Lectures on elementary mathematics

by Joseph-Louis Lagrange

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1901 edition. ...equations. in existence, and we owe to these passages at arms many important discoveries in analysis. Such was the resolution of equations of the fourth degree, which was propounded in the following problem. To find three numbers in continued proportion of which the sum is 10, and the product of the first two 6. Generalising and calling the sum of the three numbers a, the product of the first two b, and the first two numbers themselves x, y, we shall have, first, xy = b. Owing to the continued proportion, the third number v2 will then be expressed by--, so that the remaining condition will give y.x+y+-=a. From the first equation we obtain x=, which sub y stituted in the second gives b f Removing the fractions and arranging the terms, we get finally y + bf--a ly + P--, an equation of the fourth degree with the second term missing. According to Bombelli, of whom we shall speak Ferrari (1522-1565). Bombelli. again, Louis Ferrari of Bologna resolved the problem by a highly ingenious method, which consists in dividing the equation into two parts both of which permit of the extraction of the square root. To do this it is necessary to add to the two numbers quantities whose determination depends on an equation of the third degree, so that the resolution of equations of the fourth degree depends upon the resolution of equations of the third and is therefore subject to the same drawbacks of the irreducible case. The Algebra of Bombelli was printed in Bologna in 1579 in the Italian language. It contains not only the discovery of Ferrari but also divers other important remarks on equations of the second and third degree and particularly on the theory of radicals by means of which the author succeeded in several cases in extracting the...

Genres: Mathematics, Reference, Classics

38 pages, Paperback

First published May 19, 2008

About the author

French mathematician and astronomer comte Joseph Louis Lagrange developed the calculus of variations in 1755 and made a number of other contributions to the study of mechanics.

Born Giuseppe Lodovico Lagrangia (also reported as Giuseppe Luigi Lagrangia) this man of Enlightenment era of Italy made significant contributions to the fields of analysis, number theory, classical mechanics, and celestial mechanics. He died in Paris.

In 1766, on the recommendation of Leonhard Euler and Jean Le Rond d'Alembert, Lagrange succeeded Euler as the director of mathematics at the Prussian academy of sciences in Berlin, Prussia, where he stayed for more than two decades, producing volumes of work and winning several prizes of the French Academy of Sciences. Treatise of Lagrange on analytical mechanics (Mécanique Analytique, 4. ed., 2 vols. Paris: Gauthier-Villars et fils, 1888–89), written in Berlin and first published in 1788, offered the most comprehensive treatment of classical mechanics since Newton and formed a basis for the development of mathematical physics in the nineteenth century.

In 1787, at age 51, he moved from Berlin to Paris and became a member of the French Academy. He remained in France until the end of his life. He was significantly involved in the decimalisation in Revolutionary France, became the first professor of analysis at the École Polytechnique upon its opening in 1794, founding member of the Bureau des Longitudes and Senator in 1799.

Reviews

[Pardis TD · Rating 5 out of 5]

I found that he explained mathematical series the best, and I liked his sense of ethics.

[Pamela · Rating 3 out of 5]

Handy!