Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/313

 in D. Thee by cor. 1. theor. 21. will decribe ellipes having their centres in D, the magnitudes of which ellipes are known by prob. 5.

Let now a third body S attract the two former T and L with the accelerative forces ST, SL, and lee it be attracted again by them. The force ST (by cor. 2. of the laws of motion) is reolved into the forces SD, DT; and the force SL into the forces SD and DL. Now the forces DT, DL, which are as their um TL, and therefore as the accelerative forces with which the bodies T and L attract each other mutually, added to the forces of the bodies T and L, the firt to the firt, and the lat to the lat, compoe forces proportional to the ditances DT and DL as before, but only greater than thoe former forces; and therefore (by cor. 1. prop. 10. and cor. 1. and 8. prop. 4.) they will caue thoe bodies to decribe ellipes as before, but with a wifter motion. The remaining accelerative forces SD and SD, by the motive forces, SD x T and SD x L which are as the bodies, attracting thoe bodies equally, and in the direction of the lines TI, LK parallel to DS, do not at all change their ituations with repect to one another, but caue them equally to approach to the line IK; which mut be imagined drawn through the middle of the body S, and perpendicular to the line DS. But that approach to the line IK will be hindered by cauing the ytem of the bodies T and L on one ide, and the body S on the other with proper velocities to revolve round the common centre of gravity C. With uch a motion the body S, becaue the um of the motive forces SD x T and SD x L is proportional to the ditance CS, tends to the centre C,