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64
THE INDIAN ANTIQUARY.
[FEBRUARY, 1891.
Now multiply in the head the quotient with the first cipher of the divisor and subtract the result from the first cipher of the dividend, and then, because 3 X2 = 6 and 6 - 6 = 0, substitute the remainder for the first cipher of the dividend ; thus: - 3
089.
27 Then, to ascertain if the above quotient is the true first cipher of the final quotient, inultiply it by the subsequent ciphers of the divisor and subtract the result from the ciphers of the dividend immediately over them in the head, and then if there is a remainder substitute it for the cipher of the dividend affected by the process; but if there can be no remainder, i. e., if the result exceeds the cipher for which it should be substituted, then the quotient is wrong and must be lessened. E. g., in this case 3 X 7= 21, which cannot be subtracted from 08, and 80 3 cannot be the true first cipher of the final quotient and must be lessened. Begin again and try 2. Then the ciphers to be set down are 2
689.
27 Then, because 2 X 2 = 4 and 6 -4 = 2, after multiplication with the first cipher of the divisor by the revised quotient, by subtracting the result from the first cipher of tbe dividend and substituting the remainder for the first cipher of the dividend, we have 2
289. 27
Next, the result of multiplying the revised quotient with the remaining ciphers of the divisor is 2 X 7 = 14, which is capable of subtraction from the ciphers of the dividend affected by the process: 1. e., 28 - 14 = 14. So substitute the remainder for the said cipher thus: - 2
149.
27
So 2 is the true first cipher of the final quotient. Now set forward the divisor a point, thus : 3
149.
27
and proceed as before, dividing the ciphers of the dividend immediately over the first cipher of the divisor ; thus: 14 + 2 = 7. Set down as follows 27
149. 37
Now multiply the first cipher of the divisor with the quotient thus obtained as before, and substitute the remainder after subtracting it from the ciphers of the dividend affected, and, because 2 X 7 = 14 and 14 - 14 = 0, set-down 27
09.
27 Next proceed as before, to ascertain if 7 is the true second cipher of the final quotient of the division, by multiplying it with the second cipher of the divisor and subtracting the result from the ciphers of the dividend affected by the process thus 7 x 7 = 49, which cannot be sabtracted from 09. So 7 is wrong, therefore try 5. Sot down and proceed as before ; thus : 26
149.
