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Articles 715351 - 715380 of 715403

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De Summatione Innumerabilium Progressionum, Leonhard Euler Dec 1737

De Summatione Innumerabilium Progressionum, Leonhard Euler

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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).

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Constructio Aequationis Differentialis AxN Dx = Dy + Y2 Dx, Leonhard Euler Dec 1737

Constructio Aequationis Differentialis AxN Dx = Dy + Y2 Dx, Leonhard Euler

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No abstract provided.

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De Progressionibus Transcendentibus Seu Quarum Termini Generales Algebraice Dari Nequeunt, Leonhard Euler Dec 1737

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

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No abstract provided.

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Quomodo Data Quacunque Curva Inveniri Oporteat Aliam Quae Cum Data Quodammodo Iuncta Ad Tautochronismum Producendum Sit Idonea, Leonhard Euler Dec 1737

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

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No abstract provided.

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De Formis Radicum Aequationum Cuiusque Ordinis Coniectatio, Leonhard Euler Dec 1737

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.

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Von Der Gestalt Der Erden, Leonhard Euler Dec 1737

Von Der Gestalt Der Erden, Leonhard Euler

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No abstract provided.

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Methodus Generalis Summandi Progressiones, Leonhard Euler Dec 1737

Methodus Generalis Summandi Progressiones, Leonhard Euler

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This paper leads to Bernoulli numbers from an integral of an infinite series and is called a beautiful triumph by Euler.

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Observationes De Theoremate Quodam Fermatiano Aliisque Ad Numeros Primos Spectantibus, Leonhard Euler Dec 1737

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

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Euler shows that the fifth Fermat number, 225 +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.

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Specimen De Constructione Aequationum Differentialium Sine Indeterminatarum Separatione, Leonhard Euler Dec 1737

Specimen De Constructione Aequationum Differentialium Sine Indeterminatarum Separatione, Leonhard Euler

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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.

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The Method Of Fluxions And Infinite Series; : With Its Application To The Geometry Of Curve-Lines, Isaac, Sir Newton, London: : Printed By Henry Woodfall; And Sold By John Nourse ..., Dec 1735

The Method Of Fluxions And Infinite Series; : With Its Application To The Geometry Of Curve-Lines, Isaac, Sir Newton, London: : Printed By Henry Woodfall; And Sold By John Nourse ...,

Before the Textbook

An unfinished posthumous work, first published in the Latin original in v. 1 of the Opera omnia (Londini, J. Nichols, 1779-85) under title: Artis analyticae specimina, vel Geometria analytica. Another translation, without Colson's commentary, appeared London, 1737 as A treatise on the method of fluxions and infinite series. The commentary consists of annotations on the introduction, and on the first and second problems.

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Mechanica, Volume 2, Leonhard Euler Dec 1735

Mechanica, Volume 2, Leonhard Euler

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Mechanica (this volume, along with E15) is Euler's outline of a program of studies embracing every branch of science, involving a systematic application of analysis. It laid the foundations of analytical mechanics, the result of Euler's consideration of the motion produced by forces acting on both free and constrained points. It was also the first published work in which the number e appeared. In this volume, Euler considers motion of a point-mass lying on a given curve or surface. He derives some differential equations of the geodesics governing the problem of free motion on a surface. In this way, …

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Mechanica, Volume 1, Leonhard Euler Dec 1735

Mechanica, Volume 1, Leonhard Euler

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Mechanica (this volume, along with E16) is Euler's outline of a program of studies embracing every branch of science, involving a systematic application of analysis. It laid the foundations of analytical mechanics, the result of Euler's consideration of the motion produced by forces acting on both free and constrained points. It was also the first published work in which the number e appeared. This volume focuses on the kinematics and dynamics of a point-mass, introducing infinitely small bodies that can be considered to be points under certain assumptions. Euler focuses on single mass-points except for a few pages at …

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Curva Tautochrona In Fluido Resistentiam Faciente Secundum Quadrata Celeritatum, Leonhard Euler Dec 1734

Curva Tautochrona In Fluido Resistentiam Faciente Secundum Quadrata Celeritatum, Leonhard Euler

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No abstract provided.

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De Innumerabilibus Curvis Tautochronis In Vacuo, Leonhard Euler Dec 1734

De Innumerabilibus Curvis Tautochronis In Vacuo, Leonhard Euler

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No abstract provided.

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Solutio Problematis Astronomici Ex Datis Tribus Stellae Fixae Altitudinibus Et Temporum Differentiis Invenire Elevationem Poli Et Declinationem Stellae. Auct. L. Eulero, Leonhard Euler Dec 1734

Solutio Problematis Astronomici Ex Datis Tribus Stellae Fixae Altitudinibus Et Temporum Differentiis Invenire Elevationem Poli Et Declinationem Stellae. Auct. L. Eulero, Leonhard Euler

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No abstract provided.

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Constructio Aequationum Quarundam Differentialium, Quae Indeterminatarum Separationem Non Admittunt, Leonhard Euler Dec 1732

Constructio Aequationum Quarundam Differentialium, Quae Indeterminatarum Separationem Non Admittunt, Leonhard Euler

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No abstract provided.

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Solutio Problematis De Invenienda Curva, Quam Format Lamina Utcunque Elastica In Singulis Punctis A Potentiis Quibuscunque Sollicitata, Leonhard Euler Dec 1731

Solutio Problematis De Invenienda Curva, Quam Format Lamina Utcunque Elastica In Singulis Punctis A Potentiis Quibuscunque Sollicitata, Leonhard Euler

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No abstract provided.

