SirlsAAc Newton's Book I.

change the velocity of their motion: therefore this first lawof motion has been illustrated and confirmed, as much as.canbe from the transient observations, which have here been dis-coursed upon; and in the next chapter all this will be fartherestablished by more correct observations.

15*. But I shall now pass to the second law of motion jwherein, when it is asserted, that the velocity, with whichany body is moved by the action of a power upon it, is pro-portional to that power; the degree of power is supposed tobe measured by the greatness of the body, which it can movewith a given celerity. So that the sense of this law is, thatif any body were put into motion with that degree of swift-ness, as to pass in one hour the length of a thousand yards ;the power, which would give the fame degree of velocity toa body twice as great, would give this lesser body twice thevelocity, causing it to describe in the fame space of an hourtwo thousand yards. But by a body twice as great as another,I do not here mean simply of twice the bulk, but one thatcontains a double quantity of solid matter.

16. Why the power, which can move a body twice as greatas another with the fame degree of velocity, should be calledtwice as great as the power, which can give the lesser bodythe fame velocity, is evident. For if we should suppose thegreater body to be divided into two equal parts, each equalto the lesser body, each of these halves will require the famedegree of power to move them with the velocity of the lesierbody, as the lesser body it self requires; and therefore both

5* those