[ 44S ] 
More accurately, the chord of the difference of ZG 
and ZG being to the difference of their cofines, as the 
radius to the cofine of half their fum, the difference of 
the moon’s apparent diameters in C and G may be 
confidered as nearly bearing to the horizontal diameter, 
the ratio of the parallelopipedon, whofe altitude is the 
fine of the horizontal parallax', and bafe the redlangle 
under the chord of CG and the cofine of ZC, to the 
cube of the radius ; the cofine of ZC being to the cofine 
of ZB, the dilfance of the nonagefime degree from 
the zenith, as the cofine of BC, the apparent diflance 
of the moon from the nonagefime degree to the ra- 
dius. But this difference can never be any fenfible 
quantity, 
5. When the moon is in the longitude of the 
nonagefime degree, the parallax in longitude ccafcs, 
and the apparent latitude is the difi'erence of the 
moon’s apparent diffance from the zenith, and the 
diflance of the nonagefime degree from the fame. 
But now fince DC is to the horizontal parallax ns 
the redlangle under the fine of BC, and the cofine of 
ZB to the fqiiare of the radius ; if an arch be taken to 
the horizontal parallax as f. BD x of. ZB to the fquare 
of the radius, this arch will differ but little from the 
parallax in longitude, and is ufed by Kepler as fuch ; 
however, it ought to be correefed by adding it to BD, 
and taking an arch to this in the proportion of tlie 
fine of BD thus augmented to the fine fimply of BD ; 
and this laft arch will be equal to the parallax in 
longitude without fenfible error. 
Again, DE taken to the horizontal parallax as the 
fine of ZB to the radius, is conlidercd by Kepler as 
the 
