In his historical studies on the Greeks, however, Heidegger does not derive the Greek notion of a finite being from out of an analysis of a finite Greek Dasein. It is true that Dasein finds its way into many of Heidegger's commentaries on the pre-Socratics. However, the purpose of this introduction is not in order to prove that being for the Greeks was finite. It is rather the other way around. From the very beginning the Greeks conceived being (das Sein) as the being of things (Sein des Seiende), the wrong kin of de-finiteness, because it blurred over the ontological difference between being and things. In fact, being became just another thing. This "finiteness" of being falsified not only out notions being but also of Dasein.Continued.
Indeed, the reason for introducing Dasein into his various historical studies of these ancient philosophers who opened themselves up to being or thought being from out of its truth is because in Heidegger's view Dasein is already there. For that is exactly what Dasein means, i.e., his relation, his confrontation with being. Thus in his Einführung in die Metaphysik Heidegger does not introduce the Greek Dasein in order to prove the finiteness of being, but rather Dasein is shown in his authentic finiteness as defined from out of his relation to being.
But being became just another thing. And the two sides of the Greek notion of being, namely permanence and appearance, came to take separate roads in the historical process of degeneration leading through Plato and Aristotle. Upon the accentuation of one or the other of these two aspects of being, and their separation one from the other, has hung the whole destiny of being in the West.