دانلود کتاب جغرافیای ریاضی در قرن هجدهم: اویلر، لاگرانژ و لامبرت

It is no exaggeration to say that questions of geography have played a key role in the development of mathematics, both in geometry and in analysis. This is particularly true of eighteenth-century mathematics, where three of the greatest authors, Leonhard Euler, Joseph-Louis Lagrange, and Johann Heinrich Lambert, developed, each in his own way, the mathematical theory of geographical maps and brought it to a high degree of matureness. To this end, these three mathematicians formulated the classical problems of cartography in the language of the differential geometry of surfaces, opening the way to the use of differential equations, the calculus of variations, infinite series, and other techniques for solving them. At the same time, they were led to the invention of new geometric and analytical tools. A number of important ideas they introduced in this context were exploited by later prominentmathematicians of the nineteenth and twentieth centuries, including Pafnuty Chebyshev, Gaston Darboux, and others. The beautiful works of Euler, Lagrange, and Lambert on geography remain very poorly known to mathematicians today. They deserve to be read and studied, not only as historical documents, but most of all as a rich source of ideas. It is in this spirit that we have gathered in the present volume the complete writings on geography of these three authors, translated into English, putting themin perspective through explanatory and historical essays as well as commentaries and mathematical notes.