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Again-, f. ZB is to radius as the tangent of ZB to 
the fecant of ZB- i therefore DE is to the horizontal 
parallax, as t. of ZB to fee. ZB: but DC is to DE 
as f. BC to t. ZBj whence by equality DC is to the 
horizontal parallax as f. BC to the fee. ZB, or as 
h BC X cof. ZB to the fquare of the radius. 
COROLLARY. 
If the point S be taken 90 degrees from the ap- 
parent place of the moon, and the ar-ch SZ, be drawn, 
in the fpherieal triangle SBZ, the ef. ZB x cf. BCS, 
that is,, ef. ZBxf BC is equal to rad. xcf. ZS : 
therefore DC is to the horizontal' parallax as cf. ZS, 
or the fine, of the diftance of S from the horizon to 
the radius. And if the point S is. taken in conle- 
quence of the moon,, it will be above the horizon,, 
when the nonagefime degree is alfo in confequence. 
of the moon other wife below. 
PROPOSITION II. 
Let G be the apparent place of the moon out of 
the ecliptic in the circle of latitude CK, K being the 
pole of the ecliptic, and H her true place. Then 
RF, the difiance of the moon from the circle of her 
apparent latitude, when fiie is feen in the ecliptic, is 
equal to HL, her difiance from the circle of her ap- 
parent latitude, when her apparent place is G. 
If a great circle EHT be drawn through E and H, 
till it meet the circle of the apparent latitude in T, the 
four great circles CZ, GZ, CT, ET, interfeefiing 
each other, the ratio of f. ZC tof. CE is compounded 
. . 2 of 
