[ 446 ] 
ence of f. HT and f. GT to f. GT, HT not lenfibly 
differing from TL. Now FT and TL together 
make a femi- circle, and the fum of FG and GL is 
twice the difference of TL from a quadrant, and the 
difference between FG and GL equal to twice the 
difference of TG from a quadrant, alfo the difference 
between the fines of TL and TG is equal to the 
difference of the verfed fines of the differences of 
thofe arches from quadrants ; and moreover the redt- 
angle under the fines of two arches is equal to the 
reftangle under half the radius, and the difference of 
the verfed fines of the fum and difference of thofe 
arches : therefore the difference of the fines of X and 
of CG will be to the fine of CG as the redfangle 
under the fine of half FG and the fine of half GL to 
the redf angle under half the radius and the fine of 
GT, and in thefe fmall arches the difference of X and 
CG will be to CG nearly as the redlangle under the 
fines of FG and GL to the redlangle under twice 
the radius and the fine of GT, or even twice the 
fquare of the radius, this difference being to be added 
to X, when the moon’s apparent latitude, and that by 
which fhe would appear in the ecliptic, are on the 
fame fide of the ecliptic, otherwife dedudled from X 
for the final corredlion of the apparent latitude. And 
in the laft place this corre(ftion will be always fo fmall 
in quantity, that in computing it CF may be fafely 
fubftituted for GL. 
4. Moreover, the excefs of the moon’s apparent 
diameter, when feen in G, above her apparent diame- 
ter in C, bears a lefs proportion to her horizontal 
diameter than the rcdlangle under the fine of her 
horizontal 
