxx a+b+c a²b alfo alſo baſe becauſe becomes binomial binomial theorem Brook Taylor characteriſtics coefficient conftant quantity conftruction decompofe decompofition denominator divifor equal equation exponent expreffed expreffion fecond numerator fecond term feries of fractions fhall fhew fhewn figns changed fince find the expanſion find the fum find the increment Find the integral Find the limit firft differences firft factor firft term firſt fourth term fucceeding values fum required fummable fuppofe Given the feries increaſed infinite feries limit of convergency method of increments notation nth term number of factors number of terms obferved order of differences powers preceding term PROBLEM products taken propofed purpoſe required to find SCHOLIUM ſeries theorem theſe third numerator third term thoſe unity uſeful variable quantity vergency whence whofe xxxx xxxxx
Popular passages
Page iv - ... doctrine of combinations. Much has been said on the combinatorial analysis, particularly by Hindenburg, a German mathematician ; but, I do not find in his work any rules which will admit of the same application. I have not only applied the combinatorial analysis to the reduction of powers into progressions, and the reciprocals of powers into...
Page iv - ... original investigation. Though tables for reducing powers into arithmetical progressions which consist of succeeding values have been given by Stirling in his Differential Method, yet the process by which he constructs these tables is derived from principles altogether different from mine, which...
Page viii - Emerson, 3763 ; the perusal of which works will amply repay the reader for his time and trouble, by a greater variety of problems than are to be found in this Introduction, which has even been carried much farther than was at first intended.
Page iv - I first made the discovery of the transformation of products, in any form of progression, to those of any other form of professional products, as dependent on the doctrine of combinations, I have made considerable research both into English and Foreign...
Page iv - Problem in p. 52, for finding the Integrals of the successive Powers of a variable Quantity — the Method of Notation beginning at p.
Page v - I shall only first observe, that this method is perfectly indicative of the operation, either of taking the increment or integral.
Page 15 - To find the firft term of the fourth order of differences of the feries l L i- L l 1...