A Treatise On the Higher Plane Curves Intended As a Sequel to a Treatise On Con
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In our eReader you can find the full English version of the book. Read A Treatise On the Higher Plane Curves Intended As a Sequel to a Treatise On Con Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book A Treatise On the Higher Plane Curves Intended As a Sequel to a Treatise On Con
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To quickly assess the difficulty of the text, read a short excerpt:
, 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.
What to read after A Treatise On the Higher Plane Curves Intended As a Sequel to a Treatise On Con?
You can find similar books in the "Read Also" column, or choose other free books by George Salmon to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
, 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.
What to read after A Treatise On the Higher Plane Curves Intended As a Sequel to a Treatise On Con?
You can find similar books in the "Read Also" column, or choose other free books by George Salmon to read onlineMoreLess
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