AS PRACTISED BY THE ARABS. 139 



8,314,836,019,421,400,000 — 6 1 ,2 s ' 665 s ' 333 



5,204,587,207,645,350,000 — 15-2 4 665 4 333 2 



1,737,471,218,191,380,000 = 202 3 -665 3 333 s 



326,265,741,912,253,500 — 15-2 2 665 2 -333* 



32,675,636,708,806,140 - 6-2 665 333 5 



1,363,532,208,525,369 = 333 6 



665 6 =86,482,825,840,140,625)l5,617, 199,356,087,715,009 ( 180 + 64-244 



15,566,908,651,225,312,500 



•50,290,704,862,402,509 



56,290,704,862,402,509 

 Hence the deficiency in this case is 397 — 244 a quantity 



86,482,825,840, 140,625 

 36,192,120,977,738,116 



yet greater than before, being no less than 152 



86,482,825,840,140,625 



Fourth. Let there be sought the approximate 6th Root of 728 



Here M — 728, m is the same as before /■ — 728 — 64 — 664. And 



hence the the approximate Root is 2 -£-§-4. Then 2 -£-ff| 5 is 



664 664 2 664 3 664 4 664 5 664° 



2 G + 6-2 5 - + 15 2 + - 1- 20-2 3 - + 15-2 2 - — \. 62- — 1 or 



665 665 2 665 3 G65 4 665 5 665 G 



6-2 5 -665 5 -664 + 1 5-2 4 -665 4 -664 2 + 20-2 3 -665 3 -664 3 + 1 5-2 2 -665 5 -664 4 + 1 5-2-665-664 5 + 664<3 



61 _i_ or 



665 6 



16,579,733,083,771,200,000 — 62 5 .665 5 .664 



20,693,501,442,902,400,000 — 15-2 4 .665 l .664 s 



13,774,922,263,746,560,000 — 202 3 .665 3 .664 3 



5,157,828,035,598,336,000 — 15.2 2 .665 2 .664 4 



1,030,014,380,642,795,520 = 6.2.665664 5 



85,705,457,236,443,136 = 665 6 



665 fi = 86,482,825,840,140,625)57,321,704,663,897,734,656 (662 -f 64 — 726 



57,251,630,706,173,093,750 



70,073,957,724,040,906 



n 1 



