A 12(3·46410161513 9 --- 64) 300 256 ----- 686) 4400 4116 ------ 6924) 28400 27696 ------ 69281) 70400 69281 ---------- 6928201) 11190000 6928201 -------+-- 69282026) 4261799|00 4156921|56 -------+---- 692820321) 104877|4400 69282|0321 -----+------ 6928203225) 35595|407900 34641|016125 -----+-------- 69282032301) 954|39177500 692|82032301 ---+---------- 692820323023) 261|5714519900 207|8460969069 ---+---------- 53|7253550831 B 692820323026) 537253550831(77545870549 484974226118 ------------ 52279324713 48497422611 ----------- 3781902102 3464101615 ---------- 317800487 277128129 --------- 40672358 34641016 -------- 6031342 5542562 ------- 488780 484974 ------ 3806 3464 ---- 342 277 --- 65 62 -- 3 If from any remainder we cut off the ciphers, and all figures which would come under or on the right of these ciphers, by a vertical line, we find on the left of that line a contracted division, such as those in (155). Thus, after having found the root as far as 3·464101, we have the remainder 4261799, and the divisor 6928202. The figures on the left of the line are nothing more than the contracted division of this remainder by the divisor, with this difference, however, that we have to begin by striking a figure off the divisor, instead of using the whole divisor once, and then striking off the first figure. By this alone we might have doubled our number of decimal places, and got the additional figures 615137, the last 7 being obtained by carrying the contracted division one step further with the remainder 53. We have, then, this rule: When half the number of decimal places have been obtained, instead of annexing two ciphers to the remainder, strike off a figure from what would be the divisor if the process were continued at length, and divide the remainder by this contracted divisor, as in (155).