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fine of CBj whence, by equality, half the fine of 

 BCH is to the fine of DH as the fine of CHB to 

 the fine of CD : but as the fine of CHB to the fine 

 of CD, fo, in the triangle CHD, is the fine of DCH 

 to the fine of HD : confequently, the fine of DCH 

 is equal to half the fine of BCH. Hence, the dif- 

 ference of the angles BCH, DCH being given, 

 thofe angles are given, and the arc CHI is given by 

 pofition. 



Moreover, in the triangle BCH, the bafe BH 

 being bife&ed by the arc C D, the fine of the angle 

 CHD is to the line of the given angle C B D, as 

 the fine of the given angle H C D to the fine of the 

 given angle BCD; therefore, the angle C H B is 

 given ; in fomuch, that in the triangle CBH all the 

 angles are given. 



The fum of the fines of the angles BCH, DCH 

 is to the difference of their fines, as the tangent of half 

 the fum of thofe angles to the tangent of half their 

 difference ; therefore, the tangent of half the fum of 

 BCH, DCH is three times the tangent of half 

 BCD. 



Jn (Fig. 6.) the ifofceles triangle ABC, let the 

 angle B AC be equal to the fpherical angle BCD, 

 and let AE be perpendicular to BC j alfo, CF being 

 taken equal to CB, join A F : then EF is equal to 

 three times EB; and as E F to E B, fo is the tan- 

 gent of the angle E A F to the tangent of EAB; 

 but EAB is equal to half the fpherical angle BCD : 

 therefore, the angle EAF is equal to half the fum of 

 the fpherical angles BCD, BCH ; and confequently, 

 the angle C A F equal to the fpherical angle DCH. 

 Here, A F is to C F as the fine of the angle A C F 



n tO 



