26. FARTHER the angle, which the plane, wherein the moon at any time appears, makes with the plane of the earth’s motion, is called the inclination of the moon’s orbit at that time. And I shall now proceed to shew, that this inclination of the orbit, when the moon is in K, is less than when she was in A; or, that the plane L Y M, which touches the line of the moon’s motion in K, makes a less angle with the plane of the earth’s motion or with the circle A B C D, than the plane A E C makes with the same. The semicircle L Y M intersects the semicircle A E C in Y; and the arch A Y is less than L Y, and both together less than half a circle. But it is demonstrated by the writers on that part of astronomy, which is called the doctrine of the sphere, that when a triangle is made, as here, by three arches of circles A L, A Y, and Y L, the angle under Y A B without the triangle is greater than the angle under Y L A within, if the two arches A Y, Y L taken together do not amount to a semicircle; if the two arches make a complete semicircle, the two angles will be equal; but if the two arches taken together exceed a semicircle, the inner angle under Y L A is greater than the other[189]. Here therefore the two arches A Y and L Y together being less than a semicircle, the angle under A L Y is less, than the angle under B A E. But from the doctrine of the sphere it is also evident, that the angle under A L Y is equal to that, in which the plane of the circle L Y K M, that is, the plane which touches the line A K G H I in K, is inclined to the plane of the earth’s motion A B C; and the angle under B A E is equal to that, in which the plane A E C is inclined to the same plane. Therefore the inclination of the former plane is less than the inclination of the latter.