36. AGAIN, when the moon is come to the point K in its quarter, the nodes will be advanced yet farther forward, and the inclination of the orbit also more augmented. Hitherto the moon’s motion has been referred to the plane, which passing through the earth touches the path of the moon in the point, where the moon is, according to what was asserted at the beginning of this discourse upon the nodes, that it is the custom of astronomers so to do. But here in the point K no such plane can be found; on the contrary, seeing the line of the moon’s motion on one side the point K is convex to the plane B E D, and on the other side concave to the same, no plane can pass through the points T and K but will cut the line B K L in that point. Therefore instead of such a touching plane, we must here make use of what is equivalent, the plane P K Q, with which the line B K L shall make a less angle than with any other plane; for this plane does as it were touch the line B K in the point K, since it so cuts it, that no other plane can be drawn so, as to pass between the line B K and the plane P K Q. But now it is evident, that the point P, or the node, is removed from M towards G, that is, has moved yet farther forward; and it is likewise as manifest, that the angle under K P G, or the inclination of the moon’s orbit in the point K, is greater than the angle under I M G, for the reason so often assigned. 37. AFTER the moon has passed the quarter, the path of the moon being concave to the plane A G C H, the nodes, as in the preceding case, shall recede, till the moon arrives at the point L; which shews, that considering the whole time of the moon’s passing from B to L, at the end of that time the nodes shall be found to have receded, or to be placed backwarder, when the moon is in L, than when it was in B. For the moon takes a longer time in passing from K to L, than in passing from B to K; and therefore the nodes continue to recede a longer time, than they moved forwards; so that their recess must surmount their advance. 38. IN the same manner, while the moon is in its passage from K to L, the inclination of the orbit shall diminish, till the moon comes to the point, in which it is one quarter part of a circle distant from its node; suppose in the point R; and from that time the inclination shall again increase. Since therefore the inclination of the orbit increases, while the moon is passing from B to K, and diminishes itself again only, while the moon is passing from K to R, and then augments again, till the moon arrive in L; while the moon is passing from B to L, the inclination of the orbit is much more increased than diminished, and will be distinguishably greater, when the moon is come to L, than when it set out from B.