_The Science of Dynamics depends upon the three Axioms above stated respecting Cause. The First Axiom,--that every change must have a Cause,--gives rise to the First Law of Motion,--that_ a body not acted upon by a force will move with a uniform velocity in a straight line. _The Second Axiom,--that Causes are measured by their Effects,--gives rise to the Second Law of Motion,--that_ when a force acts upon a body in motion, the effect of the force is compounded with the previously existing motion. _The Third Axiom,--that_ Reaction is equal and opposite to Action,--_gives rise to the Third Law of Motion, which is expressed in the same terms as the Axiom; Action and Reaction being understood to signify momentum gained and lost._ (III. 7.) {15} LIII. _The above Laws of Motion, historically speaking, were established by means of experiment: but since they have been discovered and reduced to their simplest form, they have been considered by many philosophers as self-evident. This result is principally due to the introduction and establishment of terms and definitions, which enable us to express the Laws in a very simple manner._ (III. 7.) LIV. _In the establishment of the Laws of Motion, it happened, in several instances, that Principles were assumed as self-evident which do not now appear evident, but which have since been demonstrated from the simplest and most evident principles. Thus it was assumed that_ a perpetual motion is impossible;--_that_ the velocities of bodies acquired by falling down planes or curves of the same vertical height are equal;--_that_ the actual descent of the center of gravity is equal to its potential ascent. _But we are not hence to suppose that these assumptions were made without ground: for since they really follow from the laws of motion, they were probably, in the minds of the discoverers, the results of undeveloped demonstrations which their sagacity led them to divine._ (III. 7.) LV. _It is a_ Paradox _that Experience should lead us to truths confessedly universal, and apparently necessary, such as the Laws of Motion are. The_ Solution _of this paradox is, that these laws are interpretations of the Axioms of Causation. The axioms are universally and necessarily true, but the right interpretation of the terms which they involve, is learnt by experience. Our Idea of Cause supplies the_ Form, _Experience, the_ Matter, _of these Laws._ (III. 8.) LVI. Primary _Qualities of Bodies are those which we can conceive as directly perceived;_ Secondary _Qualities are those_ {16} _which we conceive as perceived by means of a Medium._ (IV. 1.) LVII. _We necessarily perceive bodies as_ without _us; the Idea of_ Externality _is one of the conditions of perception._ (IV. 1.) LVIII. _We necessarily assume a_ Medium _for the perceptions of Light, Colour, Sound, Heat, Odours, Tastes; and this Medium_ must _convey impressions by means of its mechanical attributes._ (IV. 1.) LIX.