E (константа) (Serbian Wikipedia)

Analysis of information sources in references of the Wikipedia article "E (константа)" in Serbian language version.

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6books.google.com

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Howard Whitley Eves (1969). An Introduction to the History of Mathematics. Holt, Rinehart & Winston. ISBN 978-0-03-029558-4.
Carl Boyer; Uta Merzbach (1991). A History of Mathematics (2nd изд.). Wiley. стр. 419. ISBN 978-0-471-54397-8.
Remmert, Reinhold (1991). Theory of Complex Functions. Springer-Verlag. стр. 136. ISBN 978-0-387-97195-7.

bnf.fr

gallica.bnf.fr

Jacob Bernoulli considered the problem of continuous compounding of interest, which led to a series expression for e. See: Jacob Bernoulli (1690) "Quæstiones nonnullæ de usuris, cum solutione problematis de sorte alearum, propositi in Ephem. Gall. A. 1685" (Some questions about interest, with a solution of a problem about games of chance, proposed in the Journal des Savants (Ephemerides Eruditorum Gallicanæ), in the year (anno) 1685.**), Acta eruditorum, pp. 219–23. On page 222, Bernoulli poses the question: "Alterius naturæ hoc Problema est: Quæritur, si creditor aliquis pecuniæ summam fænori exponat, ea lege, ut singulis momentis pars proportionalis usuræ annuæ sorti annumeretur; quantum ipsi finito anno debeatur?" (This is a problem of another kind: The question is, if some lender were to invest [a] sum of money [at] interest, let it accumulate, so that [at] every moment [it] were to receive [a] proportional part of [its] annual interest; how much would he be owed [at the] end of [the] year?) Bernoulli constructs a power series to calculate the answer, and then writes: " … quæ nostra serie [mathematical expression for a geometric series] &c. major est. … si a=b, debebitur plu quam 2½a & minus quam 3a." ( … which our series [a geometric series] is larger [than]. … if a=b, [the lender] will be owed more than 2½a and less than 3a.) If a=b, the geometric series reduces to the series for a × e, so 2.5 < e < 3. (** The reference is to a problem which Jacob Bernoulli posed and which appears in the Journal des Sçavans of 1685 at the bottom of page 314.)

books.google.com

Pickover, Clifford A. (2009). The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics (illustrated изд.). Sterling Publishing Company. стр. 166. ISBN 978-1-4027-5796-9. Extract of page 166
Wilson, Robinn (2018). Euler's Pioneering Equation: The most beautiful theorem in mathematics (illustrated изд.). Oxford University Press. стр. (preface). ISBN 978-0-19-251405-9.
Posamentier, Alfred S.; Lehmann, Ingmar (2004). Pi: A Biography of the World's Most Mysterious Number (illustrated изд.). Prometheus Books. стр. 68. ISBN 978-1-59102-200-8.
Jacob Bernoulli considered the problem of continuous compounding of interest, which led to a series expression for e. See: Jacob Bernoulli (1690) "Quæstiones nonnullæ de usuris, cum solutione problematis de sorte alearum, propositi in Ephem. Gall. A. 1685" (Some questions about interest, with a solution of a problem about games of chance, proposed in the Journal des Savants (Ephemerides Eruditorum Gallicanæ), in the year (anno) 1685.**), Acta eruditorum, pp. 219–23. On page 222, Bernoulli poses the question: "Alterius naturæ hoc Problema est: Quæritur, si creditor aliquis pecuniæ summam fænori exponat, ea lege, ut singulis momentis pars proportionalis usuræ annuæ sorti annumeretur; quantum ipsi finito anno debeatur?" (This is a problem of another kind: The question is, if some lender were to invest [a] sum of money [at] interest, let it accumulate, so that [at] every moment [it] were to receive [a] proportional part of [its] annual interest; how much would he be owed [at the] end of [the] year?) Bernoulli constructs a power series to calculate the answer, and then writes: " … quæ nostra serie [mathematical expression for a geometric series] &c. major est. … si a=b, debebitur plu quam 2½a & minus quam 3a." ( … which our series [a geometric series] is larger [than]. … if a=b, [the lender] will be owed more than 2½a and less than 3a.) If a=b, the geometric series reduces to the series for a × e, so 2.5 < e < 3. (** The reference is to a problem which Jacob Bernoulli posed and which appears in the Journal des Sçavans of 1685 at the bottom of page 314.)
Lettre XV. Euler à Goldbach, dated November 25, 1731 in: P.H. Fuss, ed., Correspondance Mathématique et Physique de Quelques Célèbres Géomètres du XVIIIeme Siècle … (Mathematical and physical correspondence of some famous geometers of the 18th century), vol. 1, (St. Petersburg, Russia: 1843), pp. 56–60, see especially. Fuss, Paul Heinrich (1843). Correspondance mathématique et physique de quelques célèbres géomètres du XVIIIème siècle: Précédé d'une notice sur les travaux de Léonard Euler, tant imprimés qu'inédits et publiée sous les auspices de l'Académie impériale des sciences de Saint-Pétersbourg. стр. 58. From p. 58: " … ( e denotat hic numerum, cujus logarithmus hyperbolicus est = 1), … " ( … (e denotes that number whose hyperbolic [i.e., natural] logarithm is equal to 1) … )
Leonhard Euler, Mechanica, sive Motus scientia analytice exposita (St. Petersburg (Petropoli), Russia: Academy of Sciences, 1736), vol. 1, Chapter 2, Corollary 11, paragraph 171, p. 68. From page 68: Erit enim ${\frac {dc}{c}}={\frac {dyds}{rdx}}$ seu $c=e^{\int {\frac {dyds}{rdx}}}$ ubi e denotat numerum, cuius logarithmus hyperbolicus est 1. (So it [i.e., c, the speed] will be ${\frac {dc}{c}}={\frac {dyds}{rdx}}$ or $c=e^{\int {\frac {dyds}{rdx}}}$ , where e denotes the number whose hyperbolic [i.e., natural] logarithm is 1.)

pacific.edu

scholarlycommons.pacific.edu

Euler, Meditatio in experimenta explosione tormentorum nuper instituta. Scribatur pro numero cujus logarithmus est unitas, e, qui est 2,7182817… (English: Written for the number of which the logarithm has the unit, e, that is 2,7182817...")

st-and.ac.uk

www-history.mcs.st-and.ac.uk

O'Connor, J J; Robertson, E F. „The number e”. MacTutor History of Mathematics.

uni-goettingen.de

leibniz.uni-goettingen.de

Leibniz, Gottfried Wilhelm (2003). „Sämliche Schriften Und Briefe” (PDF) (на језику: немачки). „look for example letter nr. 6”

wolfram.com

mathworld.wolfram.com

Weisstein, Eric W. „e”. mathworld.wolfram.com (на језику: енглески). Приступљено 2020-08-10.