Leonhard Euler

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.

Elemens d'algebre, par Leonard Euler, traduits de l'allemand avec des notes et des additionsDate de l'edition originale: 1794Ce livre est la reproduction fidele d'une oeuvre publiee avant 1920 et fait partie d'une collection de livres reimprimes a la demande editee par Hachette Livre, dans le cadre d'un partenariat avec la Bibliotheque nationale de France, offrant l'opportunite d'acceder a des ouvrages anciens et souvent rares issus des fonds patrimoniaux de la BnF. Les oeuvres faisant partie de cette collection ont ete numerisees par la BnF et sont presentes sur Gallica, sa bibliotheque numerique. En entreprenant de redonner vie a ces ouvrages au travers d'une collection de livres reimprimes a la demande, nous leur donnons la possibilite de rencontrer un public elargi et participons a la transmission de connaissances et de savoirs parfois difficilement accessibles. Nous avons cherche a concilier la reproduction fidele d'un livre ancien a partir de sa version numerisee avec le souci d'un confort de lecture optimal. Nous esperons que les ouvrages de cette nouvelle collection vous apporteront entiere satisfaction. Pour plus d'informations, rendez-vous sur www.hachettebnf.fr

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 Grüson, Professor of Mathematics to the royal cadets. Volume 1 begins with elementary mathematics of determinate quantities and includes four sections on simple calculations (addition, subtraction, division, multiplication), and progresses to compound calculations (fractions), ratios and proportions. This landmark book showed students the beauty of mathematics, and more significantly, how to do it. It provides tangible evidence of the lively and international mathematical community that flourished despite the political uncertainties of the late eighteenth century.