Chap. 3. PHILOSOPHY. 207

M, is backward in regard to the motion of the moon, whichis the other way from A to K, and from thence toward C

1 6 . Farther the angle, which the plane, wherein themoon at any time appears, makes with the plane of the earth’s-motion, is called the inclination of the moon’s orbit at thattime. And I fhall now proceed to fhew, that this inclina-tion of the orbit, when the moon is in K, is lefs than whenfhe was in A ; or, that the plane LYM, which touches the'line of the moon’s motion in K, makes a lefs angle with theplane of the earth’s motion or with the circle A B C D, thanthe plane AEC makes with the fame. The femicircle LYMinterfedts the femicircle A E C in Y; and the arch A Y is lefsthan L Y, and both together lefs than half a circle. But it is de-monftrated by the writers on that part of aftronomy, which iscalled the dodtrine of the fphere, that when a triangle is made,as here, by three arches of circles A L, AY, and Y L, the angletinder YAB without the triangle is greater than the angle underYlA within, if the two arches A Y, YL taken together donot amount to a femicircle ; if the two arches make a com-plete femicircle, the two angles will be equal; but if the twoarches taken together exceed a femicircle, the inner angle un-der YL A is greater than the other \ Here therefore the two'arches A Y and L Y together being lefs than a femicircle, theangle under ALY is lefs, than the angle under B AE. Butfrom the dodtrine of the fphere it is alfo evident, that the amSic under A L Y is equal to that, in which the plane of the

* Menelai Sphaeric. Lib. I. prop. 1 o.

circle