C 419 ] 
the plane of the lunar orbit, the plane PCI 9 being 
perpendicular to that plane, P C l a being the axe 
thereof. 
Letting fall from the point R the perpendicular 
R M upon the line s P Z, the motion of the pole 
of the earth according to P R may be refolved into 
two - y the one according to P M } the other parallel 
and equal to R M ; and this latter exprefies the pre- 
cefiion with regard to the ecliptic, and the former 
gives the alteration of the inclination of the earth’s axe 
to the plane of the ecliptic. 
The motion of the pole reprefented by M R , which 
gives the preceffion with regard to the ecliptic, is al- 
ways on the fame fide during the entire revolution of 
the pole of the lunar orbit, and is the fame on either 
fide the point / at the like diftance from it • the motion 
according to PR being then the fame, and always on 
the fame fide, as has been explained in Prob. V. 
* The motion according to P M is the fame on 
either fide of the point / at the fame diftance from it, 
but with a contrary fign, that is, in an oppofite di- 
rection. For it is manifefi:, that if another point, as 
/°, be taken on the other fide, and at an equal diftance 
from the point /, the point M , where the perpendi- 
cular R M falls, will be on the other fide with regard 
to P , than the point iff, fince the angle R P Z\ 
which is here obtufe, will then be acute, and lef$ 
than the right angle of an angle equal to L° P Z' , 
* The point 1° placed on the other fide of the point /, that is, 
between / and P, is not marked in the fig. nor the point M‘ where 
the perpendicular K AT falls; for the fake of not embarraflingthe 
fg, with too many lines, it being eafy to conceive. 
G cr 2 
? 5 ? ■ 
For 
