OP UNDISTURBED MOTION. . 65 



have been equally decreased in one instance, and the rela- 

 tions remaining the same, they will still be equally de- 

 creased(217) : the relative motion of A and B being equal 

 to that of B and G, and any absolute motion being no way 

 determinable, there can be no reason why the one should 

 be otherwise affected than the other ; therefore CE will be 

 twice DF : and a similar mode of reasoning may be ex- 

 tended to all other cases, where the proportion of the mo- 

 tions is less simple. 



Scholium 1. Having established the permanency of 

 the rectilinear direction of undisturbed motion, we come 

 to consider its uniformity. Here the idea of time enters 

 into our subject; and we must have some measure of 

 equal times, which cannot be merely intellectual, and must 

 therefore be estimated by some changes in external ob- 

 jects. Of these changes, the simplest aud most convenient 

 is the apparent motion of the sun, or rather of the stars, 

 derived from the actual rotation of the earth on its axis, 

 which is not, indeed, an undisturbed rectilinear motion, 

 but which is equally applicable to every practical purpose: 

 and hence we obtain, by astronomical observations, the 

 well known measures of the duration of time, implied by 

 the terms day, hour, minute, and second. 



Scholium 2. Now, the equality of times being thus 

 estimated from any one motion, all other bodies, moving 

 without disturbance, will describe equal successive parts 

 of their lines of direction in equal times. And this is the 

 second law of motion, which, with the former law, con- 

 stitutes Newton's first axiom or law of motion; ** that 

 every body perseveres in its state of rest or uniform rectili- 

 near motion, except so far as it is compelled by some force 

 to change it." This second law appears to be strictly 

 dcducible from the axioms and definitions which have been 



F 



