For complete demonstration, it is not sufficient that the premisses be true, immediate, and undemonstrable; they must, furthermore, be essential and appropriate to the class in hand. Unless they be such, you cannot be said to know the conclusion _absolutely_; you know it only by accident. You can only know a conclusion when demonstrated from its own appropriate premisses; and you know it best when it is demonstrated from its highest premisses. It is sometimes difficult to determine whether we really know or not; for we fancy that we know, when we demonstrate from true and universal _principia_, without being aware whether they are, or are not, the _principia_ appropriate to the case.[28] But these _principia_ must always be assumed without demonstration--the class whose essential constituent properties are in question, the universal Axioms, and the Definition or meaning of the attributes to be demonstrated. If these definitions and axioms are not always formally enunciated, it is because we tacitly presume them to be already known and admitted by the learner.[29] He may indeed always refuse to grant them in express words, but they are such that he cannot help granting them by internal assent in his mind, to which every syllogism must address itself. When you assume a premiss without demonstrating it, though it be really demonstrable, this, if the learner is favourable and willing to grant it, is an assumption or Hypothesis, valid relatively to him alone, but not valid absolutely: if he is reluctant or adverse, it is a Postulate, which you claim whether he is satisfied or not.[30] The Definition by itself is not an hypothesis; for it neither affirms nor denies the existence of anything. The pupil must indeed understand the terms of it; but this alone is not an hypothesis, unless you call the fact that the pupil comes to learn, an hypothesis.[31] The Hypothesis or assumption is contained in the premisses, being that by which the reason of the conclusion comes to be true. Some object that the geometer makes a false hypothesis or assumption, when he declares a given line drawn to be straight, or to be a foot long, though it is neither one nor the other. But this objection has no pertinence, since the geometer does not derive his conclusions from what is true of the visible lines drawn before his eyes, but from what is true of the lines conceived in his own mind, and signified or illustrated by the visible diagrams.[32] [Footnote 28: Ibid. ix. p. 75, b. 37-p. 76, a. 30.] [Footnote 29: Ibid. x. p. 76, a. 31-b. 22.] [Footnote 30: Aristot. Analyt. Post. I. x. p. 76, b. 29-34: [Greek: e)a\n me\n dokou=nta lamba/nê| tô=| mantha/nonti, u(poti/thetai, kai\ e)/stin ou)/ch a(plô=s u(po/thesis, a)lla\ pro\s e)kei=non mo/non, a)\n de\ ê)\ mêdemi/a=s e)nou/sês do/xês ê)\ kai\ e)nanti/as e)nou/sês lamba/nê| to\ au)to/, ai)tei=tai. kai\ tou/tô| diaphe/rei _u(po/thesis_ kai\ _ai)/têma_], &c. Themistius, Paraphras. p. 37, Spengel.]