Leonhard Euler's Books

Foundations of Differential Calculus

By: Euler

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Foundations of Differential Calculus

By: Euler

What differential calculus, and, in general, analysis ofthe infinite, might be can hardly be explainedto those innocent ofany knowledge ofit. Nor can we here offer a definition at the beginning of this dissertation as is sometimes done in other disciplines. It is not that there is no clear definition of this calculus; rather, the fact is that in order to understand the definition there are concepts that must first be understood. Besides those ideas in common usage, there are also others from finite analysis that are much less common and are usually explained in the courseofthe development ofthe differential calculus. For this reason, it is not possible to understand a definition before its principles are sufficiently clearly seen. In the first place, this calculus is concerned with variable quantities. Although every quantity can naturally be increased or decreased without limit, still, since calculus is directed to a certain purpose, we think of some quantities as being constantly the same magnitude, while others change through all the .stages of increasing and decreasing. We note this distinc tion and call the former constant quantities and the latter variables. This characteristic difference is not required by the nature of things, but rather because of the special question addressed by the calculus.

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Page Count

215

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Springer Science & Business Media

Published Date

ISBN 10

0387985344

ISBN 13

9780387985343

The Rational Mechanics of Flexible Or Elastic Bodies 1638 - 1788

Introduction to Vol. X and XI

By: Leonhard Euler

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The Rational Mechanics of Flexible Or Elastic Bodies 1638 - 1788

Introduction to Vol. X and XI

By: Leonhard Euler

1 We search the concepts and methods ) of the theory of deformable sonds from GALILEO to LAGRANGE. Neither of them achieved much in our subject, but their works serve as 2 termini: With GALILEO's Discorsi in 1638 our matter begins ) (for this is the history of mathematical theory), while LAGRANGE's Mechanique Analitique closed the mechanics of 1) There are three major historical works that bear on our subject. The first is A history of the theory of elasticity and of the strength of materials by I. ToDHUNTER, "edited and completed" by K. PEARSON, Vol. I, Cambridge, 1886. Unfortunately it is necessary to give warning that this book fails to meet the standard set by the histories ToDHUNTER lived to finish. Much of what ToDHUNTER left seems to be rather the rough notes for a book than the book itself; the parts due to PEARSON are fortunately distinguished by square brackets. Researches prior to 1800 are disposed of in the first chapter, 79 pages long and almost entirely the work of PEARSON; as frontispiece to a work whose title restricts it to theory he saw fit to supply a possibly original pen drawing entitled "Rupture. Sur faces of Cast-Iron".

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442

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Springer Science & Business Media

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ISBN 10

3764314419

ISBN 13

9783764314415

Commentationes physicae ad theoriam caloris, electricitatis et magnetismi pertinentes

By: Leonhard Euler

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Commentationes physicae ad theoriam caloris, electricitatis et magnetismi pertinentes

By: Leonhard Euler

This volume contains seven articles of Leonhard Euler (1707-1783) and four articles of his son, Albrecht Euler. The articles on heat, electricity and magnetism are in Latin (5 articles) and in French (6 articles). The extensive introduction is written in English. With volume 10, series tertia is now completely available.

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624

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Springer Science & Business Media

Published Date

ISBN 10

3764314699

ISBN 13

9783764314699

The Rational Mechanics of Flexible Or Elastic Bodies 1638 - 1788

Introduction to Vol. X and XI

By: Leonhard Euler

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The Rational Mechanics of Flexible Or Elastic Bodies 1638 - 1788

Introduction to Vol. X and XI

By: Leonhard Euler

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Page Count

442

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Springer Science & Business Media

Published Date

ISBN 10

3764314419

ISBN 13

9783764314415

Foundations of Differential Calculus

By: Euler

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Foundations of Differential Calculus

By: Euler

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215

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Springer Science & Business Media

Published Date

ISBN 10

0387985344

ISBN 13

9780387985343

Introduction to Analysis of the Infinite

Book I

By: Leonhard Euler

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Introduction to Analysis of the Infinite

Book I

By: Leonhard Euler

From the preface of the author: "...I have divided this work into two books; in the first of these I have confined myself to those matters concerning pure analysis. In the second book I have explained those thing which must be known from geometry, since analysis is ordinarily developed in such a way that its application to geometry is shown. In the first book, since all of analysis is concerned with variable quantities and functions of such variables, I have given full treatment to functions. I have also treated the transformation of functions and functions as the sum of infinite series. In addition I have developed functions in infinite series...

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