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In this paper we study the linear systems of degree <em>m</em> hypersurfaces in the <em>n</em>-dimensional projective space with <em>d</em> fixed points of multiplicity <em>e</em> in general position, focusing on the case <em>n=3, e=2</em>. The goal is to compute the dimension of such systems. <we present to modern readers a method due to Terracini, showing its similarities and differences to recent approaches.