This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1863 Excerpt: ..., P being rational, and R the radical in question; and that if under the sign of the square root x does not rise above the fourth degree, it may ultimately be made to depend on that of Ndx where Na rational in x. He thus laid the foundation of that part of the theory of elliptic transcendents in which a proposed ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1863 Excerpt: ..., P being rational, and R the radical in question; and that if under the sign of the square root x does not rise above the fourth degree, it may ultimately be made to depend on that of Ndx where Na rational in x. He thus laid the foundation of that part of the theory of elliptic transcendents in which a proposed integral is reduced to certain canonical or standard forms, or to the simplest combination of such forms of which the case admits. In Legendre's earliest writings on elliptic functions there is nothing relating to this part of the subject. Having thus, in the simple manner which distinguishes his analysis, reduced the general case to that which admits of the application of his method, Lagrange proceeded to prove that if we introduce a new variable whose ratio to x is the subduplicate of the ratio of 1 +j?V to 1 + qx, the last written integral is made to depend on another of similar form, but in which p and q are replaced by new quantities1 and q1. If p is'greater than q, jp1 will be greater than p, and qx less than q, and thus by successive similar transformations we ultimately come to an integral in which q is so small that the factor 1 + qlx may be replaced by unity, and the elliptic integral is therefore reduced to a circular or logarithmic form. Or by successive transformations in the opposite direction we come to an integral in which p1 and q1 are sensibly equal, in which case also the elliptic integral is reduced to a lower transcendent. This most ingenious method is the foundation of ail that has since been effected in the transformation of elliptic integrals, or at least whatever has been done has been suggested by it Thus it is to Lagrange that we owe the origin of two great divisions of the theory of these functions. In the Memoirs of the ...
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Add this copy of The Mathematical and Othe Writings of R.L. Ellis, Ed. to cart. $67.74, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2016 by Palala Press.