C 4+3 ] 
of the ratio of f. ZG to f. GH and of the ratio of 
f. SHT to f. ET [a]. But CE and GH being the 
parallaxes in altitude at the refpedtive diftances from 
the zenith ZC, ZG, f. ZC is to f. CE as f. ZG to 
f. GH : therefore the fine of HT will be equal to the 
fine of ET, and the arches HT, ET together make a 
femicircle ; whence ET is equal to HL, 
COROLLARY. 
The arch KH being drawn, the parallax in lon- 
gitude, when the moon is in H, will be to HL as 
rad. to f. KH, or the cofine of the latitude ; and EF, 
or its equal HL, to CD as f. KE to the radius. 
Therefore the moon’s parallax in longitude, when in 
H, is to the parallax in longitude, when fhe appears 
in the ecliptic, as the fine of KE to the fine of KH, 
that is, as the cofine of the latitude, when the moon 
appears in the ecliptic, to the cofine of her latitude 
in H. 
PROPOSITION III. 
When the moon appears out of the ecliptic, if her 
latitude is fmall, the difference of the moon’s latitude, 
when the moon appears in the ecliptic under the fame 
apparent longitude, if both latitudes are on the fame 
fide of the ecliptic, otherwife their fum, will be to 
the moon’s apparent latitude, nearly as the fine of the 
moon’s diftance from the zenith, when appearing in 
[a] Ptolem. Almag. L. i. c. 12. Menel. Spheric. L. iii. pr. z. 
L 1 1 2 
the 
