In like manner geometry, as its name indicates, arises from primitive perceptions of space, applied to the practical necessity of land-measuring in alluvial valleys like those of the Nile and Euphrates, where annual inundations obliterated to a great extent the dividing lines between adjoining properties. The first perceptions of space would take the form of the rectangle, or so many feet or paces, or cubits or arm-lengths, forwards, and so many sideways, to give the proper area; but as areas were irregular, it would be discovered that the triangle was necessary for more accurate measurement. Hence the science of the triangle, circle, and other regular forms, as we see it developed in Euclid and later treatises on geometry, until we see it in its latest development in speculations as to space of four dimensions. But in all these cases we see the same fundamental principle as prevails throughout the universe under the name of the ‘conservation of energy’; always something out of something, never something out of nothing. This, therefore, defines the limit of human knowledge, or boundary line between the knowable and the unknowable. Whatever is _transformation_ according to existing laws is, whether known or unknown, at any rate, knowable—whatever is _creation_ is unknowable. We have absolutely no faculties to enable us to form the remotest conception of what the essence of these primary atoms and energies really is, how they came there, and how the laws, or invariable sequences, under which they act, came to be impressed on them. We have no faculties, because we have never had any perceptions upon which the mind can work. Reason and imagination can no more work without antecedent perceptions than a bird can fly in a vacuum. Thus, for instance, the imagination can invent dragons, centaurs, and any number of fabulous monsters, by piecing together fragments of perceptions in new combinations; but ask it to invent a monster whose head shall be that of an inhabitant of Saturn and its body that of a denizen of Jupiter, and where is it? Of necessity all attempts to define or describe things of which we have never had perceptions, must be made in terms of things of which we have had perceptions, or, in other words, must be anthropomorphic.