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.

The problem of the moon's orbit was one that Leonhard Euler (1707 83) returned to repeatedly throughout his life. It provided a testing ground for Newton's theory of gravitation. Could the motion of the moon be entirely accounted for by Newton's theory? Or, as Euler initially suspected, did other forces need to be invoked? For practical purposes, if the moon's orbit could be accurately predicted, its motion would provide the universal timekeeper required to solve the longitude problem. In addition to the mathematical 'three-body problem', a topic still under investigation today, Euler was faced with the statistical problem of reconciling observations rendered inconsistent by experimental error. The present work, published in Latin in 1753, is Euler's triumphant solution. It may not be the last word on a subject which has occupied mathematicians and astronomers for over three centuries, but it showed that Newton's laws were sufficient to explain lunar motion."

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..."

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..."

In 1770, one of the founders of pure mathematics, Leonard Euler (1707 1783), published an algebra textbook for students. It was soon translated into French, with notes and additions by Joseph-Louis Lagrange, another giant of eighteenth-century mathematics, and the French edition was used as the basis of the English edition of 1822 (which also appears in this series), and of this 1790s German edition by Johann Philipp Gr son, Professor of Mathematics to the royal cadets. Volume 2 consists of two parts: 16 chapters on algebraic equations, followed by 15 chapters on analyses of indeterminate quantities. Here, Euler shows the reader several ways to solve polynomial equations up to the fourth degree. This landmark book showed students the beauty of mathematics, and more significantly, how to do it. It provides tangible evidence of the lively international mathematical community that flourished despite the political uncertainties of the late eighteenth century.

In 1770, one of the founders of pure mathematics, the Swiss-born mathematician Leonard Euler (1707 1783), published an algebra textbook for students. It was soon translated into French, with notes and additions by Joseph-Louis Lagrange, another giant of eighteenth-century mathematics, and the French edition was used as the basis of this three-volume 1790s German edition. Volume 3 consists of the German translation of Lagrange's additional material, which the German publisher printed in a separate volume to enable those who already owned Euler's Algebra to obtain the supplementary material 'without incurring unnecessary expenditure'. The translator (the tutor to the sons of the Duke of W rttemberg) added notes and further appendices of his own. This book provides tangible evidence of the lively international mathematical community that flourished despite the political uncertainties of the late eighteenth century.

Der Band enthalt 14 Korrespondenzen Eulers mit Gelehrten aus dem Umfeld der Universitat Halle, der damals groessten und bedeutendsten Universitat in Preussen. Er umfasst mehr als zweihundert Briefe aus der Zeit, als Euler in Berlin Direktor der Mathematischen Klasse der preussischen Akademie der Wissenschaften war und engen Kontakt zur Petersburger Akademie der Wissenschaften pflegte. Abgesehen von drei lateinischen Briefen, die von den Herausgebern ubersetzt wurden, sind alle Briefe in deutscher Sprache abgefasst. Die Briefpartner waren in der Zeit ihrer Korrespondenz mit Euler zwischen 20 und 60 Jahre alt. Viele der jungeren beschreiben ihre berufliche Situation und bitten Euler um Empfehlungen und Protektion, wahrend altere auch technische und mathematische Probleme eroertern und sich dabei als durchaus ebenburtige Partner erweisen. Dazu kommen Verhandlungen im Zusammenhang mit der Besetzung von Professorenstellen, die Euler im Auftrag Friedrichs II. fuhrte. Neben dem unmittelbaren und anschaulichen Einblick in das akademische Leben des 18. Jahrhunderts und speziell in die Zustande an der halleschen Universitat bezeugen viele Briefe die Sorgen und Belastungen, welche die Zeitumstande, insbesondere der Siebenjahrige Krieg, fur die Bewohner der Stadt Halle mit sich brachten. This volume of the Opera omnia contains Euler's correspondence with scientists connected to the University of Halle, the most prestigious Prussian university in the 18th century. It includes more than 200 letters dating from the period when Euler served as director of the class of mathematics of the Prussian Academy of Sciences in Berlin, yet still remained in close contact with the Russian Academy of Sciences in St. Petersburg. Except for three letters written in Latin and translated into German by the editors, all the letters were originally written in German. At the time when the correspondents were in touch with Euler, their ages varied between twenty and sixty years old. Many of the younger ones were dissatisfied with their professional situation and asked Euler for support or for letters of recommendation, whereas some of the older correspondents discussed high-level technical and mathematical problems as equal partners of the Berlin mathematician. Additional letters reveal negotiations with scientists who were being considered for university professorships by the Prussian King Frederick II. The letters provide an immediate and vivid insight into academic life, and in particular, into working conditions, at the University of Halle at the time of Euler. They shed light on the worries and hardships endured by the population of that city during the Seven Years' War and other contemporary events.

