6. Space has three dimensions, or directions in which it may be measured; it cannot have more or fewer. The simplest measurement is that of a straight line, which has length alone. A surface has both length and breadth: and solid space has length, breadth, and thickness or depth. The origin of such a difference of dimensions will be seen if we reflect that each portion of space has a boundary, and is extended both _in_ the direction in which its boundary extends, and also in a direction _from_ its boundary; for otherwise it would not be a boundary. A point has no dimensions. A line has but one dimension,--the distance from its boundary, or its _length_. A plane, bounded by a straight line, has the dimension which belongs to this line, and also has another dimension arising from the distance of its parts from this boundary line; and this may be called _breadth_. A solid, bounded by a plane, has the dimensions which this plane has; and has also a third dimension, which we may call _height_ or _depth_, as we consider the solid extended above or below the plane; or _thickness_, if we omit all consideration of up and down. And no space can have any dimensions which are not resoluble into these three. We may now proceed to consider the mode in which the idea of space is employed in the formation of Geometry. {{98}} CHAPTER IV. OF THE DEFINITIONS AND AXIOMS WHICH RELATE TO SPACE. 1. THE relations of space have been apprehended with peculiar distinctness and clearness from the very first unfolding of man's speculative powers. This was a consequence of the circumstance which we have just noticed, that the simplest of these relations, and those on which the others depend, are seen by intuition. Hence, as soon as men were led to speculate concerning the relations of space, they assumed just principles, and obtained true results. It is said that the science of _geometry_ had its origin in Egypt, before the dawn of the Greek philosophy: but the knowledge of the early Egyptians (exclusive of their mythology) appears to have been purely practical; and, probably, their geometry consisted only in some maxims of _land-measuring_, which is what the term implies. The Greeks of the time of Plato, had, however, not only possessed themselves of many of the most remarkable elementary theorems of the science; but had, in several instances, reached the boundary of the science in its elementary form; as when they proposed to themselves the problems of doubling the cube and squaring the circle.