Physical Sciences and Mathematics | Open Access Articles

Leonhardus Eulerus Mathematicus Acutissimus Ad Auctorem, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Go to article

Solutio Problematum Rectivicationem Ellipsis Requirentium, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Go to article

Inventio Summae Cuiusque Seriei Ex Dato Termino Generali, Leonhard Euler

All Works by Eneström Number

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.

Go to article

Investigatio Binarum Curvarum, Quarum Arcus Eidem Abscissae Respondentes Summam Algebraicam Constituant, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Go to article

De Oscillationibus Fili Flexilis Quotcunque Pondusculis Onusti, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Go to article

De Constructione Aequationum Ope Motus Tractorii Aliisque Ad Methodum Tangentium Inversam Pertinentibus, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Go to article

Solutio Problematis Ad Geometriam Situs Pertinentis, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Go to article

Methodus Universalis Series Summandi Ulterius Promota, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Go to article

Curvarum Maximi Minive Proprietate Gaudientium Inventio Nova Et Facilis, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Go to article

Inquisitio Physica In Causam Fluxus Ac Refluxus Maris, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Go to article

Seventeen Letters From Euler To Johann I Bernoulli, 1727-1740, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Go to article

De Infinitis Curvis Eiusdem Generis Seu Methodus Inveniendi Aequationes Pro Infinitis Curvis Eiusdem Generis, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Go to article

Solutio Problematis Arithmetici De Inveniendo Numero, Qui Per Datos Numeros Divisus Relinquat Data Residua, Leonhard Euler

All Works by Eneström Number

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.

Go to article

Solutio Problematum Quorundam Astronomicorum, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Go to article

De Minimis Oscillationibus Corporum Tam Rigidorum Quam Flexibilium. Methodus Nova Et Facilis., Leonhard Euler

All Works by Eneström Number

No abstract provided.

Go to article

De Progressionibus Harmonicis Observationes, Leonhard Euler

All Works by Eneström Number

Euler gives the now-named Euler-Mascheroni constant, accurate to five decimal places, and examines several series related to log(n).

Go to article

Additamentum Ad Dissertationem De Infinitis Curvis Eiusdem Generis, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Go to article

Tentamen Novae Theoriae Musicae, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Go to article

Dissertatio De Igne In Qua Ejus Natura Et Proprietates Explicantur, Leonhard Euler

All Works by Eneström Number

Euler argues that fire is the result of the bursting of tiny glassy balls of highly compressed air in the pores of bodies, so that "heat consists in a certain motion of the smallest particles of a body." Thus, all the phenomena associated with heat and fire can be deduced from the laws of mechanics without supposing any "occult qualities." He also says that light is the elastic vibration of the ether that is initiated by the explosions of little balls; hence, light is propagated by the same laws as sound.

Go to article

Quomodo Data Quacunque Curva Inveniri Oporteat Aliam Quae Cum Data Quodammodo Iuncta Ad Tautochronismum Producendum Sit Idonea, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Go to article

De Progressionibus Transcendentibus Seu Quarum Termini Generales Algebraice Dari Nequeunt, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Go to article

De Indorum Anno Solari Astronomico, Leonhard Euler

All Works by Eneström Number

This work is an appendix following two other appendices in a book by Euler's friend and St. Petersbrg Academy colleague T. S. Bayer, Historia regni Graecorum Bactriani (History of the Bactrian kingdom of the Greeks). The original appendices were written by a Danish missionary in Tranquebar, C. T. Walther ("The Indian Doctrine of Time," pp. 145-190), and by Bayer himself, based on his correspondence with Walther and other Tranquebar missionaries ("Supplement to the Indian Doctrine of Time," pp. 191-200). Euler's contribution appears immediately after these.

Go to article

De Summatione Innumerabilium Progressionum, Leonhard Euler

All Works by Eneström Number

This paper concerns the sum of reciprocal squares, which equals π²/6. Euler does not yet have the tools to find this value directly, but instead approximates it as 1.644934. He says this follows from E25 and E19, and also refers us forward to E736. Then Euler brings in the harmonic series: letting f(x) denote the xth partial sum of the harmonic series, he approximates it as an integral and defines his constant γ as the limit of f(x) – log(x).

Go to article

De Communicatione Motus In Collisione Corporum, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Go to article

Solutio Singularis Casus Circa Tautochronismum, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Go to article

De Curvis Rectificabilibus Algebraicis Atque Traiectoriis Reciprocis Algebraicis, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Go to article

Observationes De Theoremate Quodam Fermatiano Aliisque Ad Numeros Primos Spectantibus, Leonhard Euler

All Works by Eneström Number

Euler shows that the fifth Fermat number, 2^2⁵ +1 = 4,294,967,297, is not prime because it is divisible by 641, though he does not give any clues about how he discovered this fact. He also tacks on a few "theorems" but says that he does not yet know how to prove them.

