346. I have found that one may account for these laws by assuming that the effect is always equal in force to its cause, or, which amounts to the same thing, that the same force is conserved always: but this axiom of higher philosophy cannot be demonstrated geometrically. One may again apply other principles of like nature, for instance the principle that action is always equal to reaction, one which assumes in things a distaste for external change, and cannot be derived either from extension or impenetrability; and that other principle, that a simple movement has the same properties as those which might belong to a compound movement such as would produce [333] the same phenomena of locomotion. These assumptions are very plausible, and are successful as an explanation of the laws of motion: nothing is so appropriate, all the more since they are in accord with each other. But there is to be found in them no absolute necessity, such as may compel us to admit them, in the way one is compelled to admit the rules of logic, of arithmetic and geometry. 347. It seems, when one considers the indifference of matter to motion and to rest, that the largest body at rest could be carried along without any resistance by the smallest body in motion, in which case there would be action without reaction and an effect greater than its cause. There is also no necessity to say of the motion of a ball which runs freely on an even, horizontal plane, with a certain degree of speed, termed A, that this motion must have the properties of that motion which it would have if it were going with lesser speed in a boat, itself moving in the same direction with the residue of the speed, to ensure that the ball, seen from the bank, advance with the same degree A. For, although the same appearance of speed and of direction results through this medium of the boat, it is not because it is the same thing. Nevertheless it happens that the effects of the collision of the balls in the boat, the motion in each one separately combined with that of the boat giving the appearance of that which goes on outside the boat, also give the appearance of the effects that these same balls colliding would have outside the boat. All that is admirable, but one does not see its absolute necessity. A movement on the two sides of the right-angled triangle composes a movement on the hypotenuse; but it does not follow that a ball moving on the hypotenuse must produce the effect of two balls of its own size moving on the two sides: yet that is true. Nothing is so appropriate as this result, and God has chosen the laws that produce it: but one sees no geometrical necessity therein. Yet it is this very lack of necessity which enhances the beauty of the laws that God has chosen, wherein divers admirable axioms exist in conjunction, and it is impossible for one to say which of them is the primary.