every ſide by ſeveral bodies S, S, S, &c. diſpoſed about the orbit ESE. For by the actions of theſe bodies the action of the body T will be diminiſhed on every ſide, and decreaſe in more than a duplicate ratio of the diſtance.
Cor. 8. But ſince the progreſs or regreſs of the apſides depends upon the decreaſe of the centripetal force, that is, upon its being in a greater or leſs ratio than the duplicate ratio of the diſtance TP, in the paſſage of the body from the lower apſis to the upper; and upon a like increaſe in its return to the lower apſis again; and therefore becomes greateſt where the proportion of the force at the upper apſis to the force at the lower apſis recedes fartheſt from the duplicate ratio of the diſtances inverſely; it is plain that when the apſides are in the ſyzygies, they will, by reaſon of the ſubducting force KL or NM - LM, go forward more ſwiftly; and in the quadratures by the additional force LM go backward more ſlowly. When the velocity of the progreſs or ſlowneſs of the regreſs is continued for a long time, this inequality becomes exceeding great.
Cor. 9. If a body is obliged, by a force reciprocally proportional to the ſquare of its diſtance from any centre, to revolve in an ellipſis round that centre; and afterwards in its deſcent from the upper apſis to the lower apſis, that force by a perpetual acceſſion of new force is increaſed more than a duplicate ratio of the diminiſhed diſtance; it is manifeſt that the body being impelled always towards the centre by the perpetual acceſſion of this new force, will incline more towards that centre than if it were urged by that force alone which decreaſes in a duplicate ratio of the
