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...

Often I have considered the fact that most of the difficulties which block the progress of students trying to learn analysis stem from this: that although they understand little of ordinary algebra, still they attempt this more subtle art. From this it follows not only that they remain on the fringes, but in addition they entertain strange ideas about the concept of the infinite, which they must try to use. Although analysis does not require an exhaustive knowledge of algebra, even of all the algebraic technique so far discovered, still there are topics whose con- sideration prepares a...

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...

Eloge d'Euler par le Marquis de Condorcet

This volume of the Opera omnia will be devoted to the letters Euler exchanged in French with his friend and countryman Johann Kaspar Wettstein as well as with some Swiss scholars in and around Geneva (Louis Bertrand, Charles Bonnet, Marc-Michel Bousquet, Jean Castillon, Gabriel Cramer, Philibert Cramer, Gaspard Cuentz, Georges-Louis Lesage). It will also include a letter from Johann Michael von Loen, a remote relative of Euler mentioned in the Euler-Bertrand correspondence.

Many letters published in this volume provide new information about Euler's non-scientific activities, like...

Die Edition der ersten drei Serien der Opera omnia Leonhard Eulers, welche 1911 begonnen wurde, geht ihrem Abschluss entgegen. Die erste Serie-Opera mathematica -liegt bereits vollstandig veroffentlicht vor; sie umfasst 29 Bande (wovon einer, namlich Band 16, wegen seines Umfangs in zwei getrennten Teilen publiziert wurde). Von den insgesamt 43 Banden der zweiten und dritten Serie, umfassend die Opera mechanica et astronomica und die Opera physica et miscellanea, bleiben zurzeit nur noch 8 Bande zu veroffentlichen. Der Band, den wir hiermit den Lesern vorlegen konnen, eroffnet die vierte...