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Articles 32161 - 32174 of 32174
Full-Text Articles in Entire DC Network
Rettung Der Göttlichen Offenbahrung Gegen Die Einwürfe Der Freygeister, Leonhard Euler
Rettung Der Göttlichen Offenbahrung Gegen Die Einwürfe Der Freygeister, Leonhard Euler
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No abstract provided.
De Motu Cymbarum Remis Propulsarum In Fluviis, Leonhard Euler
De Motu Cymbarum Remis Propulsarum In Fluviis, Leonhard Euler
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No abstract provided.
Nova Theoria Lucis Et Colorum, Leonhard Euler
Nova Theoria Lucis Et Colorum, Leonhard Euler
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No abstract provided.
Enodatio Quaestionis Utrum Materiae Facultas Cogitandi Tribui Possit Necne, Leonhard Euler
Enodatio Quaestionis Utrum Materiae Facultas Cogitandi Tribui Possit Necne, Leonhard Euler
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No abstract provided.
Sur Quelques Proprietés Des Sections Coniques, Qui Conviennent À Une Infinité D'Autres Lignes Courbes, Leonhard Euler
Sur Quelques Proprietés Des Sections Coniques, Qui Conviennent À Une Infinité D'Autres Lignes Courbes, Leonhard Euler
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No abstract provided.
Recherches Physiques Sur La Nature Des Moindres Parties De La Matière, Leonhard Euler
Recherches Physiques Sur La Nature Des Moindres Parties De La Matière, Leonhard Euler
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No abstract provided.
Variae Observationes Circa Series Infinitas, Leonhard Euler
Variae Observationes Circa Series Infinitas, 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.
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.
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.
De Curvis Rectificabilibus Algebraicis Atque Traiectoriis Reciprocis Algebraicis, Leonhard Euler
De Curvis Rectificabilibus Algebraicis Atque Traiectoriis Reciprocis Algebraicis, Leonhard Euler
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No abstract provided.
De Progressionibus Transcendentibus Seu Quarum Termini Generales Algebraice Dari Nequeunt, Leonhard Euler
De Progressionibus Transcendentibus Seu Quarum Termini Generales Algebraice Dari Nequeunt, Leonhard Euler
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No abstract provided.
De Formis Radicum Aequationum Cuiusque Ordinis Coniectatio, Leonhard Euler
De Formis Radicum Aequationum Cuiusque Ordinis Coniectatio, Leonhard Euler
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For an equation of degree n, Euler wants to define a "resolvent equation" of degree n-1 whose roots are related to the roots of the original equation. Thus, by solving the resolvent one can solve the original equation. In sections 2 to 7 he works this out for quadratic, cubic, and biquadratic equations. In section 8 Euler says that he wants to try the same approach for solving the quintic equation and general nth degree equations. In the rest of the paper he tries to figure out in what cases resolvents will work.
Von Der Gestalt Der Erden, Leonhard Euler
Von Der Gestalt Der Erden, Leonhard Euler
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No abstract provided.