15. THE moon in passing from the opposition B to the next quarter will be retarded again by the same degrees, as it is accelerated before its appulse to the opposition. Because this action of the sun, which in the moon’s passage from the quarter to the opposition causes it to be extraordinarily accelerated, and diminishes the angle, which measures its distance from the opposition; will make the moon slacken its pace afterwards, and retard the augmentation of the same angle in its passage from the opposition to the following quarter; that is, will prevent that angle from increasing so fast, as otherwise it would. And thus the moon, by the sun’s action upon it, is twice accelerated and twice restored to its first velocity, every circuit it makes round the earth. This inequality of the moon’s motion about the earth is called by astronomers its variation.
16. THE next effect of the sun upon the moon is, that it gives the orbit of the moon in the quarters a greater degree of curvature, than it would receive from the action of the earth alone; and on the contrary in the conjunction and opposition the orbit is less inflected.
17. WHEN the moon is in conjunction with the sun in the point D, the sun attracting the moon more forcibly than it does the earth, the moon by that means is impelled less toward the earth, than otherwise it would be, and so the orbit is less incurvated; for the power, by which the moon is impelled toward the earth, being that, by which it is inflected from a rectilinear course, the less that power is, the less it will be inflected. Again, when the moon is in the opposition in B, farther removed from the sun than the earth is; it follows then, though the earth and moon are both continually descending to the sun, that is, are drawn by the sun toward it self out of the place they would otherwise move into, yet the moon descends with less velocity than the earth; insomuch that the moon in any given space of time from its passing the point of opposition will have less approached the earth, than otherwise it would have done, that is, its orbit in respect of the earth will approach nearer to a straight line. In the last place, when the moon is in the quarter in F, and equally distant from the sun as the earth, we observed before, that the earth and moon would descend with equal pace toward the sun, so as to make no change by that descent in the angle under F A S; but the length of the line F A must of necessity be shortned. Therefore the moon in moving from F toward the conjunction with the sun will be impelled more toward the earth by the sun’s action, than it would have been by the earth alone, if neither the earth nor moon had been acted on by the sun; so that by this additional impulse the orbit is rendred more curve, than it would otherwise be. The same effect will also be produced in the other quarter.