_The Fundamental Ideas which it is most important to consider, as being the Bases of the Material Sciences, are the Ideas of_ Space, Time (_including Number_), Cause (_including Force and Matter_), Outness _of Objects, and_ Media _of Perception of Secondary Qualities,_ Polarity (_Contrariety_), {8} _Chemical_ Composition _and_ Affinity, Substance, Likeness _and Natural_ Affinity, Means and Ends (_whence the Notion of Organization_), Symmetry, _and the Ideas of_ Vital Powers. (I. 8.) XIX. _The Sciences which depend upon the Ideas of Space and Number are_ Pure _Sciences, not_ Inductive _Sciences: they do not infer special Theories from Facts, but deduce the conditions of all theory from Ideas. The Elementary Pure Sciences, or Elementary Mathematics, are Geometry, Theoretical Arithmetic and Algebra._ (II. 1.) XX. _The Ideas on which the Pure Sciences depend, are those of_ Space _and_ Number; _but Number is a modification of the conception of Repetition, which belongs to the Idea of_ Time. (II. 1.) XXI. _The_ Idea of Space _is not derived from experience, for experience of external objects_ pre_supposes bodies to exist in Space, Space is a condition under which the mind receives the impressions of sense, and therefore the relations of space are necessarily and universally true of all perceived objects. Space is a_ form _of our perceptions, and regulates them, whatever the_ matter _of them may be._ (II. 2.) XXII. _Space is not a General Notion collected by abstraction from particular cases; for we do not speak of_ Spaces _in general, but of universal or absolute_ Space. _Absolute Space is infinite. All special spaces are_ in _absolute space, and are parts of it._ (II. 3.) XXIII. _Space is not a real object or thing, distinct from the objects which exist in it; but it is a real condition of the existence of external objects._ (II. 3.) {9} XXIV. _We have an_ Intuition _of objects in space; that is, we contemplate objects as_ made up _of spatial parts, and apprehend their spatial relations by the same act by which we apprehend the objects themselves._ (II. 3.) 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.