88 INTRODUCTION 



be expressed by the formula mv. Now no new motion 

 can come to any body from itself ; no material body is 

 self-moved, because its essence is pure extension, and the 

 idea of extension does not necessarily involve the trans- 

 ference of parts. To any quantity of matter, whether 

 large or small, motion comes entirely from without. Thus 

 at the creation of the world the whole material universe 

 received a certain fixed quantity of motion, which is con- 

 served by the * ordinary co-operation ' [concours ordinaire] 

 of God. Motion is thus a positive thing and not merely 

 relative to rest. Motion is not opposed to motion, but 

 to rest. Motions do not cancel one another ; they are 

 quantities which can merely be combined and separated. 

 And, on the other hand, each individual portion of matter 

 must remain in the state in which it is, unless it receives 

 motion from outside itself. The motion of any one body 

 is increased only by a corresponding decrease in the motion 

 of some other ; and the motion of any body is decreased 

 only by a part of it passing into some other. Motion is 

 diffused, but never destroyed \ 



1 Cf. Principia, ii. 36 (Veitch's tr.) : ' With respect to the general 

 cause of motion, it seems manifest to me that it is none other than 

 God Himself, who in the beginning created matter along with 

 motion and rest, and now by His ordinary 'concourse' alone pre- 

 serves in the whole the same amount of motion and rest that He 

 then placed in it. For, although motion is nothing in the matter 

 moved but its mode, it has yet a certain and determinate quantity, 

 which we easily understand may remain always the same in the 

 whole universe, although it changes in each of the parts of it. So 

 that, in truth, we may hold when a part of matter is moved with 

 double the quickness of another, and that other is twice the size of 

 the former, that there is just precisely as much motion, but no 

 more, in the less body as in the greater ; and that, in proportion as 

 the motion of any one part is reduced, so is that of some other and 

 equal portion accelerated. We also know that there is perfection 

 in God, not only because He is in Himself immutable, but because 

 He operates in the most constant and immutable manner possible ; 

 so that, with the exception of those mutations which manifest 

 experience or Divine revelation renders certain, and which we per- 

 ceive or believe are brought about without any change in the 

 Creator, we ought to suppose no other in His works, lest there 

 should thence arise ground for concluding inconstancy in God 

 Himself. Whence it follows, as most consonant to reason, that 

 merely because God diversely moved the parts of matter when He 



