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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 AC F 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 B C D to the fine of the 

 fpherical angle D C H. 



Let (Fig. 7.) the triangle AGB have the angle 

 A B G equal to the fpherical angle CBD, and the 

 fide AG equal to AF. Then, AG is to A B as 

 the fine of the fpherical angle BCD to the fine of 

 the fpherical angle D C H, 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 A B G to the fine of AGB; therefore, the 

 angle A B G 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 ABG, AGB and BAG 

 together exceed two right. 



Hence, (Fig. 8.) towards the equinoctial point C, 

 where the angle C B 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 lefs 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- 



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