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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).

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

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No abstract provided.

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

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No abstract provided.

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.

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

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No abstract provided.

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.

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.

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.

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, …

Mechanica, Volume 1, Leonhard Euler

All Works by Eneström Number

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 …

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

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No abstract provided.

De Innumerabilibus Curvis Tautochronis In Vacuo, Leonhard Euler

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No abstract provided.

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.

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

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No abstract provided.

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.

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

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No abstract provided.

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.

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.

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."

Tentamen Explicationis Phaenomenorum Aeris, Leonhard Euler

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No abstract provided.

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

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No abstract provided.

Methodus Inveniendi Traiectorias Reciprocas Algebraicas, Leonhard Euler

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No abstract provided.

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.

Constructio Linearum Isochronarum In Medio Quocunque Resistente, Leonhard Euler

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No abstract provided.

Phaenomena Quaedam Apocalyptica Ad Aspectum Novi Orbis Configurata. Or, Some Few Lines Towards A Description Of The New Heaven (1697), Samuel Sewall, Reiner Smolinski , Editor

Electronic Texts in American Studies

SAMUEL SEWALL (1652-1730) is best remembered as a colonial judge during the Salem Witchcraft trials, as a significant diarist, and as an ardent millenarian, who published a number of eschatological tracts on his favorite obsession. Apart from his political achievements in the colonial judicature, Sewall published a number of significant works. The Selling of Joseph (1700) is one of the earliest abolitionist documents in American history. His famous Diary of Samuel Sewall, 1674-1729 (1878-82) is a Puritan document par excellence and a window on a crucial period in the development of the colony. His millenarian tract Proposals Touching the Accomplishment …

Phaenomena Quaedam Apocalyptica Ad Aspectum Novi Orbis Configurata. Or, Some Few Lines Towards A Description Of The New Heaven, Samuel Sewall, Reiner Smolinski

Zea E-Books in American Studies

SAMUEL SEWALL (1652-1730) is best remembered as a colonial judge during the Salem Witchcraft trials, as a significant diarist, and as an ardent millenarian, who published a number of eschatological tracts on his favorite obsession. Apart from his political achievements in the colonial judicature, Sewall published a number of significant works. The Selling of Joseph (1700) is one of the earliest abolitionist documents in American history. His famous Diary of Samuel Sewall, 1674-1729 (1878-82) is a Puritan document par excellence and a window on a crucial period in the development of the colony. His millenarian tract Proposals Touching the Accomplishment …

Massachusetts: Or The First Planters Of New-England, The End And Manner Of Their Coming Thither, And Abode There: In Several Epistles (1696), John Winthrop, Thomas Dudley, John Allin, Thomas Shepard, John Cotton, Joshua Scottow, Paul Royster, Editor Of The Online Electronic Edition

Joshua Scottow Papers

In 1696 there appeared in Boston an anonymous 16mo volume of 56 pages containing four “epistles,” written from 66 to 50 years earlier, illustrating the early history of the colony of Massachusetts Bay.

The four “epistles” compiled in Massachusetts, or The First Planters were all originally addressed to English or European audiences:

1. The Humble Request of His Majesties Loyal Subjects (1630), sent from aboard the Arbella and usually attributed to John Winthrop, defended the emigrants’ physical separation from England and reaffirmed their loyalty to the Crown and Church of England.

2. Thomas Dudley’s letter “To the Right Honourable, My …

The Wonders Of The Invisible World. Observations As Well Historical As Theological, Upon The Nature, The Number, And The Operations Of The Devils (1693), Cotton Mather, Reiner Smolinski , Editor

Electronic Texts in American Studies

I. Some Accounts of the Grievous Molestations, by DÆMONS and WITCHCRAFTS, which have lately annoy’d the Countrey; and the Trials of some eminent Malefactors Executed upon occasion thereof; with several Remarkable Curiosities therein occurring.
II. Some Counsils, Directing a due Improvement of the terrible things, lately done, by the Unusual & Amazing Range of EVIL SPIRITS, in Our Neighbourhood: & the methods to prevent the Wrongs which those Evil Angels may intend against all sorts of people among us; especially in Accusations of the Innocent.
III. Some Conjectures upon the great EVENTS, likely to befall, the WORLD in General, and …

Prophesies Concerning Christs 2d Coming, Isaac Newton

Rare Books at James White Library

Written sometime in the early 1680s, in English and Latin with quotations in Greek and Hebrew, c. 19,367 words, 40 pp. on 5 quarto signatures

For more information see Kimakwa, Sarah, "James White Library Hidden Treasures Isaac Newton: Early Adventist Pioneer? A Physicist’s Perspective" (2014) at https://digitalcommons.andrews.edu/library-pubs/13/