well as of power of mathematical generalization[29\3]. And {249} thus we have here another example of that circumstance which we have already noticed in speaking of the First Law of Motion, (Art. 2 of this chapter,) and of the Law that Gravity is a uniform Force, (Art. 3); namely, that the law, though historically established by experiments, appears, when once discovered and reduced to its most simple and general form, to be self-evident. I am the more desirous of drawing attention to this feature in various portions of the history of science, inasmuch as it will be found to lead to some very extensive and important views, hereafter to be considered. [Note 29\3: I may observe that the rule that we may _compound_ motions, as the Law supposes, is involved in the step of _resolving_ them; which is done in the passage to which I refer. (_Méc. Analyt._ ptie. i. sect. i. art. 3. p. 225.) 'Si on conçoit que le mouvement d'un corps et les forces qui le sollicitent soient _decomposées_ suivant trois lignes droites perpendiculaires entre elles, on pourra considérer séparément les mouvemens et les forces relatives à chacun de ces trois directions. Car à cause de la perpendicularité des directions il est visible que chacun de ces mouvemens partiels peut être regardé comme indépendant des deux autres, et qu'il ne peut recevoir d'altération que de la part de la force qui agit dans la direction de ce mouvement; l'on peut conclure que ces trois mouvemens doivent suivre, chacun en particulier, les lois des mouvemens rectilignes accélérés ou retardés par les forces données.' Laplace makes the same assumption in effect, (_Méc. Cél._ p. i. liv. i. art. 7), by resolving the forces which act upon a point in three rectangular directions, and reasoning separately concerning each direction. But in his mode of treating the subject is involved a principle which belongs to the Third Law of Motion, namely, the doctrine that the velocity is as the force, of which we shall have to speak elsewhere.]