Go to article

Problematis Isoperimetrici In Latissimo Sensu Accepti Solutio Generalis, Leonhard Euler

All Works by Eneström Number

No abstract provided.

Go to article

Specimen De Constructione Aequationum Differentialium Sine Indeterminatarum Separatione, Leonhard Euler

All Works by Eneström Number

In this paper, Euler investigates a differential equation that he encountered in finding the arc length of an ellipse. This differential equation cannot be solved by separation of variables, as is indicated in the title of the article. Euler first develops a formula for the arc length of an ellipse by cleverly manipulating a binomial series, then shows that this formula satisfies the desired differential equation. Integrating factors make a brief appearance.

Go to article

De Solutione Problematum Diophanteorum Per Numeros Integros, Leonhard Euler

All Works by Eneström Number

Euler searches for integer solutions to axx+bx+c=yy and considers some applications to figurate numbers.

Go to article

Full-Text Articles in Physical Sciences and Mathematics

Leonhardus Eulerus Mathematicus Acutissimus Ad Auctorem, Leonhard Euler

All Works by Eneström Number

Solutio Problematum Rectivicationem Ellipsis Requirentium, Leonhard Euler

All Works by Eneström Number

Inventio Summae Cuiusque Seriei Ex Dato Termino Generali, Leonhard Euler

All Works by Eneström Number

Investigatio Binarum Curvarum, Quarum Arcus Eidem Abscissae Respondentes Summam Algebraicam Constituant, Leonhard Euler

All Works by Eneström Number

De Oscillationibus Fili Flexilis Quotcunque Pondusculis Onusti, Leonhard Euler

All Works by Eneström Number

De Constructione Aequationum Ope Motus Tractorii Aliisque Ad Methodum Tangentium Inversam Pertinentibus, Leonhard Euler

All Works by Eneström Number

Solutio Problematis Ad Geometriam Situs Pertinentis, Leonhard Euler

All Works by Eneström Number

Methodus Universalis Series Summandi Ulterius Promota, Leonhard Euler

All Works by Eneström Number

Curvarum Maximi Minive Proprietate Gaudientium Inventio Nova Et Facilis, Leonhard Euler

All Works by Eneström Number

Inquisitio Physica In Causam Fluxus Ac Refluxus Maris, Leonhard Euler

All Works by Eneström Number

Seventeen Letters From Euler To Johann I Bernoulli, 1727-1740, Leonhard Euler

All Works by Eneström Number

De Infinitis Curvis Eiusdem Generis Seu Methodus Inveniendi Aequationes Pro Infinitis Curvis Eiusdem Generis, Leonhard Euler

All Works by Eneström Number

Solutio Problematis Arithmetici De Inveniendo Numero, Qui Per Datos Numeros Divisus Relinquat Data Residua, Leonhard Euler

All Works by Eneström Number

Solutio Problematum Quorundam Astronomicorum, Leonhard Euler

All Works by Eneström Number

De Minimis Oscillationibus Corporum Tam Rigidorum Quam Flexibilium. Methodus Nova Et Facilis., Leonhard Euler

All Works by Eneström Number

De Progressionibus Harmonicis Observationes, Leonhard Euler

All Works by Eneström Number

Additamentum Ad Dissertationem De Infinitis Curvis Eiusdem Generis, Leonhard Euler

All Works by Eneström Number

Tentamen Novae Theoriae Musicae, Leonhard Euler

All Works by Eneström Number

Dissertatio De Igne In Qua Ejus Natura Et Proprietates Explicantur, Leonhard Euler

All Works by Eneström Number

Quomodo Data Quacunque Curva Inveniri Oporteat Aliam Quae Cum Data Quodammodo Iuncta Ad Tautochronismum Producendum Sit Idonea, Leonhard Euler

All Works by Eneström Number

De Progressionibus Transcendentibus Seu Quarum Termini Generales Algebraice Dari Nequeunt, Leonhard Euler

All Works by Eneström Number

De Indorum Anno Solari Astronomico, Leonhard Euler

All Works by Eneström Number

De Summatione Innumerabilium Progressionum, Leonhard Euler

All Works by Eneström Number

De Communicatione Motus In Collisione Corporum, Leonhard Euler

All Works by Eneström Number

Solutio Singularis Casus Circa Tautochronismum, Leonhard Euler

All Works by Eneström Number

De Curvis Rectificabilibus Algebraicis Atque Traiectoriis Reciprocis Algebraicis, Leonhard Euler

All Works by Eneström Number

Observationes De Theoremate Quodam Fermatiano Aliisque Ad Numeros Primos Spectantibus, Leonhard Euler

All Works by Eneström Number

Problematis Isoperimetrici In Latissimo Sensu Accepti Solutio Generalis, Leonhard Euler

All Works by Eneström Number

Specimen De Constructione Aequationum Differentialium Sine Indeterminatarum Separatione, Leonhard Euler

All Works by Eneström Number

De Solutione Problematum Diophanteorum Per Numeros Integros, Leonhard Euler

All Works by Eneström Number