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〃great。〃     What; we may be asked; is the limit of this progression? What; we retort; is the limit of beauty; or of heat? Whatever limit you impose; there is always a 〃hotter〃; yet 〃hotter〃 is accounted a relative; 〃hot〃 a pure quality。     In sum; just as there is a Reason…Principle of Beauty; so there must be a Reason…Principle of greatness; participation in which makes a thing great; as the Principle of beauty makes it beautiful。     To judge from these instances; there is contrariety in Quantity。 Place we may neglect as not strictly coming under the category of Quantity; if it were admitted; 〃above〃 could only be a contrary if there were something in the universe which was 〃below〃: as referring to the partial; the terms 〃above〃 and 〃below〃 are used in a purely relative sense; and must go with 〃right〃 and 〃left〃 into the category of Relation。     Syllable and discourse are only indirectly quantities or substrates of Quantity; it is voice that is quantitative: but voice is a kind of Motion; it must accordingly in any case 'quantity or no quantity' be referred to Motion; as must activity also。     13。 It has been remarked that the continuous is effectually distinguished from the discrete by their possessing the one a common; the other a separate; limit。     The same principle gives rise to the numerical distinction between odd and even; and it holds good that if there are differentiae found in both contraries; they are either to be abandoned to the objects numbered; or else to be considered as differentiae of the abstract numbers; and not of the numbers manifested in the sensible objects。 If the numbers are logically separable from the objects; that is no reason why we should not think of them as sharing the same differentiae。     But how are we to differentiate the continuous; comprising as it does line; surface and solid? The line may be rated as of one dimension; the surface as of two dimensions; the solid as of three; if we are only making a calculation and do not suppose that we are dividing the continuous into its species; for it is an invariable rule that numbers; thus grouped as prior and posterior; cannot be brought into a common genus; there is no common basis in first; second and third dimensions。 Yet there is a sense in which they would appear to be equal… namely; as pure measures of Quantity: of higher and lower dimensions; they are not however more or less quantitative。     Numbers have similarly a common property in their being numbers all; and the truth may well be; not that One creates two; and two creates three; but that all have a common source。     Suppose; however; that they are not derived from any source whatever; but merely exist; we at any rate conceive them as being derived; and so may be assumed to regard the smaller as taking priority over the greater: yet; even so; by the mere fact of their being numbers they are reducible to a single type。     What applies to numbers is equally true of magnitudes; though here we have to distinguish between line; surface and solid… the last also referred to as 〃body〃… in the ground that; while all are magnitudes; they differ specifically。     It remains to enquire whether these species are themselves to be divided: the line into straight; circular; spiral; the surface into rectilinear and circular figures; the solid into the various solid figures… sphere and polyhedra: whether these last should be subdivided; as by the geometers; into those contained by triangular and quadrilateral planes: and whether a further division of the latter should be performed。     14。 How are we to classify the straight line? Shall we deny that it is a magnitude?     The suggestion may be made that it is a qualified magnitude。 May we not; then; consider straightness as a differentia of 〃line〃? We at any rate draw on Quality for differentiae of Substance。     The straight line is; thus; a quantity plus a differentia; but it is not on that account a composite made up of straightness and line: if it be a composite; the composite possesses a differentiae of its own。     But 'if the line is a quantity' why is not the product of three lines included in Quantity? The answer is that a triangle consists not merely of three lines but of three lines in a particular disposition; a quadrilateral of four lines in a particular disposition: even the straight line involves disposition as well as quantity。     Holding that the straight line is not mere quantity; we should naturally proceed to assert that the line as limited is not mere quantity; but for the fact that the limit of a line is a point; which is in the same category; Quantity。 Similarly; the limited surface will be a quantity; since lines; which have a far better right than itself to this category; constitute its limits。 With the introduction of the limited surface… rectangle; hexagon; polygon… into the category of Quantity; this category will be brought to include every figure whatsoever。     If however by classing the triangle and the rectangle as qualia we propose to bring figures under Quality; we are not thereby precluded from assigning the same object to more categories than one: in so far as it is a magnitude… a magnitude of such and such a size… it will belong to Quantity; in so far as it presents a particular shape; to Quality。     It may be urged that the triangle is essentially a particular shape。 Then what prevents our ranking the sphere also as a quality?     To proceed on these lines would lead us to the conclusion that geometry is concerned not with magnitudes but with Quality。 But this conclusion is untenable; geometry is the study of magnitudes。 The differences of magnitudes do not eliminate the existence of magnitudes as such; any more than the differences of substances annihilate the substances themselves。     Moreover; every surface is limited; it is impossible for any surface to be infinite in extent。     Again; when I find Quality bound up with Substance; I regard it as substantial quality: I am not less; but far more; disposed to see in figures or shapes 'qualitative' varieties of Quantity。 Besides; if we are not to regard them as varieties of magnitude; to what genus are we to assign them?     Suppose; then; that we allow differences of magnitude; we commit ourselves to a specific classification of the magnitudes so differentiated。     15。 How far is it true that equality and inequality are characteristic of Quantity?     Triangles; it is significant; are said to be similar rather than equal。 But we also refer to magnitudes as similar; and the accepted connotation of similarity does not exclude similarity or dissimilarity in Quantity。 It may; of course; be the case that the term 〃similarity〃 has a different sense here from that understood in reference to Quality。     Furthermore; if we are told that equality and inequality are characteristic of Quantity; that is not to deny that similarity also may be predicated of certain quantities。 If; on the contrary; similarity and dissimilarity are to be confined to Quality; the terms as applied to Quantity must; as we have said; bear a different meaning。     But suppose similarity to be identical in both genera; Quantity and Quality must then be expected to reveal other properties held in common。     May the truth be this: that similarity is predicable of Quantity only in so far as Quantity possesses 'qualitative' differences? But as a general rule differences are grouped with that of which they are differences; especially when the difference is a difference of that thing alone。 If in one case the difference completes the substance and not in another; we inevitably class it with that which it completes; and only consider it as independent when it is not complementary: when we say 〃completes the substance;〃 we refer not to Subtance as such but to the differentiated substance; the particular object is to be thought of as receiving an accession which is non…substantial。     We must not however fad to observe that we predicate equality of triangles; rectangles; and figures generally; whether plane or solid: this may be given as a ground for regarding equality and inequality as characteristic of Quantity。     It remains to enquire whether similarity and dissimilarity are characteristic of Quality。     We have spoken of Quality as combining with other entities; Matter and Quantity; to form the complete Sensible Substance; this Substance; so called; may be supposed to constitute the manifold world of Sense; which is not so much an essence as a quale。 Thus; for the essence of fire we must look to the Reason…Principle; what produces the visible aspect is; properly speaking; a quale。     Man's essence will lie in his Reason…Principle; that which is perfected in the corporeal nature is a mere image of the Reason…Principle a quale rather than an essence。     Consider: the visible Socrates is a man; yet we give the name of Socrates to that likeness of him in a portrait; which consists of mere colours; mere pigments: similarly; it is a Reason…Principle which constitutes Socrates; but we apply the name Socrates to the Socrates we see: in truth; however; the colours and shapes which make up the visible Socrates are but reproductions of those in the Reason…Principle; while this Reason…Principle itself bear

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