APPENDIX I 353 



were recognized only mathematical notions, magnitude, figure, 

 place, and their changes or their tendency [conatus] to change 

 at the very moment of impact, and no account were taken of 

 metaphysical notions, namely, of moving power [potentia] in 

 the form, and of inertia (or resistance to motion) in the matter 

 [of the body], and if it were thus necessary that the result of 

 the impact should be determined by a purely geometrical 

 composition of forces [conatus], as we have explained: then 

 it ought to follow that the impulse of the impinging body, 

 however small that body may be, is communicated to the whole 

 of the body impinged upon, however large it may be, and thus 

 the very largest body at rest is moved away by an impinging 

 body, however small, without any retarding of the latter, since 

 matter, thus understood, is not repugnant but rather indifferent 

 to motion. Hence it would not be more difficult to move ^ 

 a large body at rest than a small one, and therefore there >w 

 would be action without reaction, and no estimate of power ) 

 could be made, since anything might be accomplished by / 

 anything. . . . But afterwards, having considered the whole / 

 matter more profoundly, I saw in what the systematic explana- x. . 

 tion of things ' [i. e. the explanation of things as they actually ^ 

 are] ' should consist, and I observed that my former hypothesis 

 regarding the nature of body was not complete, and that this 

 as well as other arguments proved that body must be regarded 

 as having, in addition to magnitude and impenetrability, 

 something from which arises the consideration of forces [vires], 

 the metaphysical laws of which, when combined with the laws 

 of extension, give rise to those very laws of motion which I had 

 called systematic. . . .' Specimen Dynamicum, &c. (1695) (G. 

 Math. vi. 240). ' I am of opinion that the mechanical principles 

 and reasons of the laws of motion do themselves arise not from 

 the necessity of matter, but from some higher principle than 

 imagination, and one independent of mathematics. . . . Besides 

 I began to have considerable doubts as to the nature of motion. 

 For when formerly I regarded space as an immovable real 

 place, possessing extension alone, I had been able to define 

 absolute motion as change of this real space. But gradually 

 I began to doubt whether there is in nature such an entity 

 as is called space ;> whence it followed that a doubt might 

 arise about absolute motion. Certainly Aristotle had said 

 that place is notl> : ng but the surface of what surrounds us 



A a 



