[ 444 1 
plement of half BCD, the arc of the ecliptic, be- 
tween C and the horizon, will never bi lefs than the 
arc of the equator, between the fame point C and the 
horizon. 
In the two fituations of the horizon, the angles 
CHB and KM A are equal. 
Scholium i. 
To find the point in the ecliptic, where the arc 
of the ecliptic mod: exceeds the right afcenfion, 
is a known problem : that point is, where the 
cofine of the declination is a mean proportional 
between the radius and the cofine of the greated: 
declination. 
In the preceding figure, fuppofing the angle CBD to 
be right, then, becaufe when CD mod: exceeds CB, 
the cofine of BD is to the radius as the fine of CB to 
the fine of C D, and, in the triangle CBD, the fine 
of C B is to the fine of C D as the fine of the angle 
CDB to the radius, alfo the fine of CDB is to 
the radius as the cofine of BCD to the cofine of 
BD j therefore, the coline of B D is to the radius 
as the cofine of the angle BCD to the cofine of 
the fame B D, and the cofine of B D is a mean pro- 
portional between the radius and the cofine of 
BCD. 
Scholium 2. 
In any given declination of the Sun, to find 
when the azimuth mod: exceeds the angle which 
meafures the time from noon, is a problem ana- 
logous to the preceding. 
Dr. 
