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Sir Isaac Newton’s Book II,

the moon in passing from A to I will continually change theplane of her motion. In what manner this change proceeds,

I shall now particularly explain.

1 f . L e t the plane, which touches the line AKI in the pointK (in fig.99.) intersect the plane os the earth’s orbit in the lineL T M. Then, because the line AKI is concave to the plane »A B C, it falls wholly between that plane, and the plane whichtouches it in K; so that the plane MKL will cut the plane AEC,before it meets with the plane of the earth’s motion; supposein 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 semi-circle L Y M. Now to a spectator on the earth the moon, whenin A, will appear to move in the circle A E C F, and, when inK, will appear to be moving in the semicircle L Y M. Theearth’s motion is performed in the plane of this scheme, andto a spectator on the earth the sun will appear always movingin that plane. We may therefore refer the apparent motionof the fun to the circle A B C D, described in this plane aboutthe earth. But the points where this circle, in which thefun seems to move, intersects the circle in which the moonis seen at any time to move, are called the nodes of the moon’sorbit’ at that time. When the moon is seen moving in the cir-cle AEC 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 arethe nodes. Now here it appears, from what has been said,that while the moon has moved from A to K, one of thenodes has been carried from A to L, and the other as muchfrom C to M. But the motion from A to L, and from C to

4> M, is