AS PRACTISED BY THE ARABS. 133 



d/. And since by Art. /) 18,535,911,758,593 = W p a -f C, so 

 18,535,911,758,593—16,134,619,913,216 = 2,401,291,845,377 - R' p f> -j- 

 C— (6p 5 f c + 15 jo 4 p* c n - -f 20 p 3 f c 3 -f 15 p* f c 4 + 6 p <p c 6 ), and is 

 the third Remainder, which therefore agrees with the third Remainder 

 found by the European method in Par. 34, Art. d" , and is therefore — R' 

 Par. 24. 



And by the circle of exposition there will successively be found — ■ 

 For the 4th Period — 



u" . 4,209,500,228,544, the upper number transferred in the Rank of 

 the Quadratus Cubi == 6 p' 6 . 



y". 44,973,293,040, the upper number transferred in the Rank of the 

 Biquadrate — 15 p'*. 



f. 256,258,080, the upper number transferred in the Rank of the 

 Cube = 20 jt/ 3 . 



/. 821,340, the upper number transferred in the Rank of the Square 

 = 15 ft*. 



it". 1,404, the upper number transferred in the Rank of the Latus 

 zz 6p f . 



'-r*"- 5, the sought number, or fourth figure of the Root = cl. 



cy". 2,116,025,521,169,640,625, the fourth Subtrahend = 6 p s <p s d -f- 

 15 p' 4 <p 4 d- 4- 20 p n <p 3 d* -f 15 p n <f d* -f Op' <f> d 5 + d 6 . 



