Ian bruce et al. euler's early papers mathematical papers show the influence of johan bernoulli, his mentor. E002 is a dissertation on sound, which was presented to the university at basel in a vain attempt to gain the vacant physics chair e005 is concerned with curves that intersect orthogonally, a much longer paper, and this is perhaps euler's first mature paper all of course show his mathematical brilliance, although he has not yet made the transition to completely analytical methods. E006 is concerned with the involute of the circle, formed by unwinding a string along the tangent, as a correcting mechanism for the period of a chronometer, developed originally by huygens in the horologia. E007 is an attempt to explain atmospheric phenomena in terms of air vesicles, fine matter, and centrifugal force. E008 is about the general solution of heavy planar curves under various loadings, catenaries, sails, etc.

E009 is a classic early paper on the shortest curve joining two points on a surface. E010 is the start of euler's love affair with the exponential function, related to easing the pain of solving differential equations. The papers presented here in pdf format are taken from the appropriate volumes of euler's works. E011 is a later paper, and relies on previous work not yet covered in this series of translations. E012 is a masterful work, in which euler first establishes a surprisingly simple geometric condition for tautochronic curves, and then shows how to generate such curves, both analytic and algebraic, starting from the familiar cycloid e013 extends the analysis to a resistive medium where the resistance is in proportion to the square of the speed.

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E014 is an elementary treatment of finding the pole star from three measurements on a star over time. Both the translation and the latin version are presented, the latter usually at the end. I wish to thank the members of the euler archive based at dartmouth college for providing most of the original pdf files. The erroneous construction of tautochronous curves in media with different forms of resistance. This is euler's first paper e001 the math in the translation has been clarified feb. Student translations of eule r’s mathematics the student translations of euler’s mathematics st e m project at rowan university is an exciting project that engages undergraduate math students, under the supervision of faculty members, to translate selected papers of leonard euler originally written in french, german and latin into english and to expose his works to the broader mathematical community. Translations e236 translation and synopsis by andrew fabian faculty advisor: hieu nguyen exposition de quelques paradoxes dans le calcul integral explanation of certain paradoxes in integral calculus originally published in memoires de l ' academie des sciences de berlin 12, 1758, pp.

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e308 translation by andrew fabian faculty advisor: hieu nguyen recherches sur le mouvement de rotation des corps celestes studies on the rotational movement of celestial bodies originally published in memoires de l ' academie des sciences de berlin 15, 1766, pp. e785 translation by andrew fabian faculty advisor: hieu nguyen integration d ' une espece remarqable d ' equation differentielle dans l ' analyse des fonctions a deux variables integration of a remarkable type of differential equation in analytical functions with two variables originally published in memoires de l ' academie des sciences de st. Osler sur quelques proprietes des sections coniques qui conviennent a un infinite d'autres lignes courbes on some properties of conic sections that are shared with infinitely many other curved lines originally published in memoires de l ' academie des sciences de berlin 1, 1746, pp.

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Osler methodvs vniversalis seriervm convergentivm svmmas quam proxime inveniendi a general method for finding approximations to the sums of convergent series originally published in commentarii academiae scientiarum petropolitanae 8, 1741, pp. Osler recherches sur le problem de trois nombres carres tels que la somme de deux quelconques moins le troisieme fasse un nombre carre research into the problem of three square numbers such that the sum of any two less the third one provides a square number. Osler remarques sur un beau rapport entre les series des puissances tant directes que reciproques remarks on a beautiful relation between direct as well as reciprocal power series originally published in memoires de l ' academie des sciences de berlin 17, 1768, pp.

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This article is about a mathematician who in 1775, while france was mired in revolution, was in st petersburg researching both mathematics and science. In particular it is about one of his books, elements of algebra 4 read a review in this issue of plus . This mathematician was leonhard euler and his book is an elementary algebra textbook which starts with a discussion of the nature of numbers, of the symbols such as + and , and then explains techniques for solving equations of various kinds. It might seem strange to consider an algebra textbook which is almost 250 years old, but there are a number of good reasons to do so. Leonhard euler 1707 1783 was one of the most prolific mathematical authors of all time and the 15th april 2007 was his three hundredth birthday. In 1907 the euler committee of the swiss academy of sciences was founded to publish all of euler's scientific books, papers and correspondence in one edition.

