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Articles 117331 - 117360 of 117388
Full-Text Articles in Entire DC Network
De Communicatione Motus In Collisione Corporum Sese Non Directe Percutientium, Leonhard Euler
De Communicatione Motus In Collisione Corporum Sese Non Directe Percutientium, Leonhard Euler
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No abstract provided.
De Fractionibus Continuis Dissertatio, Leonhard Euler
De Fractionibus Continuis Dissertatio, Leonhard Euler
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No abstract provided.
Solutio Problematis In Novorum Actorum Eruditorum Mense Novembri A. 1743 Propositi, Leonhard Euler
Solutio Problematis In Novorum Actorum Eruditorum Mense Novembri A. 1743 Propositi, Leonhard Euler
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No abstract provided.
De Constructione Aequationum, Leonhard Euler
De Constructione Aequationum, Leonhard Euler
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No abstract provided.
Solutio Problematis Geometrici Circa Lunulas A Circulis Formatas, Leonhard Euler
Solutio Problematis Geometrici Circa Lunulas A Circulis Formatas, Leonhard Euler
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No abstract provided.
De Variis Modis Circuli Quadraturam Numeris Proxime Exprimendi, Leonhard Euler
De Variis Modis Circuli Quadraturam Numeris Proxime Exprimendi, Leonhard Euler
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No abstract provided.
Démonstration De La Somme De Cette Suite 1 + 1/4 + 1/9 + 1/16 + ..., Leonhard Euler
Démonstration De La Somme De Cette Suite 1 + 1/4 + 1/9 + 1/16 + ..., Leonhard Euler
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No abstract provided.
De Oscillationibus Fili Flexilis Quotcunque Pondusculis Onusti, Leonhard Euler
De Oscillationibus Fili Flexilis Quotcunque Pondusculis Onusti, Leonhard Euler
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No abstract provided.
De Constructione Aequationum Ope Motus Tractorii Aliisque Ad Methodum Tangentium Inversam Pertinentibus, Leonhard Euler
De Constructione Aequationum Ope Motus Tractorii Aliisque Ad Methodum Tangentium Inversam Pertinentibus, Leonhard Euler
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No abstract provided.
Solutio Problematis Ad Geometriam Situs Pertinentis, Leonhard Euler
Solutio Problematis Ad Geometriam Situs Pertinentis, Leonhard Euler
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No abstract provided.
Inventio Summae Cuiusque Seriei Ex Dato Termino Generali, Leonhard Euler
Inventio Summae Cuiusque Seriei Ex Dato Termino Generali, Leonhard Euler
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Euler continues with the methods of E25 to attack ζ(2) for a second time. He starts with a Taylor series, builds a "Bernoulli polynomial" and uses it to evaluate 0n + 1n + 2n + 3n + ... + (x-1)n, (x = 1, 2, 3, ...) and gets the relationship (B+1)n+1 – Bn+1 = 0 for Bernoulli numbers. He gets an infinite series approximation for the nth partial sum of the harmonic series.
Solutio Problematum Rectivicationem Ellipsis Requirentium, Leonhard Euler
Solutio Problematum Rectivicationem Ellipsis Requirentium, Leonhard Euler
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No abstract provided.
Theorematum Quorundam Ad Numeros Primos Spectantium Demonstratio, Leonhard Euler
Theorematum Quorundam Ad Numeros Primos Spectantium Demonstratio, Leonhard Euler
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No abstract provided.
Curvarum Maximi Minive Proprietate Gaudientium Inventio Nova Et Facilis, Leonhard Euler
Curvarum Maximi Minive Proprietate Gaudientium Inventio Nova Et Facilis, Leonhard Euler
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No abstract provided.
Investigatio Binarum Curvarum, Quarum Arcus Eidem Abscissae Respondentes Summam Algebraicam Constituant, Leonhard Euler
Investigatio Binarum Curvarum, Quarum Arcus Eidem Abscissae Respondentes Summam Algebraicam Constituant, Leonhard Euler
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No abstract provided.
Methodus Universalis Series Summandi Ulterius Promota, Leonhard Euler
Methodus Universalis Series Summandi Ulterius Promota, Leonhard Euler
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No abstract provided.
