XXV.
Form or Figure is space limited by boundaries. Space has necessarily three dimensions, length, breadth, depth; and no others which cannot be resolved into these. (ii. 3.)
XXVI.
The Idea of Space is exhibited for scientific purposes, by the Definitions and Axioms of Geometry; such, for instance, as these:—the Definition of a Right Angle, and of a Circle;—the Definition of Parallel Lines, and the Axiom concerning them;—the Axiom that two straight lines cannot inclose a space. These Definitions are necessary, not arbitrary; and the Axioms are needed as well as the Definitions, in order to express the necessary conditions which the Idea of Space imposes. (ii. 4.)
XXVII.
The Definitions and Axioms of Elementary Geometry do not completely exhibit the Idea of Space. In proceeding to the Higher Geometry, we may introduce other additional and independent Axioms; such as that of Archimedes, that a curve line which joins two points is less than any broken line joining the same points and including the curve line. (ii. 4.)
XXVIII.
The perception of a solid object by sight requires that act of mind by which, from figure and shade, we infer distance and position in space. The perception of figure by sight requires that act of mind by which we give an outline to each object. (ii. 6.) 10
XXIX.
The perception of Form by touch is not an impression on the passive sense, but requires an act of our muscular frame by which we become aware of the position of our own limbs. The perceptive faculty involved in this act has been called the muscular sense. (ii. 6.)