A Treatise On the Higher Plane Curves Intended As a Sequel to a Treatise On Con

The book A Treatise On the Higher Plane Curves Intended As a Sequel to a Treatise On Con was written by author George Salmon Here you can read free online of A Treatise On the Higher Plane Curves Intended As a Sequel to a Treatise On Con book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is A Treatise On the Higher Plane Curves Intended As a Sequel to a Treatise On Con a good or bad book?

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, a m in the x-plane. The points a i} a k are in gen eral singular points for some of the integrals of the equation (22), but they are known a priori ; that is, they are the fixed singular points.
Let now (se, ?/ ) be any pair of values such that Q(x Q9 y ) is not zero. Then by Cauchy s fundamental theorem the equation (22) has an analytic integral, in the neighborhood of the point X Q, which takes on the value y Q for x = X Q . Suppose that we make the variable x describe any path L proceeding... from the point # and not passing through any of the points a i} a k . We can continue the analytic extension of this integral along L so long as we do not encounter any singular point. But it may happen that we are stopped by the presence of such a point; let a be the first singular point which we encounter. The integral considered is analytic in the neighbor hood of every point X of the path L included between X Q and a, but the circle of convergence of the power series which represents it, and whose center is at X, never contains the point a in its interior, however small \X a\ may be.

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