Shrga-Siddhanta 31. Divide the minutea contained in any are by two hun. dred and twenty-five ; the quotient is the number of the preceding tabula sine (jyapitaka). Multiply the remainder by the differ ence of the preceding and following tabular sines, and divide by two hundred and twenty-five; 32, The quotient thus obtained add to the tabula sine called the preceding; the result is the required sin. The sam0 method is prescribed also with respect to the versed sines. 88. Subtract from any given sine the next less tabular sine; multiply the remainder by two hundred and twonty-five, and divide by the difference between the next loss and next greater babular sines; add tle quotient to the product of the serial num ber of the next less sine into two hundre and twenty-five the result is the required arc. The table of Hines and vered sines give; only those belonging to arcs which are multiples of B२ 45 ; the first two verses of this passage state bbe nehod of frning , by simple interpolation , the site or verse situ of any intermediate are while the third verse gives the rule for the contrary process, for eonverting any given Kine or versea sime m xhe 3are manner into the corresponding are In illustration of the first rule, let us ascertain thlne Eine corresponding to an are of 24 ', 03 1440, Upon dividing the latter number by 225 , ws obtain the quoticeb 6, and the remainder 30, Phis preliminary step is necessary, because the Eindu table is not regarded as containing my designation of the ares to which the sines belong, bub as composed simply of the sines themselves in bhe order. The sine :Oresponding to the quotient obtained, as the sixth, is 1815 : the difference between it and the next following sine is 25. Now a proportion is made : it, ta& this point in the quadrana, an addition of 225’ to bha are causes an increase in the sine of 30%', wheat increase will be caused by an addition to the a¥c of 0 : that is to say, 225: 205 0:82. Upon adding the result, 82, to the sixth site, the annont, 1897, is the aine of the given are, as stated in Yese 28 'The actual value, it may be remoked, of the sine of 24°, is 189B".26. 'The other zule is the reverse of this, and does not require illustration. 'IThe extreme conciseness Bimed at in the phraseology of the text, and not unfrequently carried by it beyond thhe limit of distinctnesk, or even of intelligibility, is well illustrated by verse BB, which, literally brank ated, reads thus : having subthracted the sine, the remainder, multi . plied by 225, divided by its difference, having added to the product of