Methodus Universalis Serierum Convergentium Summas Quam Proxime Inveniendi, Leonhard Euler
Methodus Universalis Serierum Convergentium Summas Quam Proxime Inveniendi, Leonhard Euler
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This paper begins with an expression of the trapezoid rule for "formal mechanical quadrature." Euler also sums the first ten terms of ζ(2) to get 1.549768 and gives an expression for the error term. Then he determines the sum of the first million terms of the harmonic series to be 14.392669.
Methodus Computandi Aequationem Meridiei, Leonhard Euler
Methodus Computandi Aequationem Meridiei, Leonhard Euler
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No abstract provided.
Seventeen Letters From Euler To Johann I Bernoulli, 1727-1740, Leonhard Euler
Seventeen Letters From Euler To Johann I Bernoulli, 1727-1740, Leonhard Euler
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No abstract provided.
Additamentum Ad Dissertationem De Infinitis Curvis Eiusdem Generis, Leonhard Euler
Additamentum Ad Dissertationem De Infinitis Curvis Eiusdem Generis, Leonhard Euler
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No abstract provided.
De Minimis Oscillationibus Corporum Tam Rigidorum Quam Flexibilium. Methodus Nova Et Facilis., Leonhard Euler
De Minimis Oscillationibus Corporum Tam Rigidorum Quam Flexibilium. Methodus Nova Et Facilis., Leonhard Euler
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No abstract provided.
Solutio Problematis Arithmetici De Inveniendo Numero, Qui Per Datos Numeros Divisus Relinquat Data Residua, Leonhard Euler
Solutio Problematis Arithmetici De Inveniendo Numero, Qui Per Datos Numeros Divisus Relinquat Data Residua, Leonhard Euler
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Euler proves the Chinese Remainder Theorem by constructing an algorithm to find the smallest number which, divided by given numbers, leaves given remainders. He begins by solving the case in which two relatively prime divisors with corresponding remainders are given and proposes that by repeating his algorithm, he can solve similar problems with any number of constraints. Euler then discusses scenarios in which divisors are not relatively prime, and ends the paper with an application of his algorithm to a classic problem: dating events in Roman indictions.
Solutio Problematum Quorundam Astronomicorum, Leonhard Euler
Solutio Problematum Quorundam Astronomicorum, Leonhard Euler
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No abstract provided.
De Infinitis Curvis Eiusdem Generis Seu Methodus Inveniendi Aequationes Pro Infinitis Curvis Eiusdem Generis, Leonhard Euler
De Infinitis Curvis Eiusdem Generis Seu Methodus Inveniendi Aequationes Pro Infinitis Curvis Eiusdem Generis, Leonhard Euler
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No abstract provided.
De Linea Celerrimi Descensus In Medio Quocunque Resistente, Leonhard Euler
De Linea Celerrimi Descensus In Medio Quocunque Resistente, Leonhard Euler
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No abstract provided.
De Motu Planetarum Et Orbitarum Determinatione, Leonhard Euler
De Motu Planetarum Et Orbitarum Determinatione, Leonhard Euler
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No abstract provided.
Orbitae Solaris Determinatio, Leonhard Euler
Orbitae Solaris Determinatio, Leonhard Euler
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No abstract provided.
De Summis Serierum Reciprocarum, Leonhard Euler
De Summis Serierum Reciprocarum, Leonhard Euler
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Euler finds the values of ζ(2n), where ζ is now named as the Riemann zeta function. He introduces the Euler numbers En. All the odd-indexed Euler numbers are zero, E0=1, E2=-1, E4=5, E6=-61, E8=1380, and they satisfy (E+1)n+(E-1)n = 0. (The Euler numbers are the coefficients of the series expansion of sech(x) and are related to Bernoulli numbers.) Among other things, this paper includes an infinite product formula for sin(x)/x.
De Progressionibus Harmonicis Observationes, Leonhard Euler
De Progressionibus Harmonicis Observationes, Leonhard Euler
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Euler gives the now-named Euler-Mascheroni constant, accurate to five decimal places, and examines several series related to log(n).
De Communicatione Motus In Collisione Corporum, Leonhard Euler
De Communicatione Motus In Collisione Corporum, Leonhard Euler
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No abstract provided.