CHAPTER II. PLASTICS. SECTION I. 979. PLASTICS, or the science of the symmetrical relations of Figures, treat of the shapes, figures, or forms of external sense, which primarily belong to palpable sense, or touch: it accords, therefore, in the view of accepted science, with Geometry, as confined to sense and taste; and is distinguished from practical Geometry, which belongs to material magnitude and mensuration; and from the higher mathematical, or pure Geometry, which belongs to pure intellectual forms, or ideal figures,—partaking of both as pure and applied, and referring to the same ulterior and elementary principles of form or figure. 980. The three dimensions of figure,-length, breadth, and depth, are modes of magnitude or space; which is, accordingly, the patient or passive principle of this science, as position, or the point, is its agent or active principle. 981. The point and space, or position and magnitude, are, accordingly, the relative extremes, or given conditions, the agent and patient, or concurring or generating principles of all shapes or figures; and the point or position, space or magnitude, and shape or figure, may be regarded, practically, as sensible, according to our present view; or, theoretically, as intellectual, according to pure geometry. 982. We may, then, define the sensible and plastic point to be an extremely minute space indicative of place or position.* 983. Pure, or perfect figures, belong not to sense, but to intellect, as forms of the mind, although they must be supposed to exist potentially, or in capacity, in all bodies; as the statue exists in the block of marble in ideal beauty before it is extricated by the art and skill of the statuary. 984. From the simplest concurrence or progress of a point in space springs longitude, or length; from its duple procession arises latitude, or breadth; and by the triple procession of the point in space is generated profundity or depth : whence LINES, SURFACES, and SOLIDS. 985. Thus the Line is the fluent of a point, the Surface is the fluent of a line, and the Solid is the fluent of a surface; and these concur in the gener *See Vol. I., par. 648. ation of all sensible and imaginary figures: of which, and in what immediately follows, we do but repeat in another view, as essential to the philosophy of beautiful forms, that which we have already advanced under Geometry of their physical and material relations. 986. Fluence is either direct, reflect, or inflect. By the simplest, or direct fluence or concurrence of the point in or with space, is generated the RIGHT LINE; by the reflect motion is generated the ANGULAR LINE; and by the inflect, flowing, or motion of a point, the CURVE, or CIRCULAR LINE, is generated and these are the genera of lines, and the primaries of all figures; of which the second comprehends more space than the first, and the third more than the second. E. g. Fig. 37. Line. Angle. Curve. 987. As the three primary modes of magnitude, longitude, latitude, and profundity, concur in all sensible figures, it is evident that each of the primary lines partakes of them, and thence each derives three principal forms. Accordingly, the first, |