Sir Isaac New to n’s Book IL

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circle LYKM, 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 planeA E C is inclined to the fame plane. Therefore the inclina-don of the former plane is lefs than the inclination of the latter.

17. Suppose now the moon to be advanced to the pointG (in fig. 100.) and in this point to be diftant 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 ftill more diminifhed : for fuppofe the line AKGHlto ,be touched in the point G by a plane pafling through theearth T : let the interfedion of this plane with the plane ofthe earth’s motion be the line WTO, and the line TP its in-terfedion with the plane L K M. In this plane let the circleNGO be defcribed with the femidiameter TP or NT cuttingthe other circle LKM in P. Now the line AKGI is convex„to the plane LKM, which touches it in K; and therefore theplane N G O, which touches it in G, will interfed the othertouching plane between G and K; that is, the point P will fillbetween thofe two points, and die plane continued to theplane of the earth’s motion will pafs beyond L; fo 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. Befides, the inclinationof the plane NGO to the plane of the earth’s motion ABCis lefs, than the inclination of the plane L K M to the fame; forhere alfo the two arches LP and NP taken together are lefs

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