C 438 ] 
by v.'bichmaybe determined with fufficlcnt exadlnefs 
the moon’s apparent latitude, not only in ecliples, but 
in all diftances of the moon from the ecliptic. 
But to thefe proportions I fliall here premife the 
method I have generally uled for computing the 
nonagefime degree, and its diifance from the zenith ; 
this form of calculation not being encumbered with 
any diverfity from the difference of cafes. 
L E M M A. 
To find the nonagefime, or 90th degree of the 
ecliptic from the horizon, and its diifance from the 
zenith, the latitude of the place, and the point of the 
equinodial on the meridian being given. 
In Tab. XV. Fig. i. 2. 3. 4. let A B be the equi- 
nodial, A C the ecliptic, D the zenith, D E the meri- 
dian, and D F perpendicular to the ecliptic, whereby F 
is the nonagefime degree, and DF the diifance of that 
point from the zenith. Then from D E, the latitude 
of the place, and AE the difcance of the meridian 
from Aries, the arch of the ecliptic AF, and the 
perpendicular D F may be thus found. 
Let I be the pole of the equinodial, and H the 
pole of the ecliptic. Then A E augmented by 90® 
is the meafure of the angle D I H, or of its comple- 
ment to four right angles : And the Iquare of the ra- 
dius is to the redangle under the lines D I, I H, as the 
fquare of the fine of half the angle D I H, or of half 
its complement to four right angles, to the redangle 
under the radius, and half the excels of the cofine of 
the difference between D I and 1 H, above the cofine 
of D H, or the fine of D F. 
4 
In 
