C 444 ] 



plement of half BCD, the arc of the ecliptic, be- 

 tween C and the horizon, will never be lefs than the 

 arc of the equator, between the fame point C arid the 



horizon. 



In the two fituations of the horizon, the angles 

 CHB and KMA are equal. 



Scholium r. 



To find the point in the ecliptic, where the arc 

 of the ecliptic moft 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 greateft 

 declination. 



In the preceding figure, fuppofing the angle CBD to 

 be right, then, becaufe when CD moft 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 CB is to the fine of CD 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 

 B D ; therefore, the cofine 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 moft exceeds the angle which 

 meafures the time from noon, is a problem ana- 

 logous to the preceding. 



Dr. 



