ELEMENTARY SYNTHETIC GEOMETRY. BOOK I. SYMMETRY, SYMCENTRY, AND CONGRUENCE. CHAPTER I. THE PRIMARY CONCEPTS OF GEOMETRY. 1. A natural object, say a crystal, is bounded; and this boundary divides it from the air around it, but is not a thin film of the crystal itself. It is where the crystal ends and the air begins. It is also a boundary of the air where it joins the crystal, but it is not air. It is the boundary between the two, and is common to the crystal and the air. FIG. 1. 2. A boundary of the sort capable of wholly enclosing a solid, so that nothing could get into the solid except through this boundary, but itself no solid, is called a surface. 3. Surface is an ideal or imaginary concept drawn from the apparent (not real) boundaries of physical objects. We naturally associate the surface with the limited solid, not with the: |