By all this I do not mean to suggest the introduction of a new method of mathematical demonstration, nor the substitution of my own proof for that of Euclid, for which its whole nature unfits it, as well as the fact that it presupposes the conception of parallel lines, which in Euclid comes much later. I merely wished to show what the reason of being is, and wherein lies the difference between it and the reason of knowing, which latter only effects _convictio_, a thing that differs entirely from insight into the reason of being. The fact that Geometry only aims at effecting _convictio_, and that this, as I have said, leaves behind it a disagreeable impression, but gives no insight into the reason of being--which insight, like all knowledge, is satisfactory and pleasing--may perhaps be one of the reasons for the great dislike which many otherwise eminent heads have for mathematics. I cannot resist again giving fig. 6, although it has already been presented elsewhere; because the mere sight of it without words conveys ten times more persuasion of the truth of the Pythagorean theorem than Euclid's mouse-trap demonstration. [Illustration: _Fig. 6._] Those readers for whom this chapter may have a special interest will find the subject of it more fully treated in my chief work, "Die Welt als Wille und Vorstellung," vol. i. § 15; vol. ii. chap. 13. CHAPTER VII. ON THE FOURTH CLASS OF OBJECTS FOR THE SUBJECT, AND THE FORM OF THE PRINCIPLE OF SUFFICIENT REASON WHICH PREDOMINATES IN IT. § 40. _General Explanation._ The last Class of Objects for our representative faculty which remains to be examined is a peculiar but highly important one. It comprises but _one_ object for each individual: that is, the immediate object of the inner sense, the _Subject in volition_, which is Object for the Knowing Subject; wherefore it manifests itself in Time alone, never in Space, and as we shall see, even in Time under an important restriction. § 41. _Subject of Knowledge and Object._ All knowledge presupposes Subject and Object. Even self-consciousness (_Selbstbewusstsein_) therefore is not absolutely simple, but, like our consciousness of all other things (_i.e._, the faculty of perception), it is subdivided into that which is known and that which knows. Now, that which is known manifests itself absolutely and exclusively as _Will_. The Subject accordingly knows itself exclusively as _willing_, but not as _knowing_. For the _ego_ which represents, never can itself become representation or Object, since it conditions all representations as their necessary correlate; rather may the following beautiful passage from the Sacred Upanishad be applied to it: _Id videndum non est: omnia videt; et id audiendum non est: omnia audit; sciendum non est: omnia scit: et intelligendum, non est: omnia intelligit. Præter id, videns, et sciens, et audiens, et intelligens ens aliud non est._[151] [151] "Oupnekhat," vol. i. p. 202.