[ 44i ] 



and therefore, the magnitude of the angle A B D, 

 that A be the point of iongeft afcenfion, is confined 

 within two limits, of which the double of one added 

 to the angle A, as much exceeds a quadrant, as the 

 double of the other added to that angle falls fhort of 

 it j therefore, double the fum of thofe two angles, 

 together with twice A, makes a femicircle ; and the 

 fingle fum of thofe two angles added to A makes a 

 quadrant. 



Problem II. 



To find when the arc of the ecliptic differs mojl from its 

 oblique afcenfion. 



A N A L Y S I S. 



If (Fig. 5.) BD be the fituation of the horizon, 

 when C D differs mod from C B, as before, the ul- . 

 timate ratio of BE to D F will be compounded of 

 the ratio of the radius to the fine of DG (or the co- 

 fine of DB) and of the ratio of the fine of CB to the 

 fine of C D : but, when C D differs moll from C B, 

 B E and D F are ultimately equal ; therefore, then 

 the cofine of B D is to the radius as the fine of C B 

 to the fine of C D. 



Draw the arc CHI of a great circle, that D H 

 be equal to D B ; then, B H being double B D, half 

 the fine of BH is to the fine of BD or DH, as 

 the cofine of BD to the radius; therefore, half the 

 fine of BH is to the fine of DH as the fine of CB 

 to the fine of C D ; but the fine of the angle BCH is 

 to the fine of BH as the fine of the angle CH B to the 



Vol.LXII. Lll fine 



