{[ 444* J 
Hie ecliptic under the fame apparent longitude, to the 
fine of the correfponding apparent dlftancca 
Fig. 6 . When the moon appears out of the eclip- 
tic in G, the four great circles CZ, GZ, CT, FT, in- 
terfecfling each other as before, the ratio of f. CZ to f.. 
ZE will be compounded of the ratio of f. CG to fi 
EHj or of CG to EH in thefe fmali arches, and of 
the ratio of f. HT to f. GT, which lafi ratio, when 
the latitude is fmali, and HT near a quadrant, is 
nearly the ratio of equality. Now in the triangle 
EKH the arch EH exceeds the difference of KE and 
KH, that is, the difference of the latitudes, when both 
the latitudes are on the fame fide of the ecliptic, and 
their fum, v/hen the latitudes are on. the oppofite fide?.. 
But here the excels will be inconfideraWe. There- 
fore if an arch X, be taken, wlpfe fine lhall be to the 
fine of the difference, or fum of the latitudeSj^ as f. 
ZC to f. ZE, X flaall be nearly equal to CG, the ap- . 
pjirent latitude in Gi 
COROLLARIES, 
1. If the arches DE, BZ be continued to K, the- 
pole of rile ecliptic, the four great circles CB, CZ> 
DK, BK, will interfecf each other, and f. .BD will 
be to the fine of BC" in the ratio compounded of the 
ratio of f. ZE to f. ZC, and of f. DIG to f. EX, the 
kaft of which ratios, the arch DE being fmali, and 
DK a quadrant, is nearly, the ratio of equality : 
therefore f. BD is to f. BC nearly as f. ZE to f. ZC i, 
fo that f. BD will be to f. BC nearly as the difference- 
of the moon’s true latitude, when fih'e appears in G, 
from her Latitude DE, wherewith (lie would appear 
4' in 
