Takashi Kojima's Advanced abacus: Japanese theory and practice PDF

By Takashi Kojima


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The second is considered the best by sorne authoritative experts. The third is the most representative traditional method and is the most widely accepted by modern abacus operators. The method of finding the two-figure square root of a number is founded upon the method of finding the square of an ordinary binomial (or two-membered) expression, (a + b). The number is analyzed into (a2 + 2ab + b2) as in algebra, and the square root is obtained. Let us take the number 625 as an example of finding a two-figure square root.

This gives you 29 on JK. Next multiply the 8 on B by the same 2 on H; add the product 16 to the 29 on JK, and clear H of its 2. This gives you a total of 45 on JK (Fig. 165). STEP 5: Now divide the 45 on JK by 20, and you get the quotient 2 on H, with 5 left over on K (Fig. 166). STEP 6: Finally you must multiply the 4 on E by 18, and add the product 72 to the 2 on H. In this process, first multiply the 1 on A by the 4 on E, and set the product 4 on G. This gives you 42 on GH. Next multiply the 8 on B by the same 4 on E, add the product 32 to the 42 on GH, and clear E of its 4.

B) In this step, as the 2 on D is used as the first quotient figure, the procedures of setting the first quotient figure 2 and of subtracting the first digit 2 of the dividend 257 are eliminated. STEP 3: Next, suppose that you have divided the 515 on EFG by 100 and have got the 5 on E as the second quotient figure. Multiplying the 3 on A by the 5 on E, subtract the product 15 from the 15 on FG. This clears the board of the remaining dividend, and leaves, on DEF, 25 as the quotient (Fig. 102). As the dividend was practically divided by 100, the unit rod of the quotient moves to the second rod to the left of that of the dividend.

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