Excerpt from The Quarterly Journal of Pure and Applied Mathematics, 1908, Vol. 39
1. In former communication I expressed the opinion that the conic node and the binode are the only simple point singularities that an algebraic surface can possess; ana that every other singularity is a compound one which, so far as its point constituents are concerned, is formed by the union of two or more conic nodes or binodes. I have not succeeded in obtaining a rigorous proof of this theorem, but I shall assume its truth; and on this hypothesis shall proceed to investigate the point constituents of a multiple point, the tangent cone at which is autotomic or improper.
The investigation of the point constituents of any multiple point involves the solution of two distinct problems.
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