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Nova Methodus Innumerabiles Aequationes Differentiales Secundi Gradus Reducendi Ad Aequationes Differentiales Primi Gradus, Leonhard Euler Dec 1731

Nova Methodus Innumerabiles Aequationes Differentiales Secundi Gradus Reducendi Ad Aequationes Differentiales Primi Gradus, Leonhard Euler

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No abstract provided.

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De Linea Brevissima In Superficie Quacunque Duo Quaelibet Puncta Iungente, Leonhard Euler Dec 1731

De Linea Brevissima In Superficie Quacunque Duo Quaelibet Puncta Iungente, Leonhard Euler

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This article arose out of a homework assignment that Euler did for Johann Bernoulli. Bernoulli asked Euler to find the shortest line between two points on a surface. This work provided some of the first analytical foundations for the calculus of variations.

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Problematis Traiectoriarum Reciprocarum Solutio, Leonhard Euler Dec 1728

Problematis Traiectoriarum Reciprocarum Solutio, Leonhard Euler

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This article contains Euler's first published use of complex numbers and a many-axis geometric construction. Euler also defines even functions f(x) as those for which f(x) = f(-x), perhaps the first use of this term.

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Dissertatio De Novo Quodam Curvarum Tautochronarum Genere, Leonhard Euler Dec 1728

Dissertatio De Novo Quodam Curvarum Tautochronarum Genere, Leonhard Euler

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According to Eneström: "Intrigued by a clock invented by D. Sully, Euler busied himself with the construction of curves which cause a pendulum to swing isochronally."

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Tentamen Explicationis Phaenomenorum Aeris, Leonhard Euler Dec 1728

Tentamen Explicationis Phaenomenorum Aeris, Leonhard Euler

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No abstract provided.

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Meditationes Super Problemate Nautico, Quod Illustrissima Regia Parisiensis Academia Scientiarum Proposuit, Leonhard Euler Dec 1727

Meditationes Super Problemate Nautico, Quod Illustrissima Regia Parisiensis Academia Scientiarum Proposuit, Leonhard Euler

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No abstract provided.

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The Threefold Paradise Of Cotton Mather: An Edition Of "Triparadisus", Reiner Smolinski Mar 1727

The Threefold Paradise Of Cotton Mather: An Edition Of "Triparadisus", Reiner Smolinski

Electronic Texts in American Studies

No other American Puritan has fueled both the popular and academic imagination as has Cotton Mather (1663-1728). Colonial America's foremost theologian and historian, Mather was also one of its most powerful voices advocating millennialism. His lifelong preoccupation with this subject culminated in his definitive treatise, "Triparadisus" (1726/1727), left unpublished at his death. In it, Mather justified his ideological revisionism; his response to the philological, historical, and scientific challenges of the Bible as text by English and continental deists; and his hermeneutical break from the orthodox exegeses of his father, Increase Mather, and Joseph Mede. In his critical introduction to this …

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Methodus Inveniendi Traiectorias Reciprocas Algebraicas, Leonhard Euler Dec 1726

Methodus Inveniendi Traiectorias Reciprocas Algebraicas, Leonhard Euler

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No abstract provided.

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Dissertatio Physica De Sono, Leonhard Euler Dec 1726

Dissertatio Physica De Sono, Leonhard Euler

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Euler first explains his theory of what makes up the atmosphere; the basis of his theory lies in the theory of elasticity of the teacher he had before Johann Bernoulli. He also states without proof a formula for the speed of propagation and derives from it numerical values of the correct order of magnitude for air.

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Constructio Linearum Isochronarum In Medio Quocunque Resistente, Leonhard Euler Dec 1725

Constructio Linearum Isochronarum In Medio Quocunque Resistente, Leonhard Euler

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No abstract provided.

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Renati Des Cartes Geometria, : Unà Cum Notis Florimondi De Beaune, In Curia Blesensi Consiliarii Regii, & Commentariis Illustrata, Operâ Atque Studio Francisci À Schooten ... Ab Eodem Dum Viveret Diligenter Recognita, Locupletioribus Commentariis Instructa, Multisque Egregiis Accessionibus, Tam Ad Ulteriorem Explicationem, Quàm Ad Ampliandam Hujus Geometriae Excellentiam Facientibus Exornata., Reneì Descartes, Francofurti Ad Moenum, : Sumptibus Friderici Knochii, Bibliop., Dec 1694

Renati Des Cartes Geometria, : Unà Cum Notis Florimondi De Beaune, In Curia Blesensi Consiliarii Regii, & Commentariis Illustrata, Operâ Atque Studio Francisci À Schooten ... Ab Eodem Dum Viveret Diligenter Recognita, Locupletioribus Commentariis Instructa, Multisque Egregiis Accessionibus, Tam Ad Ulteriorem Explicationem, Quàm Ad Ampliandam Hujus Geometriae Excellentiam Facientibus Exornata., Reneì Descartes, Francofurti Ad Moenum, : Sumptibus Friderici Knochii, Bibliop.,

Before the Textbook

Latin edition of Geometrie issued with other works not necessarily in translation.

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The Talking Deaf Man, Or, A Method Proposed, Whereby He Who Is Born Deaf May Learn To Speak, Johann Conrad Amman Dec 1693

The Talking Deaf Man, Or, A Method Proposed, Whereby He Who Is Born Deaf May Learn To Speak, Johann Conrad Amman

Deaf Rare Books

No abstract provided.

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Mercury, Or, The Secret And Swift Messenger : Shewing, How A Man May With Privacy And Speed Communicate His Thoughts To A Friend At Any Distance, John Wilkins Dec 1693

Mercury, Or, The Secret And Swift Messenger : Shewing, How A Man May With Privacy And Speed Communicate His Thoughts To A Friend At Any Distance, John Wilkins

Deaf Rare Books

No abstract provided.

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