You can get an idea of the range of euler's work by looking at the list compiled by the swedish mathematician gustav eneström. And these numbers are a widely accepted way to refer to specific books, papers or important scientific letters. Unfortunately many of these books and scientific papers are either not available in english, are about rather obscure mathematical topics, or are simply difficult to obtain. Blanton of introduction to analysis of the infinite and foundations of differential calculus. Although, even here, some advanced mathematics is needed as background to really appreciate their significance.

On the other hand, almost anyone could read, appreciate and enjoy elements of algebra. Both from a historical and mathematical point of view it is important to read original sources, even if in translation. But why euler? anniversaries are useful reminders, but more importantly euler is unusual in the clarity of his mathematical writing. Laplace is quoted as saying read euler, read euler! he is the master of us all! while gauss apparently thought that the study of euler's works remains the best instruction in the various areas of mathematics and can be replaced by no other. The german editor claims that he dictated the book to a young servant, and through this taught him some mathematics, in this way educating a new amanuensis. the elements appears in gustav eneström's list of euler's works as volumes e387 and e388.

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However, the first published edition, by the royal academy of sciences in st petersburg, appeared in 1770 as a russian translation. A german edition followed swiftly, as did further translations into other european languages. At this stage approximately one hundred pages of additions were added by joseph louis lagrange written in the 1822 book as la grange. Francis horner took this french edition and the english translation began as a student project. He died before it was completed and it was left to john hewlett to complete the translation and editing and as a result the english translation is attributed to him. To write a commentary on euler's work is difficult mainly because the clarity of his writing is difficult to match. However, to try to justify why you as a modern reader might consider making this effort, i would like to highlight two differences from the way we shape the modern curriculum which are striking, interesting and deserve comment.

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Rather than paraphrase euler, these differences will be illustrated by generously quoting from euler himself. I have retained the paragraph numbering which is a characteristic feature of publishing at that time. The style of the language takes a little getting used to, but the effort is worthwhile. By taking this approach i hope to convince you that reading original mathematical sources is not so difficult after all. The first striking feature is the way euler introduces both irrational and complex numbers. He begins by a thorough discussion of addition, subtraction, multiplication and division of whole numbers. In particular, for example, explaining why the product of two negative numbers is positive.

Once division is introduced, it is natural to consider fractions, adding, multiplying and simplifying. After only 30 pages or so he is ready to consider square numbers and also square roots. Frequently asked questions leonhard euler is the most prolific mathematician in history.

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He was born in basel, switzerland, in 1707, and began his mathematics education under johann bernoulli at the age of 14. Over the next 50 years, he worked in both saint petersburg and berlin, and worked alongside with or corresponded with the almost all the leading mathematicians and scientists of the 18th century. During his lifetime, euler wrote over 800 papers covering every branch of mathematics known in his time, and including such applied topics as mechanics, fluid mechanics, naval science, solar and lunar motion, the tides, cartography, astronomical motion and precessions, acoustics, and optics. He wrote an enormously influential series of calculus textbooks, as well as books on over a dozen other mathematical and scientific fields. Euler's life 1707 1783 fits neatly into the european enlightenment, and he was the towering figure of european science during this time.

The historian of science clifford truesdell has estimated that in a listing of all of the mathematics, physics, mechanics, astronomy, and navigation work produced during the 18th century, a full 25% would have been written by leonhard euler. The euler archive is an online resource for leonhard euler's original works and modern euler scholarship. This dynamic library and database provides access to original publications, and references to available translations and current research. The goals of the euler archive are:

provide access to all of euler's original publications. one of the difficulties with euler research has been the lack of availability of original documents.