[ 445 1 
in the ecliptic, if the points H and E are both on the 
fame fide of the ecliptic, or as the fum of thofe lati- 
tudes, when H and E are on different fides of the 
ecliptic, to the moon’s vifible latitude. 
1 . The moon’s apparent diameter, is to her hori- 
zontal diameter, as the fine of her apparent diftance 
from the zenith to the fine of her true diftance. 
Therefore, when the moon is in C, her apparent- 
diameter is to her horizontal diameter as f. ZC to 
f ZE, and f. ZC being to f. ZE nearly as f. BC tOv 
f BD •, the moon’s apparent diameter in C will be tO- 
her horizontal diameter nearly as f. BC to f. BD. 
Again, the ratio of f. CGtof. EH is compounded' 
of', the ratio of f. ZG to f ZH, and of the ratio of 
1. CT to f. ET ;• and is alfo compounded of the ratio 
of f. ZG to f. ZEs and (f the ratio of f GT to 
f. TH ; but the fine of ET is equal to the fine of TH; 
the arches ET'and TH compofing a femi-circle ; alio . 
the fine of CT there differs little from the fine of GT j-t 
therefore f ZG is to f. ZH, tliat is, the moon’s appa- 
rent diameter, when in G, to her horizontal diameter,^ 
nearly as f. ZC'tof. ZE, or nearly as f. BC to * 
CBD. 
3. In all latitudes of the moon, EH will not greatly ,.- 
exceed the difference, or fum of the moon’s latitude,- 
jnH,, and the latitude wherewith fhe would appear 
in the ecliptic. Therefore the ratio of f. ZC to f. ZE . 
being compounded of the ratio of f CG to EH,, 
a.nd of the ratio of f. IIT to f. GT, if X be taken, . 
that its fine be to the fine of tffe difference or fum. of. 
the latitudes, as f. ZC to ZE, f X will be nearly to . 
f. CG-as f. HT to f. GT. Elence the difference of: 
f. X, and f. GtC will be to f. CG, nearly as the differ- 
