_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.) XXX. _The_ Idea of Time _is not derived from experience, for experience of changes_ pre_supposes occurrences to take place in Time. Time is a condition under which the mind receives the impressions of sense, and therefore the relations of time are necessarily and universally true of all perceived occurrences. Time is a_ form _of our perceptions, and regulates them, whatever the_ matter _of them may be._ (II. 7.) XXXI. _Time is not a General Notion collected by abstraction from particular cases. For we do not speak of particular_ Times _as examples of time in general, but as parts of a single and infinite_ Time. (II. 8.) XXXII. _Time, like Space, is a form, not only of perception, but of_ Intuition. _We consider the whole of any time as_ equal _to the_ sum _of the parts; and an occurrence as_ coinciding _with the portion of time which it occupies._ (II. 8.) XXXIII. _Time is analogous to Space of_ one dimension: _portions of both have a beginning and an end, are long or short. There is nothing in Time which is analogous to Space of two, or of three, dimensions, and thus nothing which corresponds to Figure._ (II. 8.) XXXIV. _The Repetition of a set of occurrences, as, for example, strong and weak, or long and short sounds, according to a_ {11} _steadfast order, produces_ Rhythm, _which is a conception peculiar to Time, as Figure is to Space._ (II. 8.) XXXV. _The simplest form of Repetition is that in which there is no variety, and thus gives rise to the conception of_ Number. (II. 8.) XXXVI. _The simplest numerical truths are seen by Intuition; when we endeavour to deduce the more complex from these simplest, we employ such maxims as these_:--If equals be added to equals the wholes are equal:--If equals be subtracted from equals the remainders are equal:--The whole is equal to the sum of all its parts. (II. 9.) XXXVII.