Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/65

Rh are equally changed, the changes of the velocities made towards contrary parts are reciprocally proportional to the bodies. This law takes place alo in Attractions, as will be proved in the next Scholium.



If a body in a given time, by the force M impreed apart in the place A, hould with an uniform motion be carried from A to B; and by the force N impreed apart in the ame place, hould be carried from A to C; complete the parallelogram ABCD, and, by both forces acting together, it will in the ame time be carried in the diagonal from A to D. For ince the force N acts in the direction of the line AC, parallel to BD, this force (by the econd law) will not at all alter the velocity generated by the other force M, by which the body is carried towards the line BD. The body therefore will arrive at the line BD in the ame time, whether the force N be impreed or not; and therefore at the end of that time it will be found omewhere in the line BD. By the ame argument, at the end of the ame time it will be found omewhere in the line CD. Therefore it will be found in the point D, where both lines meet. But it will move in a right line from A to D, by Law I. Rh