Articles liés à The Geometrical Lectures of Isaac Barrow
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Présentation de l'éditeur
Infinitesimal Calculus ;N ewton got the main idea of it from Barrow by personal communication; and Leibniz also was in some measure indebted to Barrow swork, obtaining confirmation of his own original ideas, and suggestions for their further development, from the copy of Bar rows book that he purchased in 1673. The above is the ultimate conclusion that I have arrived at, as the result of six months close study of a single book, my first essay in historical research. By the Infinitesimal Calculus, 1intend a complete set of standard forms for both the differential and integral sections of the subject, together with rules for their combination, such as for a product, a quotient, or a power of a function; and also a recognition and demonstration of the fact that differentiation and integration are inverse operations. The case of Newton is to my mind clear enough. Barrow was familiar with the paraboliforms, and tangents and areas connected with them, in from 1655 to 1660 at the very latest; hence he could at this time differentiate and integrate by his own method any rational positive power of a variable, and thus also a sum of such powers. He further developed it in the years 1662-3-4, and in the latter year probably had it fairly complete. In this year he communicated toN ewton the great secret of his geometrical constructions, as far as it is humanly possible to judge from a collection of tiny scraps of circumstantial evidence; and it was probably this that set Newton to work on an attempt to express everything as a sum of powers of the variable. During the next yearN ewton began to reflect on his method of fluxions, and actually did produce his Analysis per quationes. This, though composed in 1666, was not published until 1711.
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