through the arc _BD_ to the height of the horizontal _CD_. Now gentlemen, you will be pleased to see the ball rise to the horizontal line at the point _G_, and the same thing also happen if the nail be placed lower as at _F_, in which case the ball would describe the arc _BJ_, always terminating its ascent precisely at the line _CD_. If the nail be placed so low that the length of thread below it does not reach to the height of _CD_ (which would happen if _F_ were nearer _B_ than to the intersection of _AB_ with the horizontal _CD_), then the thread will wind itself about the nail. This experiment leaves no room for doubt as to the truth of the supposition. For as the two arcs _CB_, _DB_ are equal and similarly situated, the momentum acquired in the descent of the arc _CB_ is the same as that acquired in the descent of the arc _DB_; but the momentum acquired at _B_ by the descent through the arc _CB_ is capable of driving up the same moving body through the arc _BD_; hence also the momentum acquired in the descent _DB_ is equal to that which drives the same moving body through the same arc from _B_ to _D_, so that in general every momentum acquired in the descent of an arc is equal to that which causes the same moving body to ascend through the same arc; but all the momenta which cause the ascent of all the arcs _BD_, _BG_, _BJ_, are equal since they are made by the same momentum acquired in the descent _CB_, as the experiment shows: therefore all the momenta acquired in the descent of the arcs _DB_, _GB_, _JB_ are equal." [Illustration: Fig. 43.] The remark relative to the pendulum may be applied to the inclined plane and leads to the law of inertia. We read on page 124:[45] "It is plain now that a movable body, starting from rest at _A_ and descending down the inclined plane _AB_, acquires a velocity proportional to the increment of its time: the velocity possessed at _B_ is the greatest of the velocities acquired, and by its nature immutably impressed, provided all causes of new acceleration or retardation are taken away: I say acceleration, having in view its possible further progress along the plane extended; retardation, in view of the possibility of its being reversed and made to mount the ascending plane _BC_. But in the horizontal plane _GH_ its equable motion, according to its velocity as acquired in the descent from _A_ to _B_, will be continued _ad infinitum_." (Fig. 44.) [Illustration: Fig. 44.]