A main topic of Aristotle's Logic is an inference(sullogizesthai). Sullogismos has a logical muti-role in his scientific Methodology. A aspect of Sullogismos is Apodeixis(demonstration). The purpose of this articles is to examine the role(ergon) of demonstration which works on a scope of Aristotle’s logic, and also analyzing the condition and nature of archai(first principles) in demonstration. Generally, the Posterior Analytics is the only work in the Aristotelian corpus to provide a systematic account of science and the procedures by which scientific knowledge is achieved. But recent Aristotelian scholars that the work does not contribute to the understanding of, research of particular sciences suggest that Aristotle is not concerned with the methodology of scientific research, but “with the organization and presentation of the results of research(J. Barnes, Aristotle's Posterior Analytics, Oxford 1975, p.ⅹ)”. This discrepancy that is the clash between theoretical and practical method can be detected in the following points. (1) The actual procedures of research and explanation of the results achieved cannot be formulated syllogistically. Nevertheless the sullogismos(apodeixis) forms in Aristotle's theory the fundamental instrument of scientific knowledge. (2) If Aristotle provides a uniform treatment of all scientific method, for instance the mathematical sciences were moving in the direction of axiomatization, the method of particular sciences such as that of classification have little to do with that kind of deductive organization of scientific knowledge. (3) On the other hand, the sullogismos seems to be typical of science(epistêmê), as characterized in the An. Post., that it achieves the method of pedagogy of finished science. Finally, I examined the questions of how to acquire the first principles played the central concept in the theory of demonstration.