1. The block represented in the figure occupies a lim- Ited portion of space. Conceive it to be removed. form or shape may still be retained in mind. This is true of any object The space conceived to be occupied by a body, apart from its substance, is called a geometrical solid. The matter or substance of which the body is composed constitutes a physical solid. Hence a geometrical solid is simply the shape or form of a physical solid, or some form or figure conceived by Definition. A geometrical solid is a limited portion of space and has length, breadth and thickness. The term solid will hereafter be used for geometrical solid. 2. The boundary that separates a solid from the space outside of itself is called the surface of the solid. Dis- tinct flat portions of the bounding surface are called As we can think of the surface of a body without in- cluding any of its substance, surface may be regarded as CHAPTER I. RECTILINEAR FIGURES. DEFINITIONS. Its 1. The block represented in the figure occupies a limited portion of space. Conceive it to be removed. form or shape may still be retained in mind. This is true of any object or body. The space conceived to be occupied by a body, apart from its substance, is called a geometrical solid. The matter or substance of which the body is composed constitutes a physical solid. Hence a geometrical solid is simply the shape or form of a physical solid, or some form or figure conceived by the mind. Definition. A geometrical solid is a limited portion of space and has length, breadth and thickness. The term solid will hereafter be used for geometrical solid. 2. The boundary that separates a solid from the space outside of itself is called the surface of the solid. Distinct flat portions of the bounding surface are called faces. As we can think of the surface of a body without including any of its substance, surface may be regarded as having no thickness. Definition. Surface is that which has length and breadth without thickness. 3. If a surface be divided into distinct portions, the boundaries of those portions are called lines. In the solid represented on page 1, the edges, or boundaries of the faces, are lines. These lines being the intersections of faces which have no thickness can themselves have neither breadth nor thickness. Definition. A line is that which has length but has neither breadth nor thickness. 4. If a line be divided into distinct portions the limits of these portions are called points. In the solid represented on page 1, the corners, or limits of the edges, are points. These points being the intersections of lines which have neither breadth nor thickness can themselves have neither length, breadth nor thickness. Definition. A point is that which has simply position but neither length, breadth nor thickness. 5. A surface may be conceived apart from a solid, a line apart from a surface and a point apart from a line. If a point be conceived to move, the path in which it moves is a line, hence a line may be regarded as the path, or locus, of a moving point. When a line is regarded as formed by a moving point the point is said to describe the line. 6. A geometrical figure is a combination of points, lines, surfaces or solids in any given relations. Geometrical figures are ideal, i. e., mental conceptions, though none the less real, and can be represented to the eye only by some material substance; for instance, a line may be represented by a mark made by a pencil, crayon, etc. A solid may be represented by a drawing or a block of wood or some material in any given shape. |