body P as the ſquare of the periodical time of the body P directly, and the ſquare of the periodical time of the body T inverſely. And therefore the mean motion of the line of the apſides will be in a given ratio to the mean motion of the nodes; and both thoſe motions will be as the periodical time of the body P directly, and the ſquare of the periodical time of the body T inverſely. The increaſe or diminution of the eccentricity and inclination of the orbit PAB makes no ſenſible variation in the motions of the apſides and nodes, unleſs that increaſe or diminution be very great indeed.
Cor. 17. Since the line LM becomes ſometimes greater and ſometimes leſs than the radius PT, let the mean quantity of the force LM be expreſſed by that radius PT; and then that mean force will be to the mean force SK or SN (which may be alſo expreſſed by ST) as the length PT to the length ST. But the mean force SN or ST, by which the body T is retained in the orbit it deſcribes about S, is to the force with which the body P is retained in its orbit about T, in a ratio compounded of the ratio of the radius ST to the radius PT and the duplicate ratio of the periodical time of the body P about T, to the periodical time of the body T about S. And ex æquo, the mean force LM is to the force by which the body P is retained in its orbit about T (or by which the ſame body P might revolve at the diſtance PT in the ſame periodical time about any immovable point T) in the ſame duplicate ratio of the periodical times. The periodical times therefore being given, together with the diſtance PT; the mean force LM is alſo given; and that force being given; there is given alſo the force MN
