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Aristotle has a project to create a positive relationship between ‘definition’which is claimed to be the scientific method among his colleagues in the Academy and his new method called ‘demonstration’in his new theory of definition in the Posterior Analytics. He had to solve various difficulties concerning with the relationship between the two methods. I argue that Aristotle’s theory of definition in B. 10 presupposes his discussion on definition in the Topics. He has there distinguished ‘the defining-phrase (ὅρος)’by means of which one can gain a successful definitional practice from ‘the definition (ὁρισμός)’(I. 5, 101b37-102a5). On the basis of the defining-phrase which signifies the what a thing was to be,the thing becomes possible to be defined. Although none of Aristotelian scholars has distinguished one from the other, I shall argue that it is crucial to distinguish them for a correct understanding of the chapter. I shall offer alternative solutions from this perspective for the difficulties raised on this chapter by scholars. I argue that Aristotle makes use of the Topics type signifying account to endorse three types of definition of what it is. Also some difficulties involved in the Topics type of signifying account are solved by establishing the existence of a relevant thing through demonstration. Thus all of three definitions in his new theory of definition are of the what it is of a thing which exists. In this sense, Aristotle finds a way to establish the demonstration of what it is which was previously denied in B. 3-7.