This volume of the Opera omnia includes Euler's correspondences in French with his Swiss countrymen Louis Bertrand, Charles Bonnet, Marc-Michel Bousquet, Jean de Castillon, Gabriel Cramer, Philibert Cramer, Gaspard Cuentz, Albrecht von Haller, Georges-Louis Lesage et Johann Caspar Wettstein, and one letter to the German Johann Michael von Loen who is mentioned in the Euler-Bertrand correspondence. The first letter from Euler to d'Alembert recently rediscovered has been added as supplement. Whereas the correspondence with Gabriel Cramer and Georges-Louis Lesage deals mainly with mathematical and physical subjects (Cramer's rule, Cramer's paradox, Lesage's theory of gravity), many letters exchanged with other Swiss correspondents provide new information about Euler's non-scientific activities, like the commerce of almanacs, negotiations with publishers, the support of young scientists in search of a position, and a variety of private matters. ----- Ce volume contient les correspondances qu'Euler a entretenues avec plusieurs compatriotes suisses en langue francaise. Il s'agit de Louis Bertrand, Charles Bonnet, Marc-Michel Bousquet, Jean de Castillon, Gabriel Cramer, Philibert Cramer, Gaspard Cuentz, Albrecht von Haller, Georges-Louis Lesage et Johann Caspar Wettstein. Bien qu'il n'ait pas ete suisse, une lettre de Johann Michael von Loen, personnage mentionne dans la correspondance Euler-Bertrand, figure egalement dans ce volume. De plus, la premiere lettre d'Euler a d'Alembert recemment redecouverte a ete ajoutee en annexe. Tandis que les correspondances avec Gabriel Cramer et Georges-Louis Lesage portent essentiellement sur des sujets de mathematiques et de physique (regle de Cramer, paradoxe de Cramer, theorie de la gravitation de Lesage), une grande partie des lettres qu'Euler a echangees avec d'autres compatriotes refletent ses activites non scientifiques, comme le commerce d'almanachs, les negociations avec des editeurs-imprimeurs a propos de la publication de ses ouvrages, ses interventions en faveur de jeunes scientifiques a la recherche d'un poste, et des affaires privees.

in die Analysis des Une n d I i chen. Von Leonhard Euler. Erster Teil. Ins Deutsche ubertragen \'Oll H. Maser. Springer-Verlag Berlin Heidelberg GmbH 1885. Vorwort des U ebersetzers. Meisterwerke uben ihren Einfluss auf die Fortbildung der Wissen- schaft nicht allein durch die in ihnen niedergelegten Resultate des forschenden Geil'ites, es lebt in ihnen eine schoepferische Kraft, die, nie er- sterbend, immer neue Keime weckt und fort und fort bis in die spate Ferne hinaus edle Fruchte zeitigt. Derartige Geistesproducte, wenn sie selten werden, in ihrer ganzen Fulle ohne Unterlass von Neuern weiteren Kreisen zuganglich zu machen, halte ich fiir kein nutzloses Beginnen. Eben dem Zwecke soll auch die Herausgabe der vorliegenden, ganzlich nenen Uebersetzung des ersten Teils von Eu I er' s ", lntt-oductio in Analysin infinitoJ-um" dienen. Diese: durch den Reichtum seine: Inhalts, durch die Feinheit der Methoden und durch die ausserordentliche Klarheit und Pracision der Darstellung ausgezeichnete, in arithmetischer Weise aufgebaute -werk, welches weite Perspectiven eroeffnet, ist h!ltlt- zutage, trotzdem oder vielleicht gerade weil fast alle neueren Lehr- biicher aus ihm als aus einer nie versiegenden Quelle schoepfen, schon halb in Vergcst;enheit geraten, und dies ist um so mehr zu bedauern, als sich dem Anscheine nach die Erkenntnis geltend macht, dass eine scharfere Bestimmung der Begriffe auch eine weitere Entwicklung der Analysi: mit E uler' sehen Reminiscenzen auf rein arithmetischer Grundlage ermoeglichen durfte.