AS PRACTISED BY THE ARABS. 35 



c. Multiply the 2 again into this 4, and write the product 8 in the 

 Rank of the Cube, as by Art. 3.) 



d. Multiply the 2 again into this 8, and write the product 16 in the 

 Rank of the Biquadrate, as by Art. 4.) 



* e. Multiply the 2 again into this 16, and write the product 32 in the 

 Rank of the Quadratus Cubi, as by Art. 5.) 



f. Multiply the 2 again into this 32, and the product is 64, which is 

 less than 166, as by Art. 6.) 



And 2 is the highest number which will answer these conditions. 

 For let 3 be substituted in these operations and they will successively 

 become 3X3 = 9, 9 X 3 = 27, 27 x 3 = 81, 81 X 3 = 243, 243 X 3 = 729, 

 which last product is greater than 166. 



g. Call this last product 64, which answers the condition, the first 

 Subtrahend, write it opposite to and immediately under 166, the first 

 period. 



h. Write the found figure 2 above 6, the units of the first period, 

 and exterior to and immediately above the Pulpit, or as it may be called 

 the Anabathroidal Diagram. This is the first figure of the Root. 



*. Subtract the first Subtrahend from the first period, and 102 is 

 the first Remaider. 



j. Write 102, the first Remainder, on a line with the figures of the 

 second period in the next descending right hand step of the Pulpit Dia- 

 gram, so as to form the number 102,571,800. This is the first Resolvend. 



