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DEMONSTRATION. 
In the fpherical triangle Z L S, fee Fig. 2, 3,4, 
and 5th, Z reprefents the zenith, L the Moon, and 
S the ftar; the effedt of parallax deprefling the 
Moon from L to r, r is the apparent place of the 
Moon, and r S the apparent diftance of the Moon 
from the ftar; let fall the perpendicular L t upon 
r S, produced if neceffary, and r t will be the dif- 
ference of L S and r S, or the effedt of parallax. 
Draw the arch ZP perpendicular to to rS, and let 
M be the middle of rS. The Moon’s parallax in 
altitude, being to her horizontal parallax, as the 
line of her apparent zenith diftance, to the radius, 
Lr = Moon’s horizontal parallax x fine of Z r; 
and rt the effedt of parallax upon the apparent di- 
ftance of the Moon from the ftar will be — L r x 
cof. Z r S — horizontal parallax x fin. Z r x cof. 
ZrS (or, becaufe tan. rP : cof. ZrP :: tan Z r : 
rad :: fin Zr : cos Z.r ; and therefore fin. Z r xcos 
Z r S = cof. Z r x tan r P) — horizontal parallax 
X cof. Zr x tan. rP agreeably to the rule. For 
it is evident by fpherics that the arch A, found by 
the rule, is the fame with M P the diftance of the 
perpendicular from the middle of the arch rS : and 
it is evident, by the infpedion of the figures, that 
the arch B or r P is equal to the fum of rM and 
M P, if the zenith diftance of the Moon be greater 
than that of the ftar, as in Fig. 2d and 4th ; but is 
the difference of r M and M P, if the zenith dif- 
tance of the Moon be lefs than that of the ftar, as 
in Fig. 3d and 5th. Laftly, it may appear from the 
confideration 
