- [ 44i ] 
and therefore, the magnitude of the angle ABD, 
that A be the point of longed: 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 mofi from its 
oblique aficenfion. 
Analysis. 
If (Fig. 5.) BD be the fituation of the horizon, 
when CD differs mofi from CB, 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 mofi 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 DH 
be equal to DB; then, BH 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 j 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. L 1 1 fine 
