Force is primary and derivative. The primary is generated by abundance or scarcity, that is, by the increase or diminution of its cause, as with the multiplication of the air that is born from the dissolution of the clouds, which makes the wind that bends the plants and puts them in force. Again, in the muscles or sinews of animals, which the vital spirits, thickening, shorten, and draw their limbs along with them, giving to those limbs so much more power than their own weight as the power of the created force surpasses the resistance of the weight of such limbs. That is, if the created force be 10, and the ordinary weight of the member in which it arises be one, that born force surpasses by 9, and it will be exactly consumed when to such a member there is added 9, and the one that the member weighed, which makes 10. Whence it is clearly shown that 10 of power against 10 of resistance consume one another, because neither more power nor more resistance is to be found.

The derivative force is that which is born from the motion of the aforesaid primary, and in the same time in which the primary is born. The derivative can never surpass it, but it may well reach its equality. But it may indeed be made of so much greater power when, with equal motion to the primitive, the derivative is prolonged with length of time; so that the power of the derivative force will bear to the power of its primary such proportion as the times have in which the primary generates the derivative. That is, if the primary is born in one degree of time and takes 2 times to make the derivative, that derivative force will be of double power to the primary, and so successively the derivative grows together with the time in which the primary brings it forth.

When the primary force is of equal motion to the derivative, it will also be of equal power. But if the motion of the primitive be less than the derivative, those forces will have between them such proportion as was that of the length of their motions.

That motion of the primary or derivative force which is the longer will be proportionally the stronger.

When the wheel d makes one whole turn, the wheel c makes 10 of them, and the wheel b makes 100, and so the wheel a makes 1000. Whence, conversely, the force is exchanged, as was said in the 2nd of the sixth above: that where the motion is greater, there it is greater.

100 100 100 100, 10 10 10 10 10, 1000 100 10 1, a b c d, 1 1000

Between the primary force and the derivative there will be such proportion as will be that of the length and speed of their motions.