25. LET the plane, which touches the line A K I in the point K (in fig. 99.) intersect the plane of the earth’s orbit in the line L T M. Then, because the line A K I is concave to the plane A B C, it falls wholly between that plane, and the plane which touches it in K; so that the plane M K L will cut the plane A E C, before it meets with the plane of the earth’s motion; suppose in the line Y T, and the point A will fall between K and L. With a semidiameter equal to T Y or T L describe the semicircle L Y M. Now to a spectator on the earth the moon, when in A, will appear to move in the circle A E C F, and, when in K, will appear to be moving in the semicircle L Y M. The earth’s motion is performed in the plane of this scheme, and to a spectator on the earth the sun will appear always moving in that plane. We may therefore refer the apparent motion of the sun to the circle A B C D, described in this plane about the earth. But the points where this circle, in which the sun seems to move, intersects the circle in which the moon is seen at any time to move, are called the nodes of the moon’s orbit at that time. When the moon is seen moving in the circle A E C D, the points A and C are the nodes of the orbit; when she appears in the semicircle L Y M, then L and M are the nodes. Now here it appears, from what has been said, that while the moon has moved from A to K, one of the nodes has been carried from A to L, and the other as much from C to M. But the motion from A to L, and from C to M, is backward in regard to the motion of the moon, which is the other way from A to K, and from thence toward C.