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25O ON THE ASTRONOMICAL COMPUTATIONS 



circle, as the former, into signs and degrees. Note 

 the sun's mean longitude in each circle, as suppose 

 in Gemini, and from both points draw right lines to 

 the earth at © . According to the Hindu system, which 

 appears to be the same as the Ptolemaic, the angle 

 a © C will be the mean anomaly, the angle b ® C 

 the true anomaly, and the angle a ® b their differ- 

 ence, or the equation of the m?an to the true place ; 

 to be subtracted in the first six signs of anomaly, and 

 added in the last six. The Europeans, in the old 

 astronomy, found the angled© C by the following 

 proportion, and which subtracted from a © C, left 

 the equation, which as the Hindus, they inserted in 

 tables calculated for the several degrees of the qua- 

 drant ; — as the co- sine of the mean anomaly © e=Ed 

 added to the excentricity E ©, is to the sine of the 

 mean anomaly ae—bd; so is the radius to the tangent 

 of the true anomaly : or, in the right angled triangle 

 d © h, in which are given d © and bd, if d © be made 

 radius, bd$f\\\ be the tangent of the angle b © ^re- 

 quired. The Hind a, who have not the invention of 

 tcngcntsX take a different method, on principles equal- 

 ly true. They imagine the small circle or epicycle, 

 cdef, drawn round the phnet's mean place a with a 

 radius equal to the excentricity, which in this case, 

 of the sun, is 130' 30", and whose circumference in 

 degrees, or equal divisions of the deferent ABCD, 

 will be in proportion as thei^semi-diameters ; or, as 

 © £=3 43V, to A B C D=3*o°, so ^=130' 32", to 

 efgd= 1 j° 40', which is called the paridhi-ansa, or fa- 

 ridlii degrees. In the same proportion also will be 

 the correspondent sines he and ai, and their co-sines 

 cb and Ik, which are therefore known by compu- 

 tation, in minutes or equal parts of the radius a ©, 

 which contains, as before mentioned, 343s'. In the 

 right angled trangle // © c, right angled at h, there 

 are given the sides./; © (=#© + cf, because cb=ha) 



