On the Projective Methods for Investigating the Singularities at Infinity of Curves: Thesis Submitted in Partial Fulfillment of the Requirements for . School of the University of Illinois, 1916

Excerpt from On the Projective Methods for Investigating the Singularities at Infinity of Curves: Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Arts in Mathematics in the Graduate School of the University of Illinois, 1916

2. The Problem. Since the character of a curve at the infinitely distant noints cannot be studied by the ordinary means at our disposal, several methods have been devised whereby such a study can be made. It is evident at once that,in order to investigate the Singularities at infinity of a curve,the infinite points must be projected to the finite plane. Our problem then consists in the discussion of several methods by which the infinite points of a curve are transformed to the finite nlane and in such a way that the form of the curve at the point in question is preserved. When the character of the curve at the projected infinite point is determined then we have established the character of the singularity at infinity. No essentially new methods are proposed in this paper but the details of the constructions and analytical proofs of.

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