Sir Isaac Newto n’s Book II.

208

circle L Y K M, that is, the plane which touches the line A KG HI in K, is inclined to the plane of the earth’s motion ABC;and the angle under B A E is equal to that, in which the planeAEC is inclined to the fame plane. Therefore the inclina-tion of the former plane is less than the inclination of the latter.

27. Suppose now the moon to be advanced to the pointG (in fig. 100.) and in this point to be distant from its nodea quarter part of the whole circle; or in other words, to bein the midway between its two nodes. And in this cafe thenodes will have receded yet more, and the inclination of theorbit be still more diminished : for suppose the line A K G HIto be touched in the point G by a plane pasting through the•earth T : let the intersection of this plane with the plane ofthe earth’s motion be the line W T O, and the line T P its in-tersection with the plane L K M. In this plane let the circleNGO be described with the femidiameter TP or NT cuttingthe other circle LKMin P. Now the line AKGI is convexto the plane L K M, which touches it in K; and therefore theplane NGO, which touches it in G, will intersect the othertouching plane between G and K; that is, the point P will fallbetween those two points, and the plane continued to theplane of the earth’s motion will pass beyond L ; so that thepoints N and O, or the places of the nodes, when the moonis in G, will be farther from A and C than L and M, that is,will have moved farther backward. Besides, die inclinationof the plane NGO to the plane of the earth’s motion ABCis less, than the inclination of the plane I, K M to the fame; forhere also the two arches L P and N P taken together are less

than