[ 443 3 
to the fine of C A F ; and C B is to A B as the fine 
of the angle B A C to the fine of A C B : therefore, 
CF being equal to CB, and the fine of ACF to the 
fine of ACB, by equality, AF is to AB as the fine of 
the angle B A C to the fine of C A F, that is, as the 
fine of the fpherical angle BC D to the fine of the 
fpberical angle D G H. 
Let (Fig. 7.) the triangle AGB have the angle 
A B G equal to the fpherical angle CBD S and the 
fide AG equal to A F. Then, AG is to AB as 
the fine of the fpherical angle BCD to the fine of 
the fpherical angle D C FI, that is, as the fine of 
the fpherical angle CBH to the fine of the fpherical 
angle CHB : but AG is to AB alfo as the fine of the 
angle ABG to the fine of AGB; therefore, the 
angle ABG being equal to the fpherical angle 
CBH, the angle A G B is equal to the fpherical 
angle CHB : and moreover, when the angle ABG 
is greater than A B F, that is, when the fpherical 
angle C B H is greater than the complement of half 
BCD, the three angles A B G, AGB and BAG 
together exceed two right. 
Hence, (Fig. 8.) towards the equino&ial point C, 
where the angle CB D is obtufe, a fituation of the 
horizon, as BD, may always be found, wherein 
CD more exceeds CB than in any other fituation: 
and when the acute angle DBA is greater than the 
complement of half BCD, another fituation of the 
horizon, as KLM, may be found, toward the other 
equinoctial point A, wherein the arc of the ecliptic 
C K will be lels than the arc of the equator, and 
their difference be greater than in any other fituation. 
But, if the angle DBA be not greater than the com- 
L 1 1 2 plement 
