104 Sir ISAAC NEWTO N’s Book II.

improper they are for accounting for the phænomena whichhave been ascribed to them.

11. Space and time serve to measure each other, recipro-cally, by motion : time is in a perpetual flux and perishing;but a representation of it is preserved in the space described bythe motion. When the space flows as the time, that is, whenequal parts of space are described in any equal parts of the time,then the motion is uniform, and the velocity is constant orunvaried during the motion. When the parts of space, de-scribed in any equal fucceflive parts of the time, continually in-crease, the motion is accelerated ; and when those parts ofspace continually decrease, the motion is retarded. In general,the velocity of motion is always measured by the space thatwould be described by that motion continued uniformly for agiven time. It is obvious that the space, described by an uniformmotion, is in the compound proportion of the time and velocityof the motion : but in general, let ab, {Fig. i.) the base of afigure, represent the time of a motion, and the ordinate orperpendicular pm, at any point p of the base, measure thevelocity at the corresponding term of time, (that is, the spacewhich would be described by the motion continued uniformlyfrom that term for a given time) then the area of the figurea b d so formed will measure the space described by the motion,in the time represented by the base a b. Thus a rectangularparallelogram serves to measure the space described by an uni-form motion, the time being represented by the base, and theconstant velocity os the motion by the perpendicular. Thespace described by a motion which is uniformly accelerated(the velocity of which increases uniformly as the time, that is,receives equal augments in any equal fucceflive parts of time)is represented by a triangle ; the time being represented by

the