Mechanical Science depends on the Conception of Force; and is divided into 'Statics', the doctrine of Force preventing motion, and 'Dynamics', the doctrine of Force producing motion.
The Idea of Cause is expressed for purposes of science by these three Axioms:-'Every Event must have a Cause':-'Causes are measured by their Effects':-'Reaction is equal and opposite to Action'.
Among the foundations of the Higher Mathematics is also the 'Idea of a Limit'. The Idea of a Limit cannot be superseded by any other definitions or Hypotheses.
'Intuitive' is opposed to 'discursive' reason. In intuition, we obtain our conclusions by dwelling upon 'one' aspect of the fundamental Idea; in discursive reasoning, we combine several aspects of the Idea
The Perception of Time involves a constant and latent kind of memory, which may be termed a 'Sense of Succession'. The Perception of Number also involves this Sense of Succession, although in small numbers we appear to apprehend the units simultaneously and not successively.
'Form' or 'figure' is space limited by boundaries. Space has necessarily 'three' dimensions, length, breadth, depth; and no ethers which cannot be resolved into these.
In order to acquire any exact and solid knowledge, the student must possess with perfect precision the ideas appropriate to that part of knowledge: and this precision is tested by the student's 'perceiving' the axiomatic evidence of the 'axioms' belonging to each 'Fundamental Idea'.
