AS PRACTISED BY THE ARABS. 117 



k. Then by Art. a.) since 2=aso2-)-2=;4=fl-ffl-2a, and 

 is the upper number in the Rank of the Latus. 



/. Then 4 x2 = 8 = 2« x« = 2a J , and is the product written in 

 the Rank of the Square. 



m. By Art. b.) since 4 = a z so 8 -J- 4 = 12 == 2 «* -f a a = 3 «% and 

 is the upper number in the Rank of the Square. 



n. Then 12 X 2 — 24 = 3 a z X a = 3 a 3 , and is the product written 

 in the Rank of the Cube. 



p. By Art. c.) since 8 = a 3 so 24 -f 8 =: 32 =♦ 3 a 3 -j- a 3 = 4 a 3 , and 

 is the upper number in the Rank of the Cube. 



q. Then 32 X 2 = 64 = 4 a 3 X a — 4 a 4 , and is the product written 

 in the Rank of the Biquadrate. 



r. By Art. d.) since 16 — a 4 so (34 + 16 = 80 = 4 a" + a 4 — 5 a 4 , 

 and is the upper number in the Rank of the Biquadrate. 



s. Then 80 X 2 r= 160 = 5 a 4 x a — 5 a s , and is the product writ- 

 ten in the Rank of the Quadratus Cubi. 



t. By Art e.) since 32 — « 4 so 160 -f- 32 — 192 — 5 a 5 -f a 5 = 6 a 5 , 

 and is the sum written in the Rank of the Quadratus Cubi. 



ii. By the transference of 192, its units are put under the 6th place 

 of the second period, and hence 6 a s thus transferred, is the upper num- 

 ber in the Rank of the Quadratus Cubi. 



v. Then by Art. k.) since 4=2aso2 + 4 = Gz:fl + 2a = 3a, 

 and is the upper number in the Rank of the Latus. 



