in D. Theſe by cor. 1. theor. 21. will deſcribe ellipſes having their centres in D, the magnitudes of which ellipſes 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 reſolved into the forces SD, DT; and the force SL into the forces SD and DL. Now the forces DT, DL, which are as their ſum 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 firſt to the firſt, and the laſt to the laſt, compoſe forces proportional to the diſtances DT and DL as before, but only greater than thoſe former forces; and therefore (by cor. 1. prop. 10. and cor. 1. and 8. prop. 4.) they will cauſe thoſe bodies to deſcribe ellipſes as before, but with a ſwifter 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 thoſe bodies equally, and in the direction of the lines TI, LK parallel to DS, do not at all change their ſituations with reſpect to one another, but cauſe them equally to approach to the line IK; which muſt 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 cauſing the ſyſtem of the bodies T and L on one ſide, and the body S on the other with proper velocities to revolve round the common centre of gravity C. With ſuch a motion the body S, becauſe the ſum of the motive forces SD x T and SD x L is proportional to the diſtance CS, tends to the centre C,
