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In the 1789 letter to Legendre, Lacroix declared: “les livres elementaires les plus complets, le Calcul Integral d’Euler, celui de M. Cousin ont besoin d’adition” 3 . In the Preface to the second edition, he stressed this motivation [Traité, 2nd 1 “in which my goal is to assemble in a single work the materials on integral calculus that are found in the memoirs of learned societies” 2 Presumably “calcul integral” is to be read here as short for “differential and integral calculus”. 3 “the most complete elementary books, the integral calculus of Euler, that of M.

The fundamental formulas for planes and points, straight lines and distances in space are followed by more traditional subjects: second-order surfaces (that is, quadrics), and changes of coordinates. There is some discussion of contact of surfaces using their series expansions, but as the chapter proceeds power series lose ground to limits and infinitesimals. Alternatively to comparison of coefficients in series expansions, the tangent plane through a point with coordinates x , y , z is determined by the tangents to the secdz dz tions parallel to the vertical coordinate planes (these tangents have slopes dx , dy , so that dz dz (x − x ) + (y − y ) z−z = dx dy 32 Chapter 2.

This is an interesting clue on Lacroix’s views. But it becomes even more interesting when we notice that the motto of Diderot and d’Alembert’s [Encyclopédie ] was “Tantùm series juncturaque pollet, Tantùm de medio sumptis accedit honoris! ” – “Such power has a just arrangement and connection of the parts: such grace may be added to subjects merely common” 9 . In 1797-1800 probably any reader would understand the allusion. The result of this grand plan was a monumental reference work: an encyclopedic appraisal of the calculus at the turn of the century.

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Advanced Calculus of real valued functions of real variable and vectored valued functions of a vector